Generalized Functional Analysis in Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Spaces. Theory, Convergence, Compactness, and Applications

This book develops several directions in generalized functional analysis within fuzzy, intuitionistic fuzzy, Fermatean intuitionistic fuzzy, and neutrosophic normed spaces. It investigates fundamental analytical concepts including convergence, Cauchy sequences, completeness, compactness, total boundedness, finite-dimensionality, equivalence of generalized norms, and fixed point principles. The first part studies compactness and finite-dimensional structures in intuitionistic algebra fuzzy normed spaces, establishing generalized versions of classical results such as completeness of finite-dimensional subspaces, equivalence of norms, and the Heine–Borel theorem. The second part introduces Fermatean intuitionistic fuzzy (n)-normed linear spaces and develops their convergence, completeness, and fixed point theory. The third part examines Tribonacci ideal and ideal-star convergence in non-Archimedean neutrosophic normed spaces, combining matrix transformations, ideal convergence, and neutrosophic analytical methods. Together, these contributions provide a unified framework for extending classical functional analysis to mathematical environments characterized by uncertainty, hesitation, and indeterminacy, with potential applications in applied mathematics, artificial intelligence, optimization, decision-making, and information sciences.