Smart emergency multi-attribute decision-making for typhoon response based on a hybrid intuitionistic fuzzy approach.

Smart emergency multi-attribute decision-making for typhoon response based on a hybrid intuitionistic fuzzy approach - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Search Log in Primary site navigation Search Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Apr 13;16:17236. doi: 10.1038/s41598-026-45762-0 Smart emergency multi-attribute decision-making for typhoon response based on a hybrid intuitionistic fuzzy approach Sergey Gorbachev 1, ✉ , Evgeniya Gerasimenko 2 , Abhishek Dixit 1 , Ashish Mani 1 , Vladimir Kureichik 2 Author information Article notes Copyright and License information 1 School of Mathematics and Big Data, Chongqing University of Education, Chongqing, 400065 China 2 Institute of Computer Technologies and Information Security, Southern Federal University, Taganrog, Russia 347922 ✉ Corresponding author. Received 2025 May 13; Accepted 2026 Mar 21; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13233867  PMID: 41974821 Abstract The global climate crisis, which has severely damaged economies and led to migration of millions of people worldwide as a result of typhoons, tsunamis and others environmental changes and disasters, requires increased urban sustainability in decision-making and preparedness for various human mobility strategies. Despite extensive research in the field of emergency evacuation, few publications are devoted to fuzzy conditions. However, many of the attributes inherent in emergency modeling are fuzzy and uncertain by nature. Thus, we account for the necessity of evacuation as a human mobility strategy under intuitionistic fuzzy conditions, which allow experts to express hesitation when evaluating criteria. We have developed a hybrid intuitionistic fuzzy method to find the best evacuation strategy in an uncertain environment. To verify the results, we applied our method to one of the eastern regions of China, Jiangxi Province, in the event of Typhoon Maria to define the necessity of evacuation based on seven criteria. Necessity of evacuation is expressed by five response alternatives: no evacuation, alertness, recommended evacuation, mild evacuation, urgent evacuation. According to the algorithm the most desirable strategy in this situation is alertness, which means preparedness for evacuation. The results obtained demonstrate superiority of the proposed hybrid method in comparison with other intuitionistic fuzzy approaches. Subject terms: Natural hazards, Mathematics and computing Main Over the past decades, hurricanes, floods, heat waves and droughts have claimed many lives and caused enormous material damage with global warming intensifying these phenomena. Environmental changes and disasters have displaced millions of people, leading to migration and relocation within and outside their countries. Recent studies have shown that 1.2 billion people were affected by natural disasters over two decades. The damage caused by the increased number of storms, floods and heat waves amounted to at least $ 2.8 trillion. The climate crisis is costing $16 million per hour due to damage from extreme weather conditions. After floods, storms are the most frequent disasters, with 176 events in 2022 recorded in the International Disaster Database EM-DAT of Centre for Research on the Epidemiology of Disasters. The number of reported storms in 2022 was higher than the 2021–2021 average (Fig. 1 ). Fig. 1. Open in a new tab Occurrence of emergencies by disaster type: 2022 compared to the 2002–2021 annual average (EM-DAT). Figure 2 shows percentage of natural disasters by occurrence times 2002–2022. Storms represent 27.6% of natural disasters. Fig. 2. Open in a new tab Percentage of natural disasters by occurrence, 2002–2022 (EM-DAT). Different types of storms, which are also called typhoons, cyclones, or hurricanes depending on their region of development, can lead to the destruction of coastal areas. These storms are called hurricanes when they develop over the North Atlantic, central North Pacific, and eastern North Pacific. When the storms form over the South Pacific and Indian Ocean, they are known as cyclones. They are called typhoons when they develop in the Northwest Pacific. Storm surges and flooding are the two most dangerous aspects of hurricanes, accounting for three-quarters of deaths from Atlantic tropical cyclones, according to a 2014 study. Torrential rains cause further damage through flooding and landslides, which may occur many kilometers inland. Figure 3 shows the countries most affected by storms disasters from 2000 to 2023. Fig. 3. Open in a new tab Distribution of storms disasters by countries, 2000–2023. Because of the high frequency of natural disasters and their devastating effects, city authorities resort to preventive evacuation as a primary method for saving lives by moving people to safe locations. Nevertheless, mass evacuation requires the coordination of many city authorities, governments, and civil society members due to its complexity. Moreover, mass evacuation is not widely implemented because it is a drastic, expensive and time-consuming measure 1 . Therefore, it is necessary to define the need for mass evacuation accurately and to reduce unnecessary evacuations by evaluating their relevance. An optimal evacuation strategy addresses various aspects of an emergency depending on its type. Storms, in particular, have common characteristics such as intensity, path, and rainfall levels. These factors are better expressed in linguistic and fuzzy terms owing to the imprecision inherent in their nature. To estimate these factors, decision-makers (DMs) provide the evaluation as intuitionistic fuzzy numbers. This paper proposes framing the need for evacuation—the evacuation risk strategy—in fuzzy terms as a task of multi-attribute decision-making (MADM). Emergency DM 2 – 7 faces difficulties due to risky and uncertain aspects of evacuation. Current emergency response methods use flow modeling, representing evacuation networks as graphs or hypergraphs 8 . While these models help prioritize evacuation nodes and maximize evacuee counts, they fall short in handling uncertainty, particularly when deciding whether to initiate evacuation. Fuzzy decision‑making approaches could bridge this gap. Emerging techniques leverage multi‑agent systems and machine learning 9 , 10 . Multi‑agent model 9 simulates evacuation from complex spaces by age group, calculating average evacuation times. However, it assumes certain network parameters (ignoring fuzziness), disregards incomplete or noisy data, does not support multi‑criteria decisions and is confined to enclosed spaces (unsuitable for large‑scale disasters). Machine learning integration 10 merges simulation models with ML to evaluate evacuation management in building fires, offering a structural framework for effectiveness forecasting. Furthermore, it lacks empirical validation via simulations or comparisons, focuses solely on buildings (not broader transportation networks), has no module for uncertain/fuzzy conditions and fails to incorporate multiple evacuation criteria. Thus, existing methods need enhancements in uncertainty handling, scalability, and multi‑criteria support. Let us consider evacuation in the case of a storm in more detail. Some details of the evacuation process and related may be missing or uncertain. City authorities may know that wind levels could rise to a certain point, but it is difficult to predict the next phase due to uncertainty in peak intensity and the number of peaks. For large-scale evacuation decisions, it is challenging to provide all population groups owing to doubts about necessity, public reluctance to leave, and the lack of data. Evacuation effectiveness depends on the area type; in dense regions the risks of improper evacuation may increase due to storm consequences like severe flooding, extreme winds, and storm surge, leading to loss of life, damage to critical infrastructure, erosion, and defoliation. A flawed evacuation can cause not only loss of life and economic costs, but also a decline in public trust in the government, which potentially may influence future evacuation decisions. The reactions of those at risk are unpredictable, as is their preparedness to stay in place for various subconscious reasons. This uncertainty stems from constantly changing hazard risks assessments due to potentially conflicting forecasts and incomplete and ambiguous data. Past experience and evaluating the potential hazard level of an area can greatly assist the process of DM, which is why these factors should also be incorporated into evacuation planning. Based on these factors, we conclude that reliable evacuation decision-making is of great significance in emergencies. MADM handles various, often conflicting criteria during the process of DM. However, tasks of emergency DM involve uncertain data, and expert hesitation. Moreover, an uncertain and dynamic environment requires fuzzy, linguistic, and approximate assessments. In such tasks, DMs evaluate attributes using a fuzzy set (FS) 11 , intuitionistic fuzzy (IF) set (IFS) 12 , interval-valued intuitionistic fuzzy set (IVIFS) 13 , 14 , type-2 fuzzy sets 15 , or hesitant fuzzy sets 16 . However, the applicability of these sets is limited by their inherent conditions. In this regard, Yager 17 introduced Pythagorean FS, where the sum of membership and non-membership degrees can exceed one, but the square sum of membership and non-membership degrees is limited to one. Later, he 18 proposed the Q-rung orthopair fuzzy set where the sum of the qth power of the membership grade and the qth power of non-membership grade is limited to one. For q = 3, Senapati and Yager 19 denoted q-rung orthopair fuzzy sets as Fermatean FS. In 2023, Arora et al. 20 introduced Quartic fuzzy set, QFS for q = 3. Recent advances include quintic fuzzy sets 21 , where the sum of the fifth power of the membership and non-membership degrees is less than or equal to one. Paik et al. 22 focus on MCGDM problems based on intuitionistic fuzzy parameterized soft set’s structure. A soft-set in the type-2 environment to find the solution of a DM problem based-on type-2 fuzzy soft sets was considered in 23 . A modified adjustable GDMM to solve fuzzy soft set-based GDMPs by introducing weighted average ratings instead of absolute scores are presented in 24 . Das et al. 25 introduced the root mean square operation and a relative weighted score function on fuzzy soft sets for rating water-pollution levels to assess water quality indices for the Haora River in Tripura, India. The fuzzy DM process requires aggregating