ATANASSOV’S INTUITIONISTIC FUZZY TOPOLOGY BASED ON THE SPACE OF INTUITIONISTIC FUZZY REAL NUMBERS (IFRN)

This study presents a new perspective on intuitionistic fuzzy topology through the integration of intuitionistic fuzzy real numbers and universal sets. Using theoretical foundations and operations developed by Atanassov and extended by Davvaz and others, we construct a topological framework that supports generalized fuzzy reasoning. The research introduces definitions and algebraic structures for intuitionistic fuzzy real numbers, explores topological convergence and continuity, and establishes their role in defining new fuzzy functions. This framework enhances expressive power in handling uncertainty. Keyword: Intuitionistic fuzzy sets, Fuzzy real number, Fuzzy topology space, Intuitionis-tic fuzzy element, Intuitionistic fuzzy point, Fuzzy function.