L- Fuzzy (K,e)-Soft Quasi Uniform Spaces and L-Fuzzy (K,e)-Soft Topogenous Spaces

Abstract

The goal of this paper is to focus on the relationships between L-fuzzy (K, E)-soft quasi uniformities and L-fuzzy (K, E)-soft topogenous orders in complete residuated lattices. As main results, we investigate the L-fuzzy (K, E)-soft quasi uniformities induced by L-fuzzy (K, E)-soft topogenous orders. Moreover, we study the L-fuzzy (K, E)-soft topogenous orders induced by L-fuzzy (K, E)-soft uniformities. We give their examples.

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

“…Since u l,l * [l] = l * and u l⊙l,l * ⊙l * [l⊙l] = l * ⊙l * from Lemma 3.1 (12), by Theorems 2.9 and 3.2(4), we have δ U δ = δ, that is, U δ ∈ Π(δ). Then U is a [0, 1]-fuzzy (E, E)-soft pre-uniformity on X (ref.…”

“…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 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]).…”