input data into a single value using aggregation operators. Different intuitionistic fuzzy aggregation operators will be considered to choose the optimal evacuation alternative. Various fuzzy approaches to multi-criteria group decision-making exist. For example, in 26 , new operational rules for intuitionistic fuzzy credibility numbers have been introduced for railway train selection in Pakistan. Three aggregation methods—Confidence-based Intuitionistic Fuzzy Credibility Einstein Weighted Averaging, Confidence-based Intuitionistic Fuzzy Credibility Einstein Ordered Weighted Averaging, and Confidence-based Intuitionistic Fuzzy Credibility Einstein Hybrid Weighted Averaging – effectively process fuzzy data. Riaz and Farid 27 employed a linear‑Diophantine fuzzy framework that helps decision‑makers to select optimal actions and identify suitable green providers. The approach leverages two novel aggregation operators: the linear Diophantine fuzzy soft‑max average and linear Diophantine fuzzy soft‑max geometric operators. Authors 28 introduced a multi‑index, multi‑criteria decision‑making method using TOPSIS with intuitionistic fuzzy sets (based on score‑based measures) to identify the optimal smartphone. The selection process evaluates product attributes and brand values, incorporating dynamic sets of alternatives, criteria, and decision‑makers that may evolve during purchase decisions. In 29 , Frank T‑norm and T‑conorm‑based aggregation operators have been proposed for multi‑attribute group decision‑making with interval‑valued intuitionistic fuzzy sets in market risk evaluation and optimization. Location of emergency supplies is another task solved based on fuzzy decision-making approach. The study 30 addresses emergency supply placement through a fuzzy decision‑making framework. It proposes a novel approach combining unmanned aerial vehicles (UAVs) with reinforcement learning to optimize post‑flood supply distribution. This synergy enables collaborative scheduling and real‑time autonomous decision‑making for emergency material dispatch. The research 31 addresses the challenge of siting and arranging emergency material depots and rescue stations in urban environments. A multi-objective optimization model was developed to handle diverse goal combinations across varying scales, tailored to different disaster scenarios and urban emergency requirements. Authors 32 proposed a hybrid framework combining discrete‑event simulation with fuzzy multi‑criteria decision‑making (MCDM) to improve emergency department efficiency. A high‑fidelity simulation model replicates real‑world ED dynamics. By integrating this model with fuzzy AHP and fuzzy ELECTRE, authors enable data‑driven optimization of ED operations. This approach balances operational performance with patient care quality—a critical requirement in complex healthcare environments. In a review 33 the literature on emergency stockpile siting is examined, highlighting key challenges: algorithmic limitations, disaster phase dynamics, optimization criteria, and stakeholder engagement in decisions. It underscores the need for an integrated approach—one that is dynamic, diverse, intelligent, and human‑centered. The research objective is to fill the gap in fuzzy emergency decision-making by presenting a MADM hybrid method which allows to make emergency decisions in fuzzy conditions in cases when experts hesitate and have problems in defining the common assessment. To this end, MADM hybrid method was proposed based on fuzzy logic, intuitionistic fuzzy sets and intuitionistic fuzzy hybrid averaging operator (IFHA) for selecting the most effective emergency alternative as a storm response. In this operator, the weights of criteria will be given as fuzzy intuitionistic values to incorporate a certain level of hesitation in the process of DM. We apply intuitionistic fuzzy values to define the necessity of evacuation, which is expressed by five response alternatives: no evacuation, alertness, recommended evacuation, mild evacuation, and urgent evacuation. A reliable emergency response addresses various aspects of a storm emergency. These include storm intensity; the proximity of a storm path to citizens, rainfall intensity, the degree of individual preparedness to stay, the degree of neighbors’ preparedness to stay; traffic intensity, and historical risks regarding this area. The proposed approach differs from existing approaches in its capability of handling intuitionistic fuzzy weights of criteria directly to incorporate the certain level of hesitation in the process of DM. This method is based on aggregation of intuitionistic fuzzy values by IFWA operator. In our current and previous studies, it serves as a basis for integration with emergency networks for ranking hazard nodes for evacuation. The key contributions and novelty of the study can be summarized as follows. The IF-based MADM hybrid methodology, which is suitable for solving multi-criteria decision problems with intuitionistic fuzzy weights of criteria to incorporate the certain level of hesitation in the process of DM. This method is based on aggregation of intuitionistic fuzzy values by IFWA operator. The study presents a case study to prove the effectiveness, robustness and reliability of the presented methodology and to identify the most suitable evacuation alternative in the case of a typhoon Maria, which affected Guam, the Ryukyu Islands, Taiwan, and East China in July 2018. The application of the IF-based MADM hybrid methodology to the problem of selecting the most suitable evacuation alternative in the case of a storm has been tested by sensitivity and comparative analysis, and the obtained ranking has proven to be consistent and reliable. In this way, the potential and applicability of the developed IF-based MADM hybrid methodology has been fully demonstrated. Results Aggregating operators with fuzzy weights of criteria In real decision-making tasks, the weights of criteria are not always crisp. If experts hesitate, they may express criteria weights as IF numbers. However, conventional intuitionistic fuzzy aggregating operators: intuitionistic fuzzy weighted averaging operator (IFWA), intuitionistic fuzzy weighted geometric operator (IFWG), intuitionistic fuzzy ordered weighted averaging operator (IFOWA), intuitionistic fuzzy ordered weighted geometric operator (IFOWG), intuitionistic fuzzy hybrid averaging operator IFHA, and intuitionistic fuzzy hybrid geometric operator (IFHG) do not consider fuzzy weights. That is why we need a methodology that enables us to operate with fuzzy weights of criteria 34 . Let , and be three IFVs, presents the membership degree, presents the non-membership degree, k > 0. The following operation laws are valid 31 : Let and ) be two IFVs. present the membership and non-membership degrees of the IFV , correspondingly. present the membership and non-membership degrees of the IFV , as well. Considering the operational law ( 3 ) and the fact that we get 1 where is the weight vector of , j = (1,2,…,n), j = (1,2,…,n) and Considering the operational law ( 4 ) and the fact that. , we get 2 Therefore, the modified and IFWG operators with IF weights of criteria are. 3 4 Based on operational laws ( 3 ) and ( 4 ) as well as definitions of IFWA and IFWG, modified and IFOWG operators with IF weights of criteria are 5 where is a permutation of (1,2,…,n) such that for any j . 6 Let us give definitions of modified IFHA and IFHG operators. By the operational law ( 3 ) and the fact that. we get 7 where is the weight vector connected with IFHA operator, , j = (1,2,…,n) and , j = 1,2,..,n, is a permutation of the weighted IFNs such that ( , , (j = 1,2,..,n-1); is the weight vector of , j = (1,2,…,n), j = (1,2,…,n) and The balancing coefficient is n, which plays a role of balance of balance, if the vector reaches , then the vector reaches . By the operational law ( 4 ) and the fact that. we get 8 where , j = (1,2,…, n ), is a permutation of the weighted IFNs such that ( such that , ( j = 1,2,..,n-1) . MADM hybrid method based on the modified IFHA operator for emergency DM We present a hybrid method for selecting the best evacuation strategy based on the modified IFHA operator, which accommodates intuitionistic fuzzy weights of criteria. The method uses a set of n alternatives and m criteria . The method relies on the following definition. Definition 1 Let be a non-empty set. The intuitionistic fuzzy set on the set X is the set such that: 9 where and meets the condition , for each is the membership degree, non-membership degree. in is determined as the hesitation (intuitionistic) index which measures the hesitation level: 10 Experts provide assessments of alternatives by intuitionistic values. Each IFS defined by Eq. (9) reflects that experts have a degree of doubt and hesitancy in their judgements. In Eq. (9), is the membership function that indicates the expert’s level of certainty regarding the criteria ; is non-membership function that shows to which degree the alternative does not satisfy the criteria . The indeterminacy index may exist, which measures the hesitation level by Eq. (10). Let ) be the intuitionistic fuzzy weight of criteria, , , j = (1,2,…, n ) and be the weight vector of experts, , , j = (1,2,…, n ) and be the weighting vector associated with IFHA operator. The method processes intuitionistic fuzzy DM matrices obtained from various experts. Each element indicates that alternative satisfies criterion ( ; conversely, indicates the degree to which the alternative does not satisfy the criterion . The flowchart of our hybrid method is given in Fig. 4 . Fig. 4. Open in a new tab The flowchart of MADM hybrid method. Determining attribute weights using a method based on normal distribution MADM requires experience and expertise from DMs 35 , 36 . To assign preference values to n aggregated arguments, experts form a collection of n preference values. The bias or preferences of DMs may affect the final results, leading to unfair argument weighting. This happens when experts assign excessively high or low values to certain arguments. To counteract this problem, lower weights can be assigned to biased arguments. Therefore, the pivotal idea is that the closer an ideal value is to the median values, the more the weight, and, conversely, the further a value is to the median, the lower its weight. This principle underlies the normal distribution-based method 37 . Supposing is the weight vector associated with the OWA operator, then the following holds true: 11 where is the mean of collection from n numbers and is the standard deviation of the collection . and are found according to the formulas : 12 13 Given that and we get: 14 Algorithmic description of the MADM hybrid method Step 1. If a criterion in the decision matrix represents a cost‑type attribute (where lower values are preferable), normalization is necessary. In this case, cost values must be converted into benefit values to build a new IF DM . 