A Unified Approach To The Concept Of Fuzzy L-Uniform Space

On stratified L-valued filters induced by -filters

“…In fact it is the key to understand the bijection between -filters and a particular class of L-filters. This result has already been used in [2,1] in terms of the characteristic set of a -filter (see [1] for details).…”

“…Two lemmas proved in [5] under the assumption of divisibility of the underlying quantale and the existence of square roots are proved here without this assumption. The strategy to prove these lemmas is essentially the same used in [2] and [1]. In fact some proofs could be rewritten using the notion of characteristic set of a -filter (see [1] for details).…”

Some Properties of $L$-Fuzzy Preuniformities, $L$-Fuzzy Neighborhood Systems and $L$-Fuzzy Topologies

“…Fuzzy uniformities have the following different approaches as follows the entourage approach of Lowen [15,16] , the uniform covering approach of Kotzé [13] and the unification approach of Hutton [9] based on the powersets of the form (L X ) (L X ) , the unification approach of Gutiérrez García [6]. Recently, Gutiérrez García introduced L-valued Hutton uniformity where a quadruple (L, ≤, ⊗, * ) is defined by a GL-monoid (L, * ) as an extension of a completely distributive lattice L. Many researchers studied the different approach as powerset [9] or the uniform covering [13].…”

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

“…Höhle [10] introduced L-fuzzy topologies with algebraic structure L(cqm, quantales, M V -algebra). Uniformities in fuzzy sets, have the following approach of Lowen [14] based on powersets of the form L X×X as a viewpoint of the enourage approach, the uniform covering approach of Kotzé [13], the uniform operator approach of Rodabaugh [25] as a generalization of Hutton [11] based on powersets of the form (L X ) (L X ) , the unification approach of Gutiérrez García [7]. Recently, Gutiérrez García introduced L-valued Hutton uniformity where a quadruple (L, ≤, ⊗, ⋆) is defined by a GL-monoid (L, ⋆) as an extension of a completely distrbutive lattice L. Kim [12] introduced the notion of L-fuzzy uniformities as an extension of Lowen in a strictly two-sided, commutative quantale.…”