In this paper, we introduce the notions of L-fuzzy quasi-uniformities and Lfuzzy interior operators in complete residuated lattices. We investigate the L-fuzzy quasiuniformities induced by L-fuzzy interior operators. We study the relationships between Lfuzzy interior operators and L-fuzzy quasi-uniformities. We give their examples. AMS Subject Classification: 03E72, 06A15, 06F07, 54F05

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

Given a Brouwerian complete lattice (L,≤) and two referential sets K and E, and using a fuzzy relation R ∈ L which is reflexive and symmetric, certain fuzzy relations Ĥ ∈ L are characterized as solutions of X C R = X. These solutions Ĥ can be determinated by means of the L-fuzzy concepts associated with the K-labeled L-fuzzy context (L,K,E,E,R).

the aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. all values aretaken in a fixed frame $l$. a definition of (strongly) completelydistributive $l$-ordered sets is introduced. the main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $l$-ordereds...

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

in this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $l$-setting. this construction is illustrated by an example. we also prove that for an $l$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $l$-subset provided the given $l$-subset possesses sup-property.

In 1997, Fang proposed the concept of boundedness of $L$-fuzzy setsin $L$-topological vector spaces. Since then, this concept has beenwidely accepted and adopted in the literature. In this paper,several characterizations of bounded $L$-fuzzy sets in$L$-topological vector spaces are obtained and some properties ofbounded $L$-fuzzy sets are investigated.

Routing information plays a vital role in Mobile Ad-hoc Network (MANET). In MANET, each node maintains routing information that assists the routing process. Routing nodes and their routing attributes are essential in determining the performance of MANET. Thus, it is necessary to obtain knowledge on routing nodes and their attributes. Keeping this in view, we have proposed a model that uses a fu...