15 where is the complement of : . Step 2. Determine weights of experts . Let be the IF assessment of the e -th DM. The weight of expert is determined by the Eq. ( 16 ) 16 where and —the membership degree of the e -th expert, –non-membership degree of the e -th expert, –the hesitation level assessment of the e -th DM. Step 3. Apply the normal distribution 37 to find the weight vector associated with IFHA operator, where , , j = (1,2,…, n ) and Step 4. Define weights of criteria. Different criteria cannot be assessed equally. Consequently, every decision‑maker independently evaluates each criterion in order to establish its relative importance. If is the intuitionistic fuzzy assessment of the j -th attribute by the k -th DM, then W is the overall importance level from all experts. The IFWA operator is used to calculate weights of criteria. The importance of a criterion is represented using linguistic terms: 17 Step 5. Construct an aggregated IF decision matrix (AIFDM) from individual initial IF decision matrices (IFDM), where values are represented as linguistic terms. The aggregated collective matrix contains a common assessment of the alternatives. Let be the IFDM of each expert and be weights of experts. Then: 18 Step 6. Apply the modified operator, which considers intuitionistic fuzzy weights of criteria, to find IF assessments of alternatives 19 where ). Vector is the weight vector connected with IFHA operator , , j = (1,2,…, n ) and , j = 1,2,..,n, is a permutation of the weighted IFNs such that ( , , ( j = 1,2,..,n-1); is the weight vector of , j = (1,2,…, n ), j = (1,2,…, n ) and The balancing coefficient is n , which plays a role of balance of balance, if the vector reaches , then the vector reaches . Step 7. Calculate the scores of the aggregated values of criteria by Eqs. (20) and (21). To compare IFNs, the score function can be used: 20 If the IFSs are equal, they can be compared using an accuracy function h 38 : 21 where is the accuracy degree of . The larger , the higher the accuracy degree of the IFN α. Step 8. Based on the calculated scores, rank the alternatives to obtain their optimal order. If two scores and are equal, use the accuracy function and to compare the alternatives. The proposed integrated framework relies on IFHA operator that employs two weight vectors: the weight vector of criteria and aggregation-associated vector. Aggregation-associated vector employs different methods for assigning weights in order to avoid assigning the weights beforehand. Among them there are the normal distribution–based method 37 , 39 , which can relieve the influence of unfair arguments on the decision result by assigning low weights to those ‘‘false’’ or ‘‘biased’’ ones, and quantifier-based methods 40 , 41 that allow not to associate a fuzzy number with its weight, but rather associate a weight with a particular ordered position. Criteria weights are set by experts based on real conditions of problem, their experience and background. They can be given as a vector or in the form of fuzzy assessments, for example as pairwise comparison matrix for criteria 42 . The fuzzy values of criteria provided by experts allow for the modelling of uncertainty and doubts in each expert’s assessment, without forcing them to arrive at a single value. This approach leads to more accurate aggregation results. Therefore, the proposed framework enables the consideration of a wider range of uncertainty aspects and experts’ doubts when evaluating criteria, as well as the avoidance of biased assessments in the process of weight selection. The proposed method overcomes limitations of existing methods in handling fuzzy weights of experts. The proposed IFHA operator allows handling fuzzy intuitionistic values. IFWA and IFWG operators assign weights to the given IFNs, whereas IFOWA and IFOWG operators assign weights to the ordered positions of the mentioned numbers. Each of the operators however considers a single aspect. IFHA operators allow fusing both criteria. For complex problems with multiple criteria and interdependencies among them, hybrid operators are more suitable. Necessity to evacuate as an evacuation alternative We developed an MADM method under intuitionistic fuzzy conditions to find an effective emergency response alternative. The primary purpose is to determine the need for evacuation when a storm occurs as an evacuation strategy. There are five evacuation strategies: stay in place, alertness, recommended evacuation, mild evacuation and urgent evacuation. The concept “necessity to evacuate” indicates the level of urgency for evacuation in a given area. This degree reflects the level of urgency and the scale of evacuation. The higher the degree, the more urgent the evacuation should be. Intuitionistic fuzzy sets will be used to handle expert assessments of alternatives regarding attributes by indicating the satisfaction degree of each alternative 1 . The need for evacuation will be assessed as a percentage, ranging from 0 to 100%. The necessity of evacuation as an alternative will be defined based on seven criteria: storm intensity; closeness of the storm path to citizens, rainfall intensity, degree of individual preparedness to stay, degree of neighbors’ preparedness to stay; traffic intensity, and historical risks regarding this area. The hierarchical structure for selecting the best evacuation strategy, based on seven criteria and five alternatives, is given in Fig. 5 . The parameter “storm intensity” considers five categories based on wind speeds around the eye. A storm may weaken, potentially becoming a tropical storm or depression, which also needs to be considered. Residents are concerned with the degree of closeness of a storm path to their location. Rainfall occurs as a consequence of high winds and is not always directly correlated with hurricane intensity, but it can lead to flooding after the storm, which may necessitate evacuation. People sometimes prefer to stay at their locations and not evacuate due to personal circumstances, beliefs, prejudice, or health conditions. Refusal to evacuate may be linked to constantly changing hazard risk assessments, distrusts of forecasts based on previous experience, and other factors. Neighbors’ behavior may influence DM especially for inexperienced residents, as potential victims may imitate their neighbors’ behavior to evaluate the risk. Traffic intensity may affect those at risk, causing them to delay evacuation. Crowded roads block the traffic leading to traffic jams, delays and bottlenecks. Historical risks regarding this area include statistics regarding the area, vulnerability assessments, knowledge of previous hazards of the same type, their severity, and the type of evacuation if it was previously required. Fig. 5. Open in a new tab Selection of the best evacuation strategy: the hierarchical structure. In the present study, the necessity of evacuation is defined by the set of linguistic assessments: “very low”, “low”, “medium”, “high”, and “very high”. These are connected to a percentage ratio, as shown in Table 1 . Table 1. The necessity of evacuation. Evacuation alternative Interpretation Necessity to evacuate Linguistic assessment Percent % Stay in place Evacuation is not needed Very low (0,15) Alertness Preparedness for evacuation in case of potential storm risk Low (15, 40) Recommended evacuation Partial evacuation of the most vulnerable groups (e.g. disabled, injured or ill people) Medium (40, 65) Mild evacuation Regular evacuation of the majority of potential victims is required High (65,80) Urgent evacuation Total evacuation: people must urgently leave endangered areas Extremely high (80,100) Open in a new tab Evacuation DM in the case of a Typhoon Maria In this section we consider the adverse tropical cyclone Typhoon Maria, which affected Guam, the Ryukyu Islands, Taiwan, and East China in early July 2018 (Fig. 6 ). It caused severe damage to the entire infrastructure, affected 1.424 million people, and resulted in direct economic losses of $629 million. Fig. 6. Open in a new tab Tropical cyclone Typhoon Maria near east China in July 2018. All photos are from Wikimedia Commons under Public Domain. The present study illustrates the method for choosing the best emergency response from the range of evacuation alternative strategies in Jiangxi province. The most effective evacuation strategy must be chosen by DMs, who are admitted experts in emergency DM as presented in our previous studies 43 – 45 . Four experts were asked to evaluate the evacuation strategy across criteria. They provided their preferences as intuitionistic fuzzy numbers. Five evacuation strategies are available: stay in place, alertness, recommended evacuation, mild evacuation, and urgent evacuation, which are defined and interpreted in Table 1 . To determine which strategy is the most effective, four DMs assess the alternatives based on seven attributes : storm intensity, closeness of the storm path to citizens, rainfall intensity, degree of individual preparedness to stay, degree of neighbors’ preparedness to stay, traffic intensity, and historical risks regarding this area. Experts provide their evaluations as IFNs and generate four intuitionistic fuzzy decision matrices (Table 2 ) of the form . The manuscript performs simulation of the decision-making process, and intuitionistic fuzzy values are given by experts in the field of emergencies based on state-of-the art papers in this area 14 , 35 , 36 , 46 . Table 2. Linguistic concepts for evaluating DMs. Linguistic term IFNs Very low (VL) (0.10, 0.80) Low (L) (0.20, 0.70) Medium low (ML) (0.35, 0.50) Medium (M) (0.40, 0.55) Medium Important (MI) (0.60,0.35) Important (I) (0.70, 0.20) Very important (VI) (0.90, 0.05) Open in a new tab Tables 2 , 3 and 4 show linguistic terms for assessing experts, attributes, and alternatives in the form of IFs. Table 3. Linguistic concepts for evaluating criteria. Linguistic term IFNs Very poor (VP) (0.15, 0.80) Poor (P) (0.30, 0.65) Medium fair (MF) (0.45, 0.50) Fair (F) (0.55, 0.40) Medium Important (MI) (0.65,0.30) Important (I) (0.75, 0.15) Very important (VI) (0.85, 0.10) Open in a new tab Table 4. Linguistic concepts for evaluating alternatives. Linguistic term IFNs Very Low (VL) (0.10, 0.85) Low (L) (0.15, 0.75) Medium Low (ML) (0.25, 0.60) Medium (M) (0.50, 0.50) Medium Good (MG) (0.7,0.25) Good (G) (0.80, 0.10) Very Good (VG) (0.9, 0.05) Open in a new tab