This article introduces the fuzzy relation. This is the expansion of usual relation, and the value is given at the fuzzy value. At rst, the deenition of the fuzzy relation characterized by membership function is described. Next, the deenitions of the zero relation and universe relation and basic operations of these relations are shown. In this paper C 1 , C 2 are non empty sets. Let us consider...

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.

Similarity and inclusion measures between type-2 fuzzy sets have a wide range of applications. New similarity and inclusion measures between type-2 fuzzy sets are respectively defined in this paper. The properties of the measures are discussed. Some examples are used to compare the proposed measures with the existing results. Numerical results show that the proposed measures are more reasonable...

First of all, in this paper we propose a family of fuzzy implication operators, which the generalised Luckasiewicz ́s one, and to analyse the impacts of Smets and Magrez properties on these operators. The result of this approach will be a characterisation of a proposed family of inclusion grade operators (in Bandler and Kohout ́s manner) that satisfies the axioms of Divyendu and Dogherty. Second,...

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.