Picture Fuzzy topology

Abstract

This thesis is devoted to studying the mathematical structure of Picture Fuzzy Topology, representing a con temporary extension of intuitionistic fuzzy topology. The primary objective is to analyze the essential topological properties of picture fuzzy sets, characterized by membership, neutrality, and non-membership degrees. Our in vestigation focuses on formulating pivotal concepts such as picture fuzzy subspaces, neighborhood systems, and topological bases, while examining their relationships with associated order structures to provide a rigorous math ematical foundation for modeling under uncertainty.