A Study on Various Pythagorean Fuzzy Topological Spaces

Abstract

The concept of Pythagorean fuzzy sets, an extension of fuzzy sets, has been recently introduced newlineto manage imprecise data more effectively. While intuitionistic fuzzy sets were widely used in decision-making, the innovation and versatility of Pythagorean fuzzy sets have led to their increased use in this field. Pythagorean fuzzy topological spaces, a generalization of fuzzy topological spaces, have also emerged. This study explores Pythagorean fuzzy contra G^* continuous functions and their relationships, along with the properties of Pythagorean fuzzy G^*compact spaces. These concepts are applied to analyze real-time data on Indian cities temperatures. Additionally, the study introduces Pythagorean fuzzy cellular topological dynamical systems, which incorporate iterative processes to address uncertainties in data. The system s compact, normal, and homeomorphic properties are discussed, along with topological transitivity. The research also explores normality and regularity in Pythagorean fuzzy cellular spaces, extending classical topology into the fuzzy domain. Further, the study defines new concepts like and#12310;PFand#12311;_cel q-normal and other normal forms in Pythagorean fuzzy cellular spaces, examining their interrelations. The compactification of Pythagorean fuzzy cellular spaces is also studied, focusing on constructing a Pythagorean fuzzy cellular H structure using filters, prime filters, and ultrafilters. The research introduces Pythagorean fuzzy frames, a generalization of topological space subsets, and explores their properties in the Pythagorean fuzzy and#12310;F_pand#12311;^* structure space. Concepts like closed sets, dense sets, and continuous functions are examined, along with the behavior of extremally disconnected spaces in and#12310;F_pand#12311;^* mixed spaces, which combine Pythagorean fuzzy topological spaces and Pythagorean fuzzy frames. newline newline