A Pythagorean Fuzzy Set–Based Approach for Identifying the Best City for Living in Pakistan

Abstract

This work presents and formalizes the idea of Pythagorean fuzzy Ĝ compact spaces, exploring its structural aspects and distinctive features. The work broadens the theoretical underpinnings of fuzzy topology by utilizing the intrinsic flexibility of Pythagorean fuzzy sets, which have membership and non-membership values squared and summed to a maximum of one. As a practical example of this theory, the study examines its application in assessing and selecting suitable cities in Pakistan based on temperature criteria using real-time data. This application demonstrates the versatility of Pythagorean fuzzy Ĝ compact spaces in dealing with multi-dimensional and imprecise facts. Temperature fluctuations might have overlapping or gradual impacts on decision-making. The technique allows for the categorization and ranking of cities by properly simulating the ambiguity inherent in natural phenomena such as weather conditions. This is especially important in a nation like Pakistan, where climatic variety is widespread and temperature swings vary greatly between locations. Furthermore, this work sheds light on how Pythagorean fuzzy topological spaces may be used as a useful tool for data-driven decision-making in environmental science, urban planning, and resource allocation. The capacity to incorporate real-world, inaccurate data into a mathematically rigorous framework shows the link between theoretical advances and their practical applications.

This study explores the features of Pythagorean fuzzy Ĝ compact spaces, laying the groundwork for future research and practical applications in fields where uncertainty and complexity overlap. This work not only broadens our understanding of fuzzy topological structures but also illustrates their use in tackling current issues in data processing and decision-making.