An Approach to the Concept of Soft Fuzzy Proximity

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.

$L$-Fuzzy $(K,e)$-Soft Quasi-Uniform Spaces Induced by $L$-Fuzzy $(K,e)$-Soft Pre-Proximities

“…Many researchers have contributed towards the algebraic structure of soft set theory [1][2][3][4][5][6][7]. Shabir and Naz [16] initiated the study of soft topological spaces.…”

“…Aygünoglu et.al [4] introduced the concept of soft topology in a sense ofŠostak [9]. Cetkin et.al [5,6] studied soft proximities and discuss their properties. Ramadan et al [12,13] introduced the L-fuzzy (K, E)-soft topological structures, L-fuzzy (K, E)-soft pre-uniformities and soft L-fuzzy topogenous orders in a strictly two-sided commutative quantale.…”

$L$-Fuzzy $(K,e)$-Soft Topologies and $L$-Fuzzy $(K,e)$-Soft Closure Operators Induced by Fuzzy Soft Maps

“…In 2003, Maji et al [11] defined and studied several basic notions of soft set theory. Many researchers have contributed towards the algebraic structure of soft set theory [1][2][3][4][5]7]. In 2011, Shabir and Naz [19] initiated the study of soft topological spaces.…”

L-Fuzzy (K,e)-Soft Closure Operators Induced by L-Fuzzy (K,e)-Soft Quasi-Uniform Spaces

“…Molodtsov [14,15] introduced the soft set as a mathematical tool for dealing information as the uncertainty of data in engineering, physics, computer sciences and many other diverse field. Presently, the soft set theory is making progress rapidly [1,7].The topological structures of soft sets have been developed by many researchers [2][3][4][5]11,17,20].…”