In this paper, the concept of intuitionistic fuzzy congruence relation on a residuated lattice is introduced and its properties is studied. The relationship between intuitionistic fuzzy filters and intuitionistic fuzzy congruence relations on a residuated lattice is obtain. Then the intuitionistic fuzzy congruence relation corresponding to a given intuitionistic fuzzy filter on residuated latti...

The aim of this investigation is to reconsider two notions of fuzzy function, namely: a fuzzy function as a special fuzzy relation and a fuzzy function as a mapping between fuzzy spaces. We propose to combine both notions in such a way that a fuzzy function as a relation determines a fuzzy function as a mapping. We investigate conditions which guarantee that dependent values of the related fuzz...

We focus on the Ferrers property of fuzzy preference relations. We study the connection between the Ferrers property and fuzzy interval orders. A crisp total interval order is characterized by the Ferrers property of its strict preference relation. Also, a crisp preference structure is a total interval order if and only if its large preference relation satisfies the Ferrers property. For fuzzy ...

In this paper the notion of fuzzy topological r-entropy as an extension of the notion of topological r-entropy is studied. It is proved that fuzzy topological r-entropy is an invariant object under uniformly fuzzy equivalent relation and fuzzy topological equivalent relation.

In real world, customers commonly take relevant attributes into consideration for the selection of products and services. Further, the attribute assessment of a product or service is often presented by a linguistic data sequence. To partition these linguistic data sequences of customers’ assessment on a product or service, a proper clustering method is essential and proposed in this paper. In t...

In [13], we proposed that there are three kinds of negative relations which contradictory negative relation, opposite negative relation and medium negative relation in fuzzy information, and that defined a new fuzzy set FSCOM with contradictory negation, opposite negation and medium negation. In order to show applicability of FSCOM, this paper apply FSCOM to fuzzy decision making in an actual e...

In this paper we will introduce a certain collection of fuzzy subsets of a nonempty set X. This certain collection gives raise to a useful new fuzzy partition. This new fuzzy partition gives us a way of generating a fuzzy equivalence relation as in the ordinary case; any partition generates an equivalence relation. Mathematics Subject Classification: 03E72, 46S40, 26E50

Combining intuitionistic fuzzy sets and filter theory,we studied interval valued intuitionistic (T, S)-fuzzy filters on lattice implication algebras. some relation properties of it are obtained, the relation between intuitionistic (T, S)-fuzzy filters and intuitionistic fuzzy set are discussed.The investigation method and content of lattice implication algebras are extended. Mathematics Subject...

From the algorithm procedure presented in section 4 and the examples in this section, we can nd out it is easy to solve interval valued fuzzy relation equations by using fuzzy relation inequality system (8). The computation complexity of this algorithm is as same as that of the more commonly used algorithm 5] for fuzzy relation equations (1). So, the problem is more complicated than constant fu...

This paper provides an algebraic characterization of mathematical structures formed by cartesian products of fuzzy relations with sup-min composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom was given by G. Schmidt and T. Strohlein, and cartesian products of Boolean relation algebras were investigated by B. J onsson and A....