This paper provides an algebraic formalization of mathematical structures formed by fuzzy relations with sup-min composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom has been given by G. Schmidt and T. Strohlein. Unlike Boolean relation algebras, fuzzy relation algebras are not Boolean but equipped with semi-scalar multipl...

Rough fuzzy sets are an effective mathematical analysis tool to deal with vagueness and uncertainty in the area of machine learning and decision analysis. Fuzzy information systems and fuzzy objective information systems exit in many applications and knowledge reduction in them can’t be implemented by reduction methods in Pawlak information systems. Therefore, this paper provides a model for ru...

Fuzzy sets theory might provide the flexibility needed to represent the uncertainty resulting from the lack of knowledge [1-3]. The fuzzy preference relation is a kind of representation of the information about provided by the decision maker [4-6]. It is an important research topic how to choose an optimal alternative or rank alternatives from a finite set of alternatives according to the fuzzy...

The notion of extensionality of a fuzzy relation w.r.t. a fuzzy equivalence was first introduced by Höhle and Blanchard. Bělohlávek introduced a similar definition of compatibility of a fuzzy relation w.r.t. a fuzzy equality. In [14] we generalized this notion to left compatibility, right compatibility and compatibility of arbitrary fuzzy relations and we characterized them in terms of left and...

In this paper we are using intuitionistic fuzzy approach to minimize search domain in an accidental case where the data collected for investigation is intuitionistic fuzzy in nature. To handle these types of imprecise information we use intuitionistic fuzzy tolerance relation and translate intuitionistic fuzzy query to reach to the conclusion. Here we present an example of vehicle hit and run c...

In this article, we propose a fuzzy class relation assigning to each pair of finite fuzzy sets a degree to which they are equipollent, which indicates that they have the same number of elements. The concepts of fuzzy sets and fuzzy classes in the class of all countable sets are introduced, and several standard relations and constructions, such as the fuzzy power set and exponentiation, are defi...

where [f̂(x,K)]α e [X0] α are the α−levels of the fuzzy subsets f̂(x,K) and X̃0, respectively. As in [1] we saw that for each t > 0, the attainable set obtained under the Hüllermeier’s interpretation for (2), or rather, through a family of differential inclusions of the type gives in (3) coincides with the solution obtained applying the principle extension of Zadeh in deterministic solution We wil...

We study the Cauchy problem for differential equations, considering its parameters and/or initial conditions given by fuzzy sets. These fuzzy differential equations are approached in two different ways: (a) by using a family of differential inclusions; and (b) the Zadeh extension principle for the solution of the model. We conclude that the solutions of the Cauchy problem obtained by both are t...

Paraconsistent intuitionistic fuzzy set is an extension of intuitionistic fuzzy set or interval-valued fuzzy set. It relaxes the requirement that t + f ≤ 1, where t is grade of truth-membership and f is grade of false-membership. In paraconsistent intuitionistic fuzzy set, t, f ∈ [0, 1], 0 ≤ t + f ≤ 2. In this paper, we present a generalization of the relational model of data based on paraconsi...

This paper restates the results on fuzzy relation equations with sup-inf composition from the viewpoint of decomposition, presents a way to describe the solution set of fuzzy relation equations, and shows a necessary and sufficient condition, which partly answers the open problem for existence of minimal solutions over complete Brouwerian lattices. Keywords— Complete Brouwerian lattice, fuzzy r...