Fuzzy Topological Spaces and Their Applications in Decision-Making Problems

Abstract

Fuzzy topological spaces provide a powerful mathematical framework for handling uncertainty, vagueness, and imprecision that frequently arise in real-world decision-making. This paper reviews the fundamental concepts of fuzzy topology and explores their applications in multi-criteria decision-making (MCDM) problems. We discuss how fuzzy open and closed sets, fuzzy continuity, fuzzy compactness, and separation axioms can be utilized to model preference relations, aggregate expert opinions, and rank alternatives under uncertainty. Several decision-making algorithms based on fuzzy topological structures are outlined, and illustrative examples from supplier selection, medical diagnosis, and investment ranking are presented. The study demonstrates that fuzzy topological methods offer greater flexibility and robustness compared to classical crisp approaches when dealing with linguistic and incomplete information.