Abstract
The purpose of this paper is to introduce the concept of soft fuzzy proximity. Firstly, we give the definitions of soft fuzzy proximity and Katsaras soft fuzzy proximity, and also we investigate the relations between the soft fuzzy proximity and slightly modified version of Katsaras soft fuzzy proximity. Secondly, we induce a soft fuzzy topology from a given soft fuzzy proximity by using soft fuzzy closure operator. Then, we obtain the initial soft fuzzy proximity from a given family of soft fuzzy proximities. So, we describe products in the category of soft fuzzy proximities. Finally, we show that a family of all soft fuzzy proximities on a given set constitutes a complete lattice.
Highlights
In 1999, Molodtsov [1] proposed a completely new concept called soft set theory to model uncertainty, which associates a set with a set of parameters
All over the globe, soft set theory is a topic of interest for many authors working in diverse areas due to its rich potential for applications in several directions
We considered soft fuzzy proximities introduced in Definition 11, which gives the nearness relation between fuzzy soft sets with respect to the parameters, to be the proximal counterpart of soft fuzzy topologies as they are defined in [12]
Summary
In 1999, Molodtsov [1] proposed a completely new concept called soft set theory to model uncertainty, which associates a set with a set of parameters. The topological structure of fuzzy soft sets based on the sense of Sostak [11] has been studied by Aygunoglu et al [12] They proved that the category of fuzzy soft topological spaces is a topological category over SET3. The first and the most advanced one was developed on the whole by Katsaras [13, 14], the second due to Artico and Moresco [15, 16] These approaches proceed from different starting points, both of them are consistent with Chang (or Lowen) fuzzy topologies. Markin and Sostak [17] introduced the different concept of a fuzzy proximity which is consistent with the notion of a fuzzy topology as it is defined in [11]. We show that a family of all soft fuzzy proximities on a given set is a complete lattice
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