The aim of this paper is to study L-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between L-fuzzy co-topology and L-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when U is an Lfuzzy quasi-uniformity and they will be coincident when U ...

we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

We study FTOP (L), a fuzzy category related to topology with fuzzy functions in the role of morphisms.

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

It is well known that lattice-valued rough sets are important branches of fuzzy sets. The axiomatic characterization and related topology the main research directions For L=(L,⊛), a complete co-residuated lattice (CCRL), Qiao recently defined an L-fuzzy lower approximation operator (LFLAO) on basis relation. In this article, we give further study Qiao’s LFLAO around induced L-topology. Firstly,...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

In this paper, by means of operations (is called in [1, 2, 3] φ,ψ) we shall define φψ-continuity between two L-fuzzy quasi-uniform spaces. We shall prove that φψ-continuity between two L-fuzzy quasi-uniformity induces φψ-continuity between L-fuzzy topology generated by them. We shall investigate some Theorems on L-fuzzy uniform spaces. 2000 Mathematics Subject Classification:54A40, 03E72

The convergence theory not only is an significantly basic theory of fuzzy topology and fuzzy analysis but also has wide applications in fuzzy inference and some other aspects. In this paper, we introduce the concept of α-generalized-remoteneighborhood of fuzzy points and establish the Moore-Smith α-generalized-convergence theory of L-fuzzy nets. Then, we introduce and study the concept of L-fuz...

In this paper, we investigate two L-neighborhood systems induced by an Lfuzzy topology in a complete residuated lattice L. We study the relationships among L-fuzzy topology, L-topologies and L-neighborhood systems. Finally, we give their examples. AMS Subject Classification: 03E72, 06A15, 06F07, 54A05

The concept of an M-approximative system is introduced. Basic properties of the category of M-approximative systems and in a natural way defined morphisms between them are studied. It is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of M-approximative systems. Keywords— Approximative operator...