This paper is devoted to a class of fuzzy or derings which play a fundamental role in de cision analysis and fuzzy control strongly linear fuzzy weak orderings First we see that any relation of that kind can be decom posed into a crisp linear ordering and a fuzzy equivalence relation As a consequence a general representation theorem follows Fi nally a method for constructing strongly lin ear fu...

in this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. thena relation between totally fuzzy bounded sets and n-compactness is discussed.finally, a geometric characterization for fuzzy totally bounded sets in i- topologicalvector spaces is derived.

New types of systems of fuzzy relation inequalities and equations, called weakly linear, have been recently introduced in [J. Ignjatović, M. Ćirić, S. Bogdanović, On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081–3113.]. The mentioned paper dealt with homogeneous weakly linear systems, composed of fuzzy relati...

we de ne approximate xed point in fuzzy norm spaces and prove the existence theorems, we also consider approximate pair constructive map- ping and show its relation with approximate fuzzy xed point.

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...

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...