Some Properties of Fuzzy Soft Metric Space

Abstract

In this paper we introduce the notion fuzzy soft metric space after that we define open fuzzy soft ball, fuzzy soft bounded set, fuzzy soft convergence of sequences, fuzzy soft continuous function from a fuzzy soft metric space to another fuzzy metric space then we study this space and some basic results are investigated.

Compactness Property of Fuzzy Soft Metric Space and Fuzzy Soft Continuous Function

“…Consequently, the notion of the fuzzy soft metric space given in [23] is different from the fuzzy soft metric space given in [21] and also different from other definitions of fuzzy soft metric space presented in [24] and [25]. The first aim of this paper is to define the compactness property of the fuzzy soft metric space given in [23] and to investigate some fundamental theorems about compact fuzzy soft metric space. The second aim is to introduce the concepts of sequentially compact and locally compact fuzzy soft metric spaces and to establish their properties.…”

“…The family of all fuzzy soft sets over will be denoted by F( , ). Kider [23] relied on the notions of the fuzzy soft set presented in [22] to provide a new definition of fuzzy soft metric space. It is worth mentioning that the fuzzy soft set definition given in [19] is different from the fuzzy soft set given in [22].…”

“…It is worth mentioning that the fuzzy soft set definition given in [19] is different from the fuzzy soft set given in [22]. Consequently, the notion of the fuzzy soft metric space given in [23] is different from the fuzzy soft metric space given in [21] and also different from other definitions of fuzzy soft metric space presented in [24] and [25]. The first aim of this paper is to define the compactness property of the fuzzy soft metric space given in [23] and to investigate some fundamental theorems about compact fuzzy soft metric space.…”

“…Then, for : or simply written as . The limit point is called the fuzzy soft limit of ( ) [23]. The next characterization is provided for the fuzzy soft metric space.…”

“…For some [ ] there is [ ] such that ̃ . Kider[23] presented the notion of fuzzy soft metric space as follows. Let be a universe set and let F( , ) be the family of all soft fuzzy sets over .…”