Homeomorphism via δβ-open Sets in Fermatean Fuzzy Topological Spaces and Application in Entropy Measure

Abstract

Classical set theory failed to cover non-probabilistic uncertain situations in to the set format, but fuzzy set theory can do this job perfectly with the fuzzy number of vagueness of non-probabilistic uncertainty. Topologist adopt this fuzzy set and fit in to the topological concepts to extent and apply their innovations for the needs and growth of the humans. Even though the fuzzy concept convert every situation, it hire the concept of intuitionistic fuzzy set to evident the importance of non-membership of the situation. Pythagorean fuzzy set is one of by membership and non-membership, more forceful to seize indeterminacy to cover the uncertain situations which are unable to covered by intuitionistic fuzzy sets. Then any Intuitionistic fuzzy subset or Phythagorean fuzzy subset of a set can be considered as Fermatean fuzzy subset, we observe that any Intuitionstic fuzzy topological space or Phythagorean fuzzy topological space is a Fermatean fuzzy topological space as well. In this paper, we contribute our concept of  (resp.  )-homeomorphism, -homeomorphism in Fermatean fuzzy topological spaces and the properties for the Fermatean field of fuzzy topological spaces. To register importance of Fermatean fuzzy sets we applied a proposed entropy measure for multiple criteria decision making problem.