Fuzzy soft metric and fuzzifying soft topology induced by fuzzy soft metric

Abstract

Our main goal with this paper is to construct soft topology and fuzzifying soft topology induced by fuzzy soft metric. For this, we present fuzzy soft metric spaces compatible to soft set theory and studied some of its basic properties. Then we investigate soft topological structures induced by fuzzy soft metrics.

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

“…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.…”

The Net in a Fuzzy Soft Topological Space and Its Applications

“…Meanwhile, the theory of fuzzy soft set has been developed rapidly. In particular, the research on fuzzy soft topology has made a lot of achievements (see [14][15][16][17][18][19][20][21][22][23][24]).…”

Near Soft Connected Spaces

“…In 2001 combined fuzzy sets and soft sets and introduced the concept of fuzzy soft sets, and they presented an application of fuzzy soft sets in a decision making problem. Recently, many authors (Aygunoğlu, et al, 2019;Beaula and Gunaseeli, 2014;Beaula and Priyanga, 2015;Beaula and Raja, 2015), etc. studied on fuzzy soft sets.…”