New notions of generalized closed sets in fuzzy topological spaces

Abstract

By considering A as a set in a space of points X which is characterized by a membership function,μ A (x), fuzzy sets and their properties are studied. Based on the concept of fuzzy set, Chang (1968) developed fuzzy topological spaces. In this thesis, two new notions of fuzzy generalized closed sets namely fuzzy θ-semigeneralized closed set and fuzzy θ-generalized semi-closed set are introduced. Moreover, some properties and characterizations of these two notions are obtained and the relationships among other notions from previous research are investigated. Counterexamples are shown if the implications of the relation are not true. Based on these two notions, new types of fuzzy separation axioms called fuzzy θ-generalized semi-T1/2, fuzzy semi-θ-T0, fuzzy semi-θ-T1 and fuzzy semi-θ-T2 spaces are obtained. Various mappings are developed from these new notions such as fuzzy θ-semi-generalized continuity, fuzzy θ-generalized semi-continuity, fuzzy θ-semi*generalized continuity, fuzzy θ-semi-generalized irresolute mapping, fuzzy θ-generalized semi-irresolute mapping, fuzzy θ-semi-generalized closed mapping and fuzzy θ-generalized semi-closed mapping.