What question did this study set out to answer?

February 6, 2026Open Access

Dynamical Systems on Intuitionistic Fuzzy Topological Spaces with Symmetry

Key Points

The aim is to develop a framework for discrete dynamical systems on intuitionistic fuzzy topological spaces that preserves specific structures.
Defined evolution operators preserving intuitionistic fuzzy structure
Constructed symmetry-preserving operators using group actions
Introduced an entropy-like functional as an order parameter
Established existence results for fixed points and periodic orbits
Established formal definitions for time evolution on intuitionistic fuzzy sets
Demonstrated the preservation of the μ+ν+π=1 constraint
Provided results on the existence of fixed points and periodic orbits

Abstract

This paper introduces a discrete dynamical system on intuitionistic fuzzy topologicalspaces. We define a class of evolution operators that preserve the intuitionisticfuzzy structure while incorporating radial symmetry and local interactions. Themain contributions are: (1) a formal definition of time evolution on intuitionisticfuzzy sets preserving the μ+ν +π = 1 constraint, (2) a symmetry-preserving operatorconstruction using group actions, (3) the introduction of an entropy-like functionalas an order parameter, and (4) existence results for fixed points and periodicorbits. The framework provides a mathematically rigorous foundation for studyingtemporal evolution in non-classical topological spaces, with potential applications insymbolic and cognitive modeling.

Dynamical Systems on Intuitionistic Fuzzy Topological Spaces with Symmetry

Key Points

Abstract

Cite This Study

Also Consider

Also Consider