Table 2 provides a mapping between linguistic terms (verbal assessments) and intuitionistic fuzzy numbers (IFNs) for evaluating DMs. Table 3 provides a linguistic scale to assess the importance of criteria using intuitionistic fuzzy numbers (IFNs). Table 4 provides a linguistic scale to assess the quality or importance of alternatives using intuitionistic fuzzy numbers (IFNs). Table 5 shows the assessments of 7 criteria ( by 4 experts using linguistic terms (from Table 3 ) to evaluate the importance of each criterion. Each expert assigns a linguistic label (VP, P, MF, F, MI, I, VI) reflecting their judgment of the criterion’s weight. Table 5. The importance weights of criteria. MF F MF I I P F F MI F MI VI MF VP MI I P F F VP P P VI P P MF P P Open in a new tab The evacuation alternatives were assessed by DMs, taking into account the linguistic concepts in Table 4 for each criterion. The following fuzzy intuitionistic matrices of four experts were formed (Tables 6 , 7 , 8 and 9 ). Table 6 presents the first expert’s evaluations of five evacuation strategies across seven criteria using IFs (VL, L, ML, M, MG, G, VG). Table 6. Intuitionistic fuzzy decision matrix of the first expert . Alternative Criterion M MG VG L ML VG ML G ML VG L MG G L MG VG M ML VL ML MG G MG ML L VL M G G ML ML L VL G MG Open in a new tab Table 7. Intuitionistic fuzzy decision matrix of the second expert . Alternative Criterion ML ML G ML L VG M VG L G ML M G ML M G MG VL ML G MG G G ML L ML M G M ML MG VL M L MG Open in a new tab Table 8. Intuitionistic fuzzy decision matrix of the second expert . Alternative Criterion ML L VG L ML G M G ML VG VL G M ML MG VG M L MG MG G MG G M MG M MG VG M VG ML M ML VL MG Open in a new tab Table 9. Intuitionistic fuzzy decision matrix of the second expert . Alternative Criterion M M ML VG L VG ML ML L G L MG MG MG G M MG L G M VG G MG M VG MG G G MG G L G M L M Open in a new tab Table 7 presents the second expert’s evaluations of five evacuation strategies across seven criteria using IFs (VL, L, ML, M, MG, G, VG). Table 8 presents the third expert’s evaluations of five evacuation strategies across seven criteria using IFs (VL, L, ML, M, MG, G, VG). Table 9 presents the fourth expert’s evaluations of five evacuation strategies across seven criteria using IFs (VL, L, ML, M, MG, G, VG). The DM process requires the certain level of experience of four experts involved in the DM. Expert 1 (contributed to decision matrix —Table 6 ) is senior emergency response coordinator with 15 + years of experience in hurricane preparedness and response in coastal regions. His approach is conservative, i.e. tends to overestimate risks to ensure maximum safety. The area of expertise: assessment of storm intensity and historical risks. Known for conservative estimates to ensure maximum safety. The main focus in evaluation prioritizes storm intensity and historical risks, tends to lean towards more cautious strategies (mild/urgent evacuation). The style of IFN assessment: uses higher values of non-membership degree for «stay in place» and «alertness» in high-risk scenarios. Expert 2 (contributed to decision matrix —Table 7 ) is a meteorologist specializing in tropical storms and rainfall prediction, 10 years of experience with national weather services. His area of expertise: rainfall intensity and storm path prediction with providing data-driven, precise forecasts. The main focus in evaluation: centers on rainfall intensity and closeness of storm path to populated areas, tends to balance between “recommended evacuation” and “mild evacuation”. The style of IFN assessment: assigns higher membership degrees to evacuation strategies when rainfall and path data indicate high risk. Expert 3 (contributed to decision matrix —Table 8 ) is a community safety officer with expertise in social preparedness and neighborhood resilience, 12 years in local emergency management. His area of expertise: assessment of individual and neighbors’ preparedness with a focus on ground-level readiness and communication. The targets in evaluation evaluates preparedness levels to determine feasibility of «stay in place» or «alertness» strategies. The style of IFN assessment: assigns higher non-membership degrees to evacuation strategies if community preparedness is high. Conversely, assigns higher membership degrees to evacuation if preparedness is low. Finally, expert 4 (contributed to decision matrix —Table 9 ) is a transportation analyst with focus on emergency evacuation routes and traffic management, 8 years in urban planning and disaster response. His area of expertise: traffic intensity and its impact on evacuation efficiency. Specializes in modelling evacuation logistics. The main focus in evaluation: analyses traffic conditions to determine viability of evacuation strategies, prioritizes «urgent evacuation» if traffic congestion is anticipated. The style of IFN assessment: uses high membership degrees for urgent evacuation when traffic intensity is expected to hinder safe evacuation, considers «stay in place» only if traffic conditions are guaranteed to remain stable. Each expert contributed a critical dimension (meteorology, logistics, sociology, safety), ensuring a comprehensive risk analysis. The predefined linguistic scales are symmetric relative to the central value, logically sequential, consistent, unambiguous in formulations for experts, balanced between detail and simplicity (seven levels provide sufficient granularity to capture nuances in assessments while keeping the scale manageable and not overwhelming for users. A smaller number of points might lack detail, while a larger number could complicate decision-making). A logically consistent 7-point scale combines strict hierarchical ordering, transparent criteria, and practical applicability, making it an effective tool for qualitative and quantitative evaluations. Linguistic scales allow experts to express their assessments in a form that is familiar to them, which increases the reliability and relevance of the data. This is especially important in situations where objective metrics are absent or insufficient. Different authors use various linguistic scales with a slight difference in the values of intuitionistic fuzzy values. For example, authors in 47 employ the 7-point linguistic scale: absolutely low, low, fairly low, medium, fairly high, high, absolutely high is used. In 48 , the following 5-point scale is used to assess DMs: Very Important (0.80, 0.10) Important (0.50, 0.20) Medium (0.50, 0.50) Bad (0.30, 0.50) Very Bad (0.20, 0.70) for rating DMs; Very Important (0.90, 0.10) Important (0.75, 0.20) Medium (0.50, 0.45) Unimportant (0.35, 0.60) Very Unimportant (0.10, 0.90)—for evaluating criteria; Very Good (VG) [1.00, 0.00, 0.00] Good (G) [0.85, 0.05, 0.10] Moderately Good (MG) [0.70, 0.20, 0.10] Fair (F) [0.50, 0.50, 0.00] Moderately Poor (MP) [0.40, 0.50, 0.10] Poor (P) [0.25, 0.60, 0.15] Very Poor (VP) [0.00, 0.90, 0.10]—7-point scale for evaluating alternatives. Authors 42 employ assessments for criteria by 9-point scale: Absolutely less important than, Very strongly less important than, Strongly Less important than, Slightly less important than, Exactly equal importance, Slightly more important than, Strongly more important than, Very strongly more important than, Absolutely more important than. 9-point scale for alternatives: Absolutely Low Value, Very Low Value, Low Value, Slightly Low Value, Medium Value, Slightly High Value, High Value, Very High Value, Absolutely High Value. Step 1. The initial attributes are of two types: cost and benefit. Therefore, attribute values of cost type should be transformed to benefit. Attributes and are of cost type. S o, all the matrices should be transformed into matrices of the benefit type (Tables 10 , 11 , 12 and 13 ), where the assessments are given in the form IFs . Table 10 shows the transformed assessments of the first expert, where cost-type criteria and are converted to benefit type. The intuitionistic fuzzy sets (IFSs) reflect —degree of preference for the alternative regarding the criterion and —degree of rejection. Table 10. Intuitionistic fuzzy decision matrix of the first expert . Alternative Criterion (0.50, 0.50) (0.25,0.70) (0.05, 0.90) (0.15, 0.75) (0.25, 0.60) (0.90, 0.05) (0.60, 0.25) (0.10, 0.80) (0.60, 0.25) (0.05, 0.90) (0.15, 0.75) (0.70,0.25) (0.80, 0.10) (0.75, 0.15) (0.25,0.70) (0.05, 0.90) (0.50, 0.50) (0.25, 0.60) (0.10, 0.85) (0.25, 0.60) (0.25,0.70) (0.10, 0.80) (0.25,0.70) (0.60, 0.25) (0.15, 0.75) (0.10, 0.85) (0.50, 0.50) (0.10, 0.80) (0.10, 0.80) (0.60, 0.25) (0.60, 0.25) (0.15, 0.75) (0.10, 0.85) (0.80, 0.10) (0.25,0.70) Open in a new tab Table 11. Intuitionistic fuzzy decision matrix of the second expert . Alternative Criterion (0.60, 0.25) (0.60, 0.25) (0.10, 0.80) (0.25, 0.60) (0.15, 0.75) (0.90, 0.05) (0.50, 0.50) (0.05, 0.90) (0.75, 0.15) (0.10, 0.80) (0.25, 0.60) (0.50, 0.50) (0.80, 0.10) (0.60, 0.25) (0.50, 0.50) (0.10, 0.80) (0.25,0.70) (0.10, 0.85) (0.25, 0.60) (0.80, 0.10) (0.25,0.70) (0.10, 0.80) (0.10, 0.80) (0.60, 0.25) (0.15, 0.75) (0.25, 0.60) (0.50, 0.50) (0.10, 0.80) (0.50, 0.50) (0.60, 0.25) (0.25,0.70) (0.10, 0.85) (0.50, 0.50) (0.15, 0.75) (0.25,0.70) Open in a new tab Table 12. Intuitionistic fuzzy decision matrix of the third expert . Alternative Criterion (0.60, 0.25) (0.75, 0.15) (0.05, 0.90) (0.15, 0.75) (0.25, 0.60) (0.80, 0.10) (0.50, 0.50) (0.10, 0.80) (0.60, 0.25) (0.05, 0.90) (0.10, 0.85) (0.80, 0.10) (0.50, 0.50) (0.60, 0.25) (0.25,0.70) (0.05, 0.90) (0.50, 0.50) (0.15, 0.75) (0.70,0.25) (0.70,0.25) (0.10, 0.80) (0.25,0.70) (0.10, 0.80) (0.50, 0.50) (0.70,0.25) (0.50, 0.50) (0.70,0.25) (0.05, 0.90) (0.50, 0.50) (0.05, 0.90) (0.60, 0.25) (0.50, 0.50) (0.25, 0.60) (0.10, 0.85) (0.70,0.25) Open in a new tab Table 13. Intuitionistic fuzzy decision matrix of the fourth expert . Alternative Criterion (0.50, 0.50) (0.50, 0.50) (0.60, 0.25) (0.9, 0.05) (0.15, 0.75) (0.9, 0.05) (0.60, 0.25) (0.60, 0.25) (0.75, 0.15) (0.10, 0.80) (0.15, 0.75) (0.7,0.25) (0.7,0.25) (0.25,0.70) (0.10, 0.80) (0.50, 0.50) (0.25,0.70) (0.15, 0.75) (0.80, 0.10) (0.50, 0.50) (0.05,0.90) (0.10, 0.80) (0.25,0.70) (0.50, 0.50) (0.9, 0.05) (0.7,0.25) (0.80, 0.10) (0.10, 0.80) (0.25,0.70) (0.10, 0.80) (0.75, 0.15) (0.80, 0.10) (0.50, 0.50) (0.15, 0.75) (0.50, 0.50) Open in a new tab Table 11 shows the transformed assessments of the second expert, where cost-type criteria and are converted to benefit type. The intuitionistic fuzzy sets (IFSs) reflect – degree of preference for the alternative regarding the criterion and – degree of rejection. Table 12 shows the transformed assessments of the first expert, where cost-type criteria and are converted to