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

Abstract

In this paper, we introduce the notion of L-fuzzy (K, E)-soft pre-uniform spaces induced by L-fuzzy (K, E)-soft pre-proximity spaces in a strictly two-sided commutative quantale having an order reversing involution. We investigate the relations between L-fuzzy (K, E)-soft pre-uniform spaces and L-fuzzy (K, E)-soft pre-proximity spaces.We give their examples.

(L,⊙)-Fuzzy (K,E)-Soft Filter

“…Aygüno ǧlu et al [14] presented the notion of (L, )-fuzzy (K, E)-soft topology in the sense of Šostak [15]. Many concepts in fuzzy topological spaces in the sense of Chang [16] and in the sense of Šostak [15] were extended to fuzzy soft theory (see [17][18][19][20][21][22][23][24]).…”

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].…”

“…It is an important mathematical tool for algebraic structures [8,9,18]. Kim et al [10,17] investigated the relationships between L-fuzzy (K, E)-soft quasi-uniform structures and L-fuzzy (K, E)-soft topological structures.…”

L-Fuzzy (K,e)-Soft Quasi-Uniformities and L-Fuzzy (K,e)-Soft Preclosure Operators

“…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,[11][12][13][14][15][16]19].The topological structures of soft sets have been developed by many researchers [2][3][4][5]10,17,20,21].…”

“…On the other hand, Hájek [8] introduced a complete residuated lattice which is an algebraic structure for many valued logic. It is an important mathematical tool for algebraic structures [8][9][10]17,18]. Ramadan et al [10,17] investigated the relationships between L-fuzzy (K, E)-soft quasi-uniform structures and L-fuzzy (K, E)-soft topological structures in a complete residuated lattice.…”