This paper presents, by means of Alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces, a systematic investigation of the interrelationship between fuzzy preordered sets, topological spaces, and fuzzy topological spaces. © 2006 Elsevier B.V. All rights reserved.

In this paper, we introduce new definitions of L-fuzzy neighborhood systems, L-fuzzy interior operators and L-fuzzy closure operators. Three characterizations of the category L-FTOP of L-fuzzy topological spaces and their L-fuzzy continuous mappings are presented by means of the category L-FNS of L-fuzzy neighborhood spaces and their continuous mappings, the category L-FIS of L-fuzzy interior s...

In this paper, we used the supra fuzzy topology which generated from a fuzzy bitopological space [1] to introduce and study the concepts of continuity (resp. openness, closeness) of mapping, separation axioms and compactness for a fuzzy bitopological spaces. Our definition preserve much of the correspondence between concepts of fuzzy bitopological spaces and the associated fuzzy topological spa...

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 ...

Using the idea of approach space due to Robert Lowen [Approach spaces. The missing link in the topology-uniformitymetric triad], we define the notion of fuzzy approach spaces as a natural generalization of fuzzy metric spaces due to Kramosil and Michalek [Kybernetika , 11, 1975, 336–344] and prove some properties of fuzzy approach spaces. Keywords— Approach spaces, Fuzzy approach spaces, Fuzzy ...

network sensors consist of sensor nodes in which every node covers a limited area. the most common use ofthese networks is in unreachable fields.sink is a node that collects data from other nodes.one of the main challenges in these networks is the limitation of nodes battery (power supply). therefore, the use oftopology control is required to decrease power consumption and increase network acce...

In this article we study a type of directed completion for posets and T0-spaces introduced by O. Wyler [Wy81] that we call the D-completion. The category D of monotone convergence spaces is a full reflective subcategory of the category of topological spaces and continuous maps, and the D-completion gives the reflection of a topological space into D, and as such exhibits a useful universal prope...