In 1965, Zadeh [30] introduced a concept of a fuzzy set as the generalization of a crisp set. Also, in 1971, he introduced a fuzzy relation naturally, as a generalization of a crisp relation in [31]. