Abstract
We study the fuzzy soft proximity spaces in Katsaras's sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft δ-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy soft proximities. Finally, we investigate relationship between fuzzy soft proximities and proximities.
Highlights
In 1999, Molodtsov [1] initiated the concept of soft set theory as a new approach for coping with uncertainties and presented the basic results of the new theory
This new theory does not require the specification of a parameter
(i) the union of these fuzzy soft sets is the fuzzy soft set h defined by h(e) = ∨i∈Jfi(e) for every e ∈ E and this fuzzy soft set is denoted by ⊔i∈Jfi; (ii) the intersection of these fuzzy soft sets is the fuzzy soft set h defined by h(e) = ∧i∈Jfi(e) for every e ∈ E and this fuzzy soft set is denoted by ⊓i∈Jfi
Summary
In 1999, Molodtsov [1] initiated the concept of soft set theory as a new approach for coping with uncertainties and presented the basic results of the new theory. By using fuzzy soft sets, Cetkin et al [35] introduced soft fuzzy proximity spaces on the base of the axioms suggested by Markin and Sostak [32] and Katsaras [28], respectively. All these works have generalized versions of many of the well-known results on proximity spaces. We prove the existences of initial fuzzy soft proximity structures Based on this fact, we introduce products of fuzzy soft proximity spaces. The relation between a fuzzy soft proximity and a proximity is investigated
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