In this paper, the concept of extended intersection and restricted union of intuitionistic fuzzy soft sets are introduced. Some operations on intuitionistic fuzzy soft sets are investigated, and we prove that De Morgan’s laws hold in intuitionistic fuzzy soft sets theory. Based on these properties, we discuss the algebraic structures of intuitionistic fuzzy soft sets, which is lattice structure...

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).

In a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0,i] X) is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule "lira" which to any prefilter on X assigns, a function lira E [0,i] X. We give necessary and sufficient conditions for the function lim in order that it can be derived f...

Galois connection in crisp binary relations has proved to be useful for several applications in computer science. Unfortunately, data is not always presented as a crisp binary relation but may be composed of fuzzy values, thus forming a fuzzy binary relation. This paper aims at defining the notion of fuzzy galois connection corresponding to a fuzzy binary relation in two steps: firstly by defin...

In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

Defining a relation between granules and computing ever-changing granules are two important issues in granular computing. In view of this, this work proposes a partial order relation and lattice computing, respectively, for dealing with the aforementioned issues. A fuzzy lattice granular computing classification algorithm, or FL-GrCCA for short, is proposed here in the framework of fuzzy lattic...

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 study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...

In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC)L or (TC)R axioms and the L-relations induced by two L-fuzzy topologi...