Generalized ψ

The aim of this work is to introduce ψ-operations on fuzzy topological spaces and to use them to study fuzzy generalized ψρ-closed sets and fuzzy generalized ψρ-open sets. Also, we introduce some characterizations and properties for these concepts. Finally we show that certain results of several publications on the concepts of weakness and strength of fuzzy generalized closed sets are considered as corollaries of the results of this research

Generalized ψρ-Operations on Fuzzy Topological Spaces

The aim of this work is to introduce ψ-operations on fuzzy topological spaces and to use them to study fuzzy generalized ψρ-closed sets and fuzzy generalized ψρ-open sets. Also, we introduce some characterizations and properties for these concepts. Finally we show that certain results of several publications on the concepts of weakness and strength of fuzzy generalized closed sets are considered as corollaries of the results of this research. Preliminaries The concept of fuzzy topology was first defined in 1968 by Chang 1 based on the concept of a fuzzy set introduced by Zadeh in 2 . Since then, various important notions in the classical topology such as generalized closed, generalized open set, and weaker and stronger forms of generalized closed and generalized open sets have been extended to fuzzy topological spaces. The purpose of this paper is to introduce and study the concept of ψ-operations, and by using these operations, we will study fuzzy generalized ψρ-closed sets and fuzzy generalized ψρ-open sets in fuzzy topological spaces. Also, we show that some results in several papers 3-15 considered as corollaries from the results of this paper. Let X, τ be a fuzzy topological space fts, for short , and let μ be any fuzzy set in X. We define the closure of μ to be Cl μ ∧{λ | μ ≤ λ, λ is fuzzy closed} and the interior of μ to be Int μ ∨{λ | λ ≤ μ, λ is fuzzy open}. A fuzzy point x r 16 is a fuzzy set with support x and value r ∈ 0, 1 . For a fuzzy set μ in X, we write x r ∈ μ if and only if r ≤ μ x . Evidently, every fuzzy set μ can be expressed as the union of all fuzzy points which belongs to μ. A fuzzy point x r is said to be quasicoincident 17 with μ denoted by x r qμ if and only if r μ x > 1. A 2 Abstract and Applied Analysi