Generalized fuzzy b-closed and generalized ⋆-fuzzy b-closed sets in double fuzzy topological spaces

Abstract

The purpose of this paper is to introduce and study a new class of fuzzy sets called (r, s)generalized fuzzy b-closed sets and (r, s)-generalized ⋆-fuzzy b-closed sets in double fuzzy topological spaces. Furthermore, the relationships between the new concepts are introduced and established with some interesting examples.

Certain algebraic structures associated with a double fuzzy topological space

“…Mohammed et al [6] introduced the concepts of (p, q)fuzzy b-closed sets and (p, q)-fuzzy b-open sets in a dfts and studied various properties of them. Definition 2.11 (see [6]) Let ðX; F; F Ã Þ be a dfts. A fuzzy set f is called…”

“…In [6], the authors also introduced the concepts (p, q)generalized fuzzy b-closed sets and (p, The collection of all (p, q)-gfbc sets is denoted by GbC F;p;q ; and the collection of all (p, q)-gfbo sets is denoted by GbO F;p;q .…”

“…In [6], it is claimed that every (p, q)-gfc set is a (p, q)fbc set. That is, with respect to our notations, the claim is GC F;p;q bC F;p;q .…”

“…Later, the notions of (p, spaces were set up and studied in [5] and [6]. These sets were further explored in [7][8][9][10].…”

An $(iota,kappa)$-fuzzy $M$ closed and $(iota,kappa)$ - generalized fuzzy $M$ closed sets in double fuzzy topological spaces

“…In 2005, Garcia and Rodabaugh [7] coined the term "double" instead of "intuitionistic". In the past two decades many researchers [9][10][11]16] doing more applications on double fuzzy topological spaces. From 2011, El-Maghrabi and Al -Johany [3][4][5][6] introduced and studied some properties on M-open sets and maps in topological spaces.…”