Intuitionistic Fuzzy Topology for Psychological Structures: Formal Properties and Non-Trivial Examples

This paper introduces a rigorous mathematical framework for modeling psycho-logical structures using intuitionistic fuzzy topology. We develop the complete theoryof intuitionistic fuzzy topological spaces with a focus on boundary operators, sepa-ration axioms, and compactness properties. Our main contributions are: (1) formaldefinitions of intuitionistic fuzzy topological spaces; (2) construction and analysis ofnon-trivial examples exhibiting psychologically meaningful boundary structures; (3)proof of key topological properties including boundary non-triviality; (4) introduc-tion of psychologically motivated separation axioms (T P 0 , T P 1 , T P 2 ). We demonstrate that intuitionistic fuzzy topology provides a richer mathematicallanguage than stan-dard fuzzy topology for capturing gradedness, co-existence of affirmation/negation, and inherent indeterminacy. The psychological interpretation is not intended as empirical validation, but as a conceptual mapping suggesting potential applications in formalizing psychological concepts from analytical psychology .