benefit type. The intuitionistic fuzzy sets (IFSs) reflect – degree of preference for the alternative regarding the criterion and – degree of rejection. Table 13 shows the transformed assessments of the first expert, where cost-type criteria and are converted to benefit type. The intuitionistic fuzzy sets (IFSs) reflect – degree of preference for the alternative regarding the criterion and – degree of rejection. Step 2. Calculate weights of experts. Weights of experts are based on the linguistic concepts in Table 2 and can be found by Eq. ( 16 ). As a result, the following importance weights are obtained Table 14 , which presents the relative importance of four decision makers (DM 1 –DM 4 ) and their corresponding weights ( ) in the multi-expert evaluation process. The weights are derived from linguistic assessments of their importance, converted into numerical values for aggregation in the decision model. Table 14. The importance and weights of DMs’ opinions. DM 1 DM 2 DM 3 DM 4 Linguistic concept Important Medium important Very important Medium 0.280 0.227 0.341 0.152 Open in a new tab Step 3. Calculate the weight vector by the normal distribution method of Xu 27 , 37 to omit the influence of unduly low and high weights by Eqs. (11)–(14). Step 4. Table 15 presents the importance weights of seven criteria ( – ), derived from DMs’ linguistic assessments (Table 3 ) using Eq. ( 17 ). These weights are expressed as intuitionistic fuzzy numbers (IFNs) in the form . Table 15. The weights of criteria. (0.533, 0.415) (0.706, 0.217) (0.408, 0.541) (0.615, 0.306) (0.693, 0.229) (0.292, 0.657) (0.354, 0.595) Open in a new tab Step 5. Build the aggregated intuitionistic fuzzy decision matrix (AIFDM) from individual initial intuitionistic fuzzy decision matrices (IFDM) in the form of IFNs using Eq. 18 , as shown in Table 16 . This matrix reflects the collective opinion of all decision makers (DMs), weighted by their importance (Table 14 ) and the criteria weights (Table 15 ). Table 16. Aggregated collective intuitionistic fuzzy decision matrix (AIFDM). (0.560 0.337) (0.580, 0.311) (0.177, 0.721) (0.403, 0.473) (0.214, 0.653) (0.873, 0.063) (0.546, 0.371) (0.194, 0.689) (0.665, 0.206) (0.069, 0.861) (0.158, 0.744) (0.707, 0.214) (0.709, 0.199) (0.614, 0.253) (0.297, 0.662) (0.149, 0.802) (0.417, 0.568) (0.169, 0.725) (0.527, 0.374) (0.618, 0.288) (0.173, 0.761) (0.154, 0.764) (0.168, 0.755) (0.553, 0.352) (0.569, 0.342) (0.402, 0.544) (0.634, 0.309) (0.083, 0.833) (0.373, 0.600) (0.392, 0.462) (0.570, 0.292) (0.423, 0.495) (0.323, 0.617) (0.422, 0.445) (0.295, 0.665) Open in a new tab Step 6. Use the modified IFHA operator (Eq. 19 ) to aggregate the data from the aggregated intuitionistic fuzzy decision matrix (AIFDM) (Table 16 ) into overall IFHA values for each alternative ( as shown in Table 17 . Table 17. Intuitionistic fuzzy hybrid averaging (IFHA) values. (0.9443 0.0129) (0.9442, 0.0104) (0.8045, 0.1013) (0.8605, 0.0597) (0.8547, 0.0521) Open in a new tab Step 7. Apply Eqs.(20)-(21) to calculate the scores. We get Step 8. Therefore, we have . This means that . According to the algorithm the most desirable strategy in this situation is alertness, which means preparedness for evacuation in the case of potential storm risk in Jiangxi province. Sensitivity analysis We conducted sensitivity analysis to observe how the variations in input parameters influence alternative rankings. To check the robustness of the proposed algorithm, the sensitivity of variations in weights of DMs and in weights of criteria to the ranking results were examined. To do that, the weight of the third expert , which is the largest in the range of experts’ weights was chosen. We adjusted its weight (both increasing and decreasing it within the interval [0.28–0.42]), redistributing the resulting delta value evenly among the weights of the other criteria. Table 18 shows that reducing the weight does not lead to the change in the rankings of alternatives. However, increasing the weight of turns to a subtle change in ranking of and . At the same time, sensitivity analysis reveals that the ranking of the top two alternatives and the worst one remains stable across a wide range of weight variations, confirming the robustness of the results. Table 18. Set of experts’ weights for sensitivity analysis. Set of experts’ weights Ranking Present case 0,280 0,227 0,341 0,152 (0.931, 0.934, 0.703, 0.801, 0.803) 2≻1≻5≻4≻3 Set 1 0,300 0,248 0,280 0,172 (0.933, 0.936, 0.695, 0.799, 0.814) 2≻1≻5≻4≻3 Set 2 0,294 0,241 0,300 0,165 (0.933, 0.935, 0.698, 0.800, 0.811) 2≻1≻5≻4≻3 Set 3 0,287 0,234 0,320 0,159 (0.932, 0.934, 0.700, 0.800, 0.806) 2≻1≻5≻4≻3 Set 4 0,280 0,228 0,340 0,152 (0.931, 0.934, 0.703, 0.801, 0.803) 2≻1≻5≻4≻3 Set 5 0,274 0,221 0,360 0,145 (0.931, 0.933, 0.706, 0.801, 0.800) 2≻1≻4≻5≻3 Set 6 0,267 0,214 0,380 0,139 (0.930, 0.933, 0.708, 0.802, 0.796) 2≻1≻4≻5≻3 Set 7 0,260 0,208 0,400 0,132 (0.929, 0.932, 0.711, 0.803, 0.793) 2≻1≻4≻5≻3 Open in a new tab Furthermore, we analyzed the impact of criteria’s weight variation on the ranking of alternatives. For this reason, the criterion (degree of neighbors’ preparedness to stay) was chosen arbitrary and modified within the interval [− 0.04, 0.04] while redistributing the resulting delta value evenly among the weights of the other criteria. Table 19 illustrates that changes in weight do not lead to the change in the rankings of alternatives, which confirms the robustness of the results. Table 19. Set of criteria’ weights for sensitivity analysis. Set of criteria’ weights Ranking Present case (0.533, 0.415) (0.706, 0.217) (0.408, 0.541) (0.615, 0.306) (0.693, 0.229) (0.292, 0.657) (0.354, 0.595) (0.931, 0.934, 0.703, 0.801, 0.803) 2≻1≻5≻4≻3 Set 1 (0.540, 0.408) (0.713, 0.210) (0.415, 0.53] (0.622, 0.299) (0.653, 0.269) (0.299, 0.650) (0.361, 0.588) (0.931, 0.935, 0.705, 0.803, 0.804) 2≻1≻5≻4≻3 Set 2 (0.538, 0.410) (0.711, 0.212] (0.413, 0.536) (0.620, 0.301) (0.664, 0.258) (0.297, 0.652) (0.359, 0.590) (0.931, 0.935, 0.705, 0.803, 0.803) 2≻1≻5≻4≻3 Set 3 (0.536, 0.412) (0.709, 0.214) (0.411, 0.538) (0.618, 0.303) (0.676, 0.246) (0.295, 0.654) (0.357, 0.592) (0.931, 0.934, 0.704, 0.802, 0.803) 2≻1≻5≻4≻3 Set 4 (0.534, 0.414) (0.707, 0.216) (0.409, 0.540) (0.616 0.305) (0.687, 0.235) (0.293, 0.656) (0.355, 0.594) (0.931, 0.934, 0.704, 0.801, 0.803) 2≻1≻5≻4≻3 Set 5 (0.532, 0.416) (0.705, 0.218) (0.407, 0.542) (0.614, 0.307) (0.699, 0.223) (0.291, 0.658) (0.353, 0.596) (0.931, 0.934, 0.703, 0.801, 0.803) 2≻1≻5≻4≻3 Set 6 (0.530, 0.418) (0.703, 0.220) (0.405, 0.544) (0.612, 0.309) (0.710, 0.212) (0.289, 0.660) (0.351 0.598) (0.931, 0.933, 0.703, 0.800, 0.802) 2≻1≻5≻4≻3 Set 7 (0.528, 0.420) (0.701, 0.222)) (0.403, 0.546) (0.610, 0.311) (0.722, 0.200) (0.287, 0.662) (0.350, 0.560) (0.931, 0.933, 0.702, 0.799, 0.802) 2≻1≻5≻4≻3 Set 8 (0,526, 0.422) (0.699, 0.224) (0.401, 0.548) (0.608, 0.313) (0.733, 0.189) (0.285, 0.664) (0.347, 0.602) (0.931, 0.932, 0.701, 0.798, 0.802) 2≻1≻5≻4≻3 Open in a new tab Comparative analysis To justify the relevance of the proposed method, we provide a comparison of the results from the proposed hybrid method with other aggregation operators and IF-TOPSIS, which were also modified by Eqs. ( 1 )–( 6 ) for intuitionistic fuzzy numbers, which is shown in Table 20 . Table 20. IFHA and other operators. IFHA IFGH IFWA IFWG IFOWA IFOWG IF-TOPSIS 0.521 0.612 0.412 0.587 0.483 Open in a new tab The comparison of methods based on various aggregation operators is presented in Fig. 7 . Fig. 7. Open in a new tab The results of IFHA and other operators. We compared the results of the IFHA operator, which accommodates fuzzy attribute weights, with other intuitionistic fuzzy averaging and geometric operators to prove the reliability of our hybrid method. IFWA, IFOWA, and IFHA operators show the same order of evacuation alternatives: . This means the most desirable strategy is alertness, which indicates preparedness for evacuation in the case of potential storm risk in Jiangxi province. All the intuitionistic fuzzy geometric operators indicate as the worst alternative as the best, with a slight difference between the second and the third desirable options: for IFWG and IFHG operators and or for the IFOWG operator. This means that the best option is to stay in place. Furthermore, we provide a comparative analysis of the proposed algorithm with IF-TOPSIS, which leads to the following ranking . The best and the worst two alternatives remain the same with a slight difference in the ranking of the second and the third alternatives, which justifies the robustness of the proposed algorithm. Discrepancies in results of operators arise from the following: IFWA and IFWG operators only weight the IFNs, while the IFOWA and IFOWG operators weight the ordered positions of the IFNs instead of the IFNs themselves. Therefore, the weights represent two different aspects in these operators. However, each of the operators considers only one of the two aspects. IFHA, IGHG try to overcome this limitation by weighting both the given IFNs and their ordered positions. The choice of an aggregation operator (IFWA, IGWG, IFHA, IGHG, IFOWA, IFOWG) depends on the specifics of the task, the type of data, and the required aggregation properties. These operators are used in an intuitionistic fuzzy environment (intuitionistic fuzzy sets), where not only the degree of an element’s belonging to a set is taken into account, but also the degree of its non-belonging, which allows for more flexible modelling of uncertainty. If the criteria are independent, simpler operators can be used (e.g., IFWA). If there are dependencies between the criteria (such as correlations or preference relations), more complex operators may be required to take these interdependencies into account. IFHA is used in hybrid tasks that require simultaneous consideration of argument weights and their ordering. This approach is suitable for complex multi-criteria problems. Let us provide a comprehensive analysis to justify that IFHA performs the best results in comparison with other operators. To do this: Calculate Spearman’s rank correlation coefficients between all pairs of operators (based on their profiles of 5 scores). Assess the stability of each operator (the spread of its 5 values). Select the optimal operator based on these two criteria. Spearman’s rank correlation coefficient measures the rank-order correlation between the profiles of two operators. The formula (for n = 5): where is the difference between the ranks of corresponding values in the two profiles, n is the number of paired observations (in this case, n = 5). Let us present only the significant pairs (full enumeration includes 15 pairs): IFHA vs