Fuzzy topology on fuzzy sets: fuzzy semicontinuity and fuzzy semiseparation axioms

摘要

The concept of a fuzzy topology on a fuzzy set was introduced in [Fuzzy Set Syst. 45 (1992) 103]. The aim of this paper is to introduce fuzzy semicontinuity and fuzzy semiseparation axioms in this new situation and validity of some characterization of these concepts have been examined. Also, we define a fuzzy generalized semiopen set and introduce fuzzy separation axioms by using this concept. Fuzzy semiconnected and fuzzy semicompact spaces are introduced and some of their properties are discussed.