in this paper, new definitions of $l$-fuzzy closure operator, $l$-fuzzy interior operator, $l$-fuzzy remote neighborhood system, $l$-fuzzy neighborhood system and $l$-fuzzy quasi-coincident neighborhood system are proposed. it is proved that the category of $l$-fuzzy closure spaces, the category of $l$-fuzzy interior spaces, the category of $l$-fuzzy remote neighborhood spaces, the category of ...

In this paper, new definitions of $L$-fuzzy closure operator, $L$-fuzzy interior operator, $L$-fuzzy remote neighborhood system, $L$-fuzzy neighborhood system and $L$-fuzzy quasi-coincident neighborhood system are proposed. It is proved that the category of $L$-fuzzy closure spaces, the category of $L$-fuzzy interior spaces, the category of $L$-fuzzy remote neighborhood spaces, the category of ...

in this paper, we investigate the l-fuzzy proximities and the relationships betweenl-fuzzy topologies, l-fuzzy topogenous order and l-fuzzy uniformity. first, we show that the category of-fuzzy topological spaces can be embedded in the category of l-fuzzy quasi-proximity spaces as a coreective full subcategory. second, we show that the category of l -fuzzy proximity spaces is isomorphic to the ...

in this paper, we establish the theory of fuzzy ideal convergence on completely distributive lattices and give characterizations of some topological notions. we also study fuzzy limit structures and discuss the relationship between fuzzy co-topologies and fuzzy limit structures.

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 ...

Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system...

In this paper,  fuzzy convergence theory in the framework of $L$-convex spaces is introduced. Firstly, the concept of $L$-convex remote-neighborhood spaces is introduced and it is shown that the  resulting category is isomorphic to that of $L$-convex spaces. Secondly, by means of $L$-convex ideals, the notion of $L$-convergence spaces is introduced and it is proved that the  category of $L$-con...

The theory of neighborhood systems is abstracted from the geometric notion of "near" or "negligible distances." It is a "new" theory of the classical concept of neighborhood systems within the context of advanced computing. By definition neighborhood systems include both rough sets and topological spaces as special cases. The deeper and more interesting part is in its interactions with fuzzy se...

The purpose of this paper is to introduce Shi’s (quasi-)uniformity structure in the context of fuzzy soft sets. We define the notion of a fuzzy soft (quasi-)uniformity in the sense of Shi. We give the relations between a fuzzy soft (quasi-)uniformity and a fuzzy soft cotopology. Also, we investigate the relations between fuzzy soft remote neighborhood structures which are generated by a given f...