IFWA: (perfect rank concordance). IFHA vs IFOWA: IFHA vs IFOWG: IFHA vs IFGH: IFHA vs IFWG: IFGH vs IFWG: IFWA vs IFOWA: IFWA vs IFOWG: IFOWA vs IFOWG: Thus, positive operators: IFHA, IFWA, IFOWA, IFOWG. Negative operators: IFGH, IFWG. The correlation between the two groups is lower, with . Operator stability analysis Let us assess the dispersion of the 5 values for each operator. Standard deviation and Coefficient of variation (CV), will be used for this reason. Stability of operators is presented in Table 21 . Table 21. Stability of operators. Operator CV (%) Stability IFHA 0.094 11.3 High IFGH 0.051 5.6 Very high IFWA 0.103 12.9 High IFWG 0.038 4.1 Very high IFOWA 0.178 523.5 Very low IFOWG 0.138 75.6 Low Open in a new tab Operators will be assessed by the following criteria: high stability (low CV), consistency with other “positive” operators (high with IFHA/IFWA), positive sign of the scores (if the goal is maximization). According to the mentioned criteria, IFHA is considered to be the best operator because of its high stability (CV = 11.3%); fully consistency with IFWA and IFOWA ( , i.e., it reflects the opinion of the “positive” group; robustness (it does not have extreme outliers unlike IFOWA and IFOWF); interpretability (the positive assessments are preferable especially in maximization tasks); moderate consistency with IFGH . Therefore, IFOWA and IFOWG should be excluded because they are highly unstable. IFHA is the primary operator for ranking and selecting the best alternatives. IFGH can be applied as an additional tool for risk analysis, for example, to check which alternatives are considered average by IFHA but worst by IFGH. If the goal is to identify the worst alternatives (to minimize risks), IFGH may be useful—but it requires clear interpretation. Discussion The global climate crisis has had devastating consequences. It has severely damaged economies and triggered the migration of millions of people worldwide. This displacement is caused by typhoons, tsunamis, and other environmental changes and disasters. As a result, there is an urgent need to enhance urban sustainability in decision-making. Additionally, we must be prepared for various human mobility strategies. Mass evacuation can be considered a powerful tool for dealing with environmental changes by moving potential victims from a dangerous urban area to a secure destination. Meanwhile, mass evacuation management 49 , 50 , 51 , especially if urgent, is connected with risks of injury, loss of goods or property, and may be expensive and time-consuming while also potentially decreasing public trust in the city government. Therefore, it is necessary to define the need for mass evacuation accurately and reduce unnecessary evacuations by evaluating their relevance. The present research presents a new hybrid method for selecting the most suitable evacuation alternative in the case of a storm (typhoon) as a IFMADM problem. It is based on fuzzy logic, intuitionistic fuzzy sets, and the intuitionistic fuzzy hybrid averaging operator (IFHA). We provided five evacuation alternatives: stay in place, alertness, recommended evacuation, mild evacuation, and urgent evacuation. We showed that a desirable evacuation strategy addresses various aspects of emergency, such as storm intensity, closeness of the storm path to citizens, rainfall intensity, degree of individual preparedness to stay, degree of neighbors’ preparedness to stay; traffic intensity, and historical risks regarding this city area. These factors are proven difficult to represent with precise values because of their uncertainty and incompleteness. In this regard, we applied fuzzy sets to evaluate these factors. By evaluating the factors underlying the emergency in the region, we provided feasible suggestions for the public to deal with unconventional emergencies and make decisions about evacuation. The proposed hybrid method of MADM relies on the IFHA operator, which accommodates intuitionistic fuzzy weights of criteria to consider uncertainty when choosing specific values. This operator weighs both the given intuitionistic fuzzy numbers and their ordered position. We provide a sensitivity analysis to observe how the variations in experts’ weights and criteria’s weights influence alternative rankings. The experiments show that reductions in the third expert’s weight do not lead to the change in the rankings of alternatives. Increasing turns to a subtle change in ranking of and . At the same time, sensitivity analysis reveals that the ranking of the top two alternatives and the worst one remains stable across a wide range of weight variations, confirming the robustness of the results. Furthermore, we analyzed the impact of criteria’s weight variation on the ranking of alternatives. For this reason, the criterion (degree of neighbors’ preparedness to stay) was chosen arbitrary and modified within the interval [-0.04, 0.04]. The experiments illustrate that changes in weight do not lead to the change in the rankings of alternatives, which confirms the robustness of the results. We compared the results of the IFHA operator, which allows fuzzy attribute weights, with other intuitionistic fuzzy averaging and geometric operators and IF-TOPSIS to prove the reliability of the presented method. IFWA, IFOWA, and IFHA operators show the same order of evacuation alternatives: , which means the most desirable strategy is alertness, indicating preparedness for evacuation in the case of potential storm risk in Jiangxi province. All the intuitionistic fuzzy geometric operators indicate as the worst alternative as the best with a slight difference between the second and the third desirable options: for the IFWG and IFHG operators and or for the IFOWG operator. This means the best option is to stay in place. IF-TOPSIS presents the following order of alternatives: The best and the worst two alternatives remain the same with a slight difference in the ranking of the second and the third alternatives, which justifies the robustness of the proposed algorithm. Stability of operators was calculated, which proves that IFHA is the most suitable operator for the given DM task. The proposed method enables DMs to find the best evacuation strategy under fuzzy conditions without moving affected individuals toward safe locations. We suggest that incorporating a module to find the maximum possible number of evacuees, as a maximum flow allowing intermediate storage, makes a model more effective when an emergency occurs. Such a model will handle a city evacuation network whose parameters will have capacities to ensure the safest transportation by storing an extra number of affected individuals at safe city locations. IFDM tools will be applied to select the optimal order of node-shelters for transporting the maximum flow value. These tools may include both preference relations and DM based on aggregation operators. The results of this algorithm can be applied both in actual population evacuation during large scale emergencies and in developing evacuation response plans. While the method offers advantages in handling uncertainty and fuzzy criterion weights, it also has several significant limitations that must be clearly acknowledged. The algorithm’s limitations include its dependence on the accuracy of expert assessments, which is complicated by experts’ doubts and uncertainty when selecting membership functions—due to the lack of historical data or precise network parameter estimates . The results may depend on linguistic scales which contain some level of subjectivity: various assessments may be interpreted individually by experts. Furthermore, variations in how terms are perceived lead to heterogeneity in input data. The semantics of linguistic terms vary depending on the language and cultural background of the experts. To mitigate these problems, calibration of scales using pilot data and usage standardized term dictionaries can be employed. Another problem is connected with scalability challenges for Large‑Scale Urban Networks. As the number of criteria ( n ) and alternatives ( m ) increases, computational load grows as and for large urban networks (thousands of nodes, dozens of criteria), computation time becomes unacceptable. Moreover, operations on intuitionistic fuzzy sets demand more resources than classical methods. Results for thousands of alternatives are difficult to present in a decision‑maker‑friendly format. To combat these problems, metaheuristics (genetic algorithms, swarm intelligence) and decomposition of the network into subsystems can be applied to reduce search space. In future research related with environmental change and human mobility, we will study the evacuation procedure from dangerous areas, which may affect the evacuation route, thereby maximizing the transportation of victims. Furthermore, integration with real-time sensor data and coupling with traffic flow or network optimization models will be considered as well as extension of studies to various types of uncertain numbers including interval-valued or q-rung orthopair fuzzy sets. Methods Fuzzy logic Fuzzy logic presents an effective approach for fusing multiple attributes with experts’ experience. Fuzzy sets theory, proposed by L. Zadeh in 1965 11 , has become a powerful tool in multiple research and industrial areas of modern society. These include artificial pacemaker control systems, water boilers, chemical reactors and devices, blood pressure control systems, heart disease warning systems, power systems, traffic control, and biomedicine 52 . Fuzzy sets use the concept of a membership function taking a distinct value from the closed interval [0,1]. Consider the concept of a fuzzy set. Definition 2 Let be a non-empty set. A fuzzy set on the set X is the set such that: 22 where is called the membership function of F. shows the membership degree of the element x to F and takes the value from the interval [0.1]. Intuitionistic fuzzy sets Atanassov in 1986 12 proposed the concept of intuitionistic fuzzy set (IFS) 53 to extend the fuzzy set theory. This concept includes a level of hesitation (hesitation margin), or indeterminacy function, along with a membership function and a non-membership function. The intuitionistic index is not necessarily equal to zero, as in fuzzy sets. Utilizing IFSs throughout algorithms, provides a comprehensive and holistic description of fuzzy parameters, which yields effective results in addressing inherent uncertainty 54 , 55 . Consider the basic concepts regarding the theory of IFNs. The definition of an intuitionistic fuzzy set is given in Eq. 9. in as the hesitation (intuitionistic) index is presented in Eq. 10. An intuitionistic fuzzy number, or