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This research aims to create a mathematical framework to model Jungian archetypes using intuitionistic fuzzy topology.

February 6, 2026Open Access

Intuitionistic Fuzzy Topology as a Formal Framework for Jungian Archetypes

Key Points

This research aims to create a mathematical framework to model Jungian archetypes using intuitionistic fuzzy topology.
Developed formal definitions of intuitionistic fuzzy topology.
Constructed examples that demonstrate psychologically significant boundaries.
Explored relationships between topological and psychological concepts.
Demonstrated how archetypes gradually manifest and coexist.
Established correspondences between topological ideas and psychological states.
Provided a framework for formalizing psychological hypotheses and enhancing interdisciplinary research.

Abstract

This article proposes a formal mathematical framework for modeling archetypalstructures from Jungian psychology using intuitionistic fuzzy topology. Unlikeprevious approaches based on binary logic or standard fuzzy sets, our frameworksimultaneously captures: (1) the gradual manifestation of archetypes, (2) the coexistenceof membership and non-membership, and (3) the inherent indeterminacyof unconscious material. We present formally precise definitions of intuitionisticfuzzy topology, construct non-trivial examples exhibiting psychologically significantboundaries, and establish conceptually well-defined correspondences between topologicalconcepts (open sets, boundaries, compactness) and psychological ones (consciousstates, Shadow, integration). The framework serves as a basis for formalizingpsychological hypotheses, informing the future design of measurement instruments,and structuring future interdisciplinary empirical research

Intuitionistic Fuzzy Topology as a Formal Framework for Jungian Archetypes

Key Points

Abstract

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