FUZZY β-SETS AND FUZZY βS –SETS IN FUZZY TOPOLOGICAL SPACES

Abstract

Some new kinds of fuzzy subsets are defined such as the definition of fuzzy β- sets and fuzzy βs- set. Moreover, some properties, theorems and certain relations between them are proved., some interesting properties of fuzzy β- compactness are investigated. The purpose of this paper is devoted to introduce and study the concepts of β-compactness and β-closed spaces in fuzzy setting., A fuzzy set is one to which objects can belong to different degrees, called grades of membership. The fuzzy set as a number ranging from zero (absolutely false) to 1 (absolutely true). Before dealing with fuzzy systems preliminary definitions should be known. In these sections we will illustrate some important definitions and concepts.