intuitionistic fuzzy value 46 is , where , To compare IFNs, the score function is used, as in Eq. 20. If IFSs are equal, they can be compared by an accuracy function h 38 , given in Eq. 21. The larger , the higher the accuracy degree of the IFN α. Definition 3 Let and be two intuitionistic fuzzy values; and be the scores of these values; and – accuracy functions of , then: If , then If , then. 2.1) if , then 2.2) if , then 2.3) if then . Aggregating operators The DM process requires aggregation of each input datum into a single value via aggregation operators. Yager 56 developed the ordered weighted aggregation (OWA) operator by assigning the weights to all variables based on their ordering position. Among the most common aggregating operators are the weighted averaging operator (WA), weighted geometric operator (WG), ordered weighted averaging operator (OWA), ordered weighted geometric (OWG) operator, the hybrid averaging (HA) operator, the hybrid geometric (HG) operator, and the generalized ordered weighted averaging (GOWA) operator 57 . The intuitionistic fuzzy geometric aggregation operator (IFG) was applied by Xu and Yager 58 . Later, in 2007 Xu 46 presented intuitionistic fuzzy weighted averaging (IFWA) and fuzzy hybrid averaging operators (IFHA). Wei and Wang 59 introduced ordered weighted geometric aggregation operators (IFOWG) for IFNs of the interval type. Zhao et al. 60 presented the ordered weighted averaging operator (IFOWA). Xu and Yager 61 developed intuitionistic fuzzy Bonferroni mean aggregation operators. Wang and Liu 62 introduced various weighted geometric, ordered weighted geometric, and weighted average aggregation operations based on Einstein norm operations. In 2014, Xu et al. 63 introduced the concept of Einstein Choquet integral for IFNs. He et al. 64 introduced some interactive averaging aggregation operators. Liu 65 developed weighted averaging aggregation operators under the Hamacher-norm operations. Later, Garg 66 introduced modified interactive aggregation operators for different IFNs. Ye 67 presented hybrid averaging and geometric aggregation operators for IFNs to rank alternatives. Rahman et al. 68 introduced some generalized hybrid aggregation operators for DM tasks. Chen and Lee 49 described fuzzy DM techniques which rely on interval type-2 fuzzy sets and their ranks. The problems of DM with type-2 fuzzy sets were discussed in a paper 61 based on various aggregation operators and information measures including general t-norms and their dual t-conorms. Garg et al. 50 introduced interval type-2 intuitionistic fuzzy aggregation operators based on triangular norm operations. In the following, we provide an overview of these operators: Definition 4 Let , j = 1,2,…n be a collection of IFNs, then 23 is the weight vector of , j = (1,2,…, n ), j = (1,2,…, n ) and Definition 5 The aggregated value by IFWA operator is 24 Definition 6 Let , j = 1,2,…n be a collection of IFNs, then 25 IFWG presents the intuitionistic fuzzy weighted geometric (IFWG) operator, where is the weight vector of , j = (1,2,…, n ), j = (1,2,…, n ) and Definition 7 The aggregated value by IFWG operator is 26 is the weight vector of , j = (1,2,…, n ), j = (1,2,…, n ) and Both IFWA and IFWG operators weight all the arguments firstly and then aggregate these weighted arguments. However, IFWG is more sensitive to predefined values. Definition 8 IFOWA illustrates an intuitionistic fuzzy ordered weighted averaging operator such that , j = (1,2,…, n ) and 27 where is a permutation of (1,2,…,n) such that for any j . Definition 9 The aggregated value based on IFOWA operator is IFV in the form 28 is the weight vector connected with IFOWA operator, j = (1,2,…, n ) and Definition 10 IFOWA operator presents an intuitionistic fuzzy ordered weighted geometric such that , j = (1,2,…, n ) and 29 where is a permutation of (1,2,…, n ) such that for any j . Definition 11 The aggregated value using IFOWG operator is IFN in the form: 30 is the weight vector connected with IFOWG operator , j = (1,2,…, n ) and IFOWA and IFOWG operators first rearrange the predetermined values in decreasing order, and then weight their ordered positions. Ordered weighted operators aggregate the ordered arguments and weight their ordered positions. Therefore, the argument is not connected with a specific weight; conversely, the specific weight is connected with the specific ordered position of the argument. The aforementioned aggregation operators of average values assign weights to the given IFNs, whereas IFOWA and IFOWG operators assign weights to the ordered positions of the mentioned numbers. Each of the operators however considers a single aspect. In order to fuse these two weights, IFHA operators 51 were introduced, which weigh the predetermined IFNs and their ordered positions. Definition 12 An intuitionistic fuzzy hybrid averaging (IFHA) operator represents a mapping such that 31 where is the weight vector connected with IFHA operator , , j = (1,2,…, n ) and , j = 1,2,..,n, is a permutation of the weighted IFNs such that ( such that , ( j = 1,2,..,n-1); is the weight vector of , j = (1,2,…, n ), j = (1,2,…, n ) and The balancing coefficient is n. Definition 13 Let , (j = 1,2,.., n ). The aggregated value using IFHA operator is IFN in the form: 32 Definition 14 An intuitionistic fuzzy hybrid geometric (IFHG) operator is such a mapping that 33 where , j = (1,2,…, n ), is a permutation of the weighted IFNs such that ( such that , ( j = 1,2,..,n−1); Definition 15 Let , (j = 1,2,.., n ). The aggregated value using IFHG operator is IFN in the form: 34 Hybrid operators IFHA and IFHG require the following steps: Weight the IFNs , j = (1,2,…, n ) according to the values of the associated weights , j = (1,2,…, n ) and find or j = (1,2,…, n ). Secondly, obtain the weighted IFNs or j = (1,2,…, n ) by multiplying the values by the balancing coefficient n. Make a list of weighted IFNs or j = (1,2,…, n ) in decreasing order, or , where is the j - the largest value of , i = (1,2,…, n ), and is the j- the largest value of j = (1,2,…, n ). Weight the obtained ordered weights IFNs or j = (1,2,…, n ) using IFHA or IFHG weights j = (1,2,…, n ). Finally, aggregate all the weighted IFNs or j = (1,2,…, n ) into a collective value. Acknowledgements We would like to express our heartfelt gratitude to the study participants. This study would not have been possible without their contributions. Author contributions S.G. and E.G. designed the study. The experimental part was provided by A.D., A.M. and V.K. S.G. and E.G. performed analysis experiments and wrote the preliminary manuscript. All authors participated in the revision of the manuscript to its final version. Funding This study was supported by the Russian Science Foundation Project No. 22–71-10121-П, implemented by the Southern Federal University; Hybrid AI and Big Data Research Center of Chongqing University of Education (2023XJPT02). Data availability The datasets analyzed during the current study are publicly available from the International Disaster Database https://www.emdat.be Code availability Our source code is publicly available at https://github.com/IntFuz/MADM-based-on-intuitionistic-fuzzy-hybrid-averaging-operator Declarations Competing interests The authors declare no competing interests. Footnotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. References 1. Jia, X., Morel, G., Martell Flores, H., Hissel, F. & Batoz, J. L. Fuzzy logic-based decision support for mass evacuations of cities prone to coastal or river floods. Environ. Model. Softw. 85 , 1–10 (2016). [ Google Scholar ] 2. Zabihi, O., Siamaki, M., Gheibi, M., Akrami, M. & Hajiaghaei-Keshteli, M. A smart sustainable system for flood damage management with the application of artificial intelligence and multi-criteria decision-making computations. Int. J. Disaster Risk Reduct. 84 , 103470 (2023). [ Google Scholar ] 3. Levy, J.K., Gopalakrishnan, C. & Lin, Z. Advances in decision support systems for flood disaster management: Challenges and opportunities. Water Resources Development 21(4) , 593–612 (2005). 4. Cremen, G., Bozzoni, F., Pistorio, S. & Galasso, C. Developing a risk-informed decision-support system for earthquake early warning at a critical seaport. Reliab. Eng. Syst. Saf. 10.1016/j.ress.2021.108035 (2022). [ Google Scholar ] 5. Xu, W., Wang, T., Chen, R. & Zhao, J. L. Prediction of initial coin offering success based on team knowledge and expert evaluation. Decis. Support Syst. 10.1016/j.dss.2021.113574 (2021). [ Google Scholar ] 6. Güler, M. G. & Geçici, E. A decision support system for scheduling the shifts of physicians during COVID-19 pandemic. Comput. Ind. Eng. 10.1016/j.cie.2020.106874 (2020). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 7. Deveci, M., Pamucar, D., Gokasar, I., Delen, D. & Martínez, L. A fuzzy Einstein-based decision support system for public transportation management at times of pandemic. Knowl.-Based Syst. 10.1016/j.knosys.2022.109414 (2022). [ Google Scholar ] 8. Ford, J. & Fulkerson, D. R. Maximal flow through a network. Can. J. Math. 8 (3), 399–404 (1956). [ Google Scholar ] 9. Gamayunova, V. O., Bogomolov, A. S., Kushnikov, V. A. & Ivashchenko, V. A. [ Mul’tiagentnoe modelirovanie evakuacii iz pomeshchenij s uchetom stolknovenij agentov]. Izvestiya Saratovskogo universiteta. Novaya seriya. Seriya: Matematika. Mekhanika. Informatika. 25 (1), 106–115 (2025). [ Google Scholar ] 10. Kotkova, E. A. & Matveev, A. V. [ Metodika intellektual’nogo prognozirovaniya effektivnosti upravleniya evakuaciej lyudej iz obshchestvennyh zdanij]. Vestnik Sankt-Peterburgskogo universiteta Gosudarstvennoj protivopozharnoj sluzhby MChS Rossii. 4 , 107–120 (2021). [ Google Scholar ] 11. Zadeh, L. A. Fuzzy sets. Inf. Control 8 , 338–353 (1965). [ Google Scholar ] 12. Atanassov, K. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20 , 87–96 (1986). [ Google Scholar ] 13. Atanassov, K. & Gargov, G. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31 , 343–349 (1989). [ Google Scholar ] 14. Xu, Z. S. Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis. 22 , 215–219 (2007). [ Google Scholar ] 15. Miyamoto, S. Remarks on basics of fuzzy sets and fuzzy multisets. Fuzzy Sets Syst. 156 , 427–431 (2005). [ Google Scholar ] 16. Torra, V. & Narukawa, Y. On hesitant fuzzy sets and decision. In Proc. 18th IEEE international conference on fuzzy systems , 1378–1382 (2009). 17. Yager, R. R. Pythagorean membership grades in multicriteria decision making. IEEE Trans. Fuzzy Syst. 22 (4), 958–965 (2014). [ Google Scholar ] 18. Yager, R. R. Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25 (5), 1222–1230 (2016). [ Google Scholar ] 19. Senapati, T. & Yager, R. R. Fermatean fuzzy sets. J. Ambient Intell. Human Comput. 11 , 663–674 (2020). [ Google Scholar ] 20. Arora, H. D., Naithani, A. & Gupta, S. Distance measures of Pythagorean fuzzy TOPSIS approach for online food delivery apps. Int. J. Eng. 35 (10), 1877–1886 (2022). [ Google Scholar ] 21. Dutta, P. & Konwar, A. Quintic fuzzy sets: A new class of fuzzy sets for solving multi-criteria decision-making problems under uncertainty. Decis. Anal. J. 10.1016/j.dajour.2024.100449 (2024). [ Google Scholar ] 22. Paik, B. & Mondal, S. K. Scoring rule and its application in intuitionistic fuzzy parameterized soft set-based decision-making problem. J. Ambient Intell. Human Comput. 14 , 14209–14224 (2023). [ Google Scholar ] 23. Paik, B. & Mondal, S. K. Representation and application of fuzzy soft sets in type-2 environment. Complex Intell. Syst. 7 , 1597–1617 (2021). [ Google Scholar ] 24. Das, A. K. & Granados, C. An advanced approach to fuzzy soft group decision-making using weighted average ratings. SN Comput. Sci. 2 , 471 (2021). [ Google Scholar ] 25. Das, A. K. et al. An innovative fuzzy multi-criteria decision making model for analyzing anthropogenic influences on urban river water quality. Iran J Comput Sci 8 , 103–124 (2025). [ Google Scholar ] 26. Rahman, K. & Iqbal, Q. Optimizing railway train selection in Pakistan using confidence-driven intuitionistic fuzzy methods with Einstein-based operators. J. Intell Manag. Decis. 4 (1), 66–77 (2025). [ Google Scholar ] 27. Riaz, M. & Farid, H. M. A. Enhancing green supply chain efficiency through linear diophantine fuzzy soft-max aggregation operators. J. Ind. Intell. 1 (1), 8–29 (2023). [ Google Scholar ] 28. Chakraborty, J., Mukherjee, S. & Sahoo, L. Intuitionistic fuzzy multi-index multi-criteria decision-making for smart phone selection using similarity measures in a fuzzy environment. J. Ind. Intell. 1 (1), 1–7 (2023). [ Google Scholar ] 29. Sarfraz, M. & Božanić, D. Optimization of market risk via Maclaurin symmetric mean aggregation operators: An application of interval-valued intuitionistic fuzzy sets in multi-attribute group decision-making. J. Eng. Manag. Syst. Eng. 3 (2), 100–115 (2024). [ Google Scholar ] 30. Gao, J., Zhang, Y., Wu, Z. & Yu, L. N. Optimized collaborative scheduling of unmanned aerial vehicles for emergency material distribution in flood disaster management. Mechatron. Intell Transp. Syst. 4 (1), 1–15 (2025). [ Google Scholar ] 31. Liu, C. J. et al. Optimizing emergency supply location selection in urban areas: A multi-bjective planning model and algorithm. J. Urban Dev. Manag. 2 (1), 34–46 (2023). [ Google Scholar ] 32. Lazarashouri, H. & Najafi, S. E. Enhancing emergency department efficiency through simulation and fuzzy multi-criteria decision-making integration. J. Oper. Strateg. Anal. 2 (1), 56–71 (2024). [ Google Scholar ] 33. Liu, H. Y., Wu, Z. & Yu, L. N. Optimization of emergency stockpile siting: A review of models, influencing factors, and future research directions. J. Eng. Manag. Syst. Eng. 3 (4), 226–235 (2024). [ Google Scholar ] 34. Li, B. & He, W. Intuitionistic fuzzy PRI-AND and PRI-OR aggregation operators. Inf. Fusion 14 , 450–459 (2013). [ Google Scholar ] 35. Kacprzyk, J., Bozhenyuk, A. & Gerasimenko, E. Lexicographic maximum dynamic evacuation modeling with partial lane reversal based on hesitant fuzzy TOPSIS [Formula presented]. Appl. Soft Comput. 144 , 110435 (2023). [ Google Scholar ] 36. Gerasimenko, E. Code for “Lexicographic maximum dynamic evacuation modelling with partial lane reversal based on hesitant fuzzy TOPSIS” Applied Soft Computing Journal Code Ocean https://codeocean.com/capsule/9378267/tree/v1 (2023). 37. Xu, W. Z. An overview of methods for determining OWA. Int. J. Intell. Syst. 20 , 843–865 (2005). [ Google Scholar ] 38. Hong, D. H. & Choi, C. H. Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst. 114 , 103–113 (2000). [ Google Scholar ] 39. Kureichik, V. & Gerasimenko, E. Integrated algorithm for multi-criteria group decision-making in evacuation tasks. Informatics Autom. 24 (5), 1284–1332 (2025). [ Google Scholar ] 40. Khorshid, S. Soft consensus model based on coincidence between positive and negative ideal degrees of agreement under a group decision-making fuzzy environment. Expert Syst. Appl. 37 (5), 3977–3985 (2010). [ Google Scholar ] 41. Lu, Y., Xu, Y. & Herrera-Viedma, E. Consensus progress for large-scale group decision making in social networks with incomplete probabilistic hesitant fuzzy information. Appl. Soft Comput. 10.1016/j.asoc.2022.109249 (2022). [ Google Scholar ] 42. Alkan, N. & Kahraman, C. Continuous intuitionistic fuzzy sets (CINFUS) and their AHP&TOPSIS extension: Research proposals evaluation for grant funding. Appl. Soft Comput. 10.1016/j.asoc.2023.110579 (2023). [ Google Scholar ] 43. Gerasimenko, E. & Kureichik, V. Minimum cost lexicographic evacuation flow finding in intuitionistic fuzzy networks. J. Intell. Fuzzy Syst. 42 (1), 251–263 (2022). [ Google Scholar ] 44. Gerasimenko, E. & Kureichik, V. Hesitant fuzzy emergency decision-making for the maximum flow finding with intermediate storage at nodes. Lect. Notes Netw. Syst. 307 , 705–713 (2022). [ Google Scholar ] 45. Gerasimenko, E., Kureichik, V. & Kuliev, E. Maximum dynamic flow model for hesitant fuzzy evacuation with intermediate storage at nodes. Lect. Notes Netw. Syst. 307 , 696–704 (2022). [ Google Scholar ] 46. Xu, Z. S. Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15 , 1179–1187 (2007). [ Google Scholar ] 47. Ren, H., Liu, M. & Zhou, H. Extended TODIM method for MADM problem under trapezoidal intuitionistic fuzzy environment. Int. J. Comput. Commun. Control 14 (2), 220–232 (2019). [ Google Scholar ] 48. Erdebilli, B., Yıldızbaşı, A. & Arıkan, Ü. Z. B. Using intuitionistic fuzzy TOPSIS in site selection of wind power plants in Turkey August 2018. Adv. Fuzzy Syst. (5–6), 1–14 (2018). 49. Chen, S. M. & Lee, L. W. Fuzzy multiple attributes group decision-making based on ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert. Syst. Appl. 37 (1), 824–833 (2010). [ Google Scholar ] 50. Garg, H. & Rani, D. Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process. Arab. J. Sci. Eng. 44 , 2679–2698 (2019). [ Google Scholar ] 51. Torra, V. The weighted OWA operator. Int. J. Intell. Syst. 12 , 153–166 (1997). [ Google Scholar ] 52. Piegat, A. Fuzzy modelling and control (Springer-Verlag, 2001). [ Google Scholar ] 53. Dong, J. Y. & Wan, S. P. Interval-valued intuitionistic fuzzy best-worst method with additive consistency. Exp. Syst. Appl. 236 (3), 121213 (2024). [ Google Scholar ] 54. Dabiri, M., Sarvari, H., Chan, D. W. & Olawumi, T. O. Developing a hybrid risk assessment method for prioritizing the critical risks of temporary accommodation sites after destructive earthquakes. Habitat Int. 10.1016/j.habitatint.2022.102667 (2022). [ Google Scholar ] 55. Sadeghi, J. et al. A hybrid risk assessment approach for assessing the earthquake risks in worn out urban fabrics: A case study in Iran. Int. J. Disaster Resil. Built Environ. 14 (2), 193–211 (2023). [ Google Scholar ] 56. Yager, R. R. On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Syst. Man Cybern. 18 , 183–190 (1988). [ Google Scholar ] 57. Xu, Z. S. Linguistic aggregation operators: an overview. In Fuzzy sets and their extensions: representation, aggregation and models (eds Bustince, H. et al.) 163–181 (Springer, 2008). [ Google Scholar ] 58. Xu, Z. S. & Yager, R. R. Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35 , 417–433 (2006). [ Google Scholar ] 59. Wei, G. & Wang, X. Some geometric aggregation operators based on interval-valued intuitionistic fuzzy sets and their application to group decision making. In Proc. IEEE international conference on computational intelligence and security , 495–499 (2007). 60. Zhao, H., Xu, Z. S., Ni, M. F. & Liu, S. S. Generalized aggregation operators for intuitionistic fuzzy sets. Int. J. Intell. Syst. 25 , 1–30 (2010). [ Google Scholar ] 61. Xu, Z. S. & Yager, R. R. Intuitionistic fuzzy Bonferroni means. IEEE Trans. Syst. Man Cybern. 41 (2), 568–578 (2011). [ DOI ] [ PubMed ] [ Google Scholar ] 62. Wang, W. & Liu, X. Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Trans. Fuzzy Syst. 20 (5), 923–938 (2012). [ Google Scholar ] 63. Xu, Y., Wang, H. & Merigo, J. M. Intuitionistic fuzzy Einstein Choquet integral operators for multiple attribute decision making. Technol. Econ. Dev. Econ. 20 (2), 227–253 (2014). [ Google Scholar ] 64. He, Y., Chen, H., Zhau, L., Liu, J. & Tao, Z. Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making. Inf. Sci. 259 , 142–159 (2014). [ Google Scholar ] 65. Liu, P. Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Trans. Fuzzy Syst. 22 (1), 83–97 (2014). [ Google Scholar ] 66. Garg, H. Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making. Comput. Ind. Eng. 101 , 53–69 (2016). [ Google Scholar ] 67. Ye, J. Intuitionistic fuzzy hybrid arithmetic and geometric aggregation operators for the decision-making of mechanical design schemes. Appl. Intell. 47 , 743–751 (2017). [ Google Scholar ] 68. Rahman, K., Abdullah, S., Jamil, M. & Khan, M. Y. Some generalized intuitionistic fuzzy Eeinstein hybrid aggregation operators and their application to multiple attribute group decision making. Int. J. Fuzzy. Syst. 20 (3), 1567–1575 (2018). [ Google Scholar ] Associated Data This section collects any data citations, data availability statements, or supplementary materials included in this article. Data Availability Statement The datasets analyzed during the current study are publicly available from the International Disaster Database https://www.emdat.be Our source code is publicly available at https://github.com/IntFuz/MADM-based-on-intuitionistic-fuzzy-hybrid-averaging-operator Articles from Scientific Reports are provided here courtesy of Nature Publishing Group ACTIONS View on publisher site PDF (6.0 MB) Cite Collections Permalink RESOURCES Similar articles Cited by other articles Links to NCBI Databases Follow NCBI NCBI on X (formerly known as Twitter) NCBI on Facebook NCBI on LinkedIn NCBI on GitHub NCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter) NLM on Facebook NLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top

Related documents

• AI, Hyperstructural, SuperHyperstructural, Fuzzy, and Uncertain Analogues of the P versus NP Problem#693923
• Spherical bipolar fuzzy decision model for green infrastructure selection.#13807
• A Utility Based Evaluation of Logico-probabilistic Systems#772776
• A Semantic Information Formula Compatible with Shannon and Popper's Theories#749525
• A novel intelligent hybrid reinforcement learning framework for autonomous decision making in complex health cognitive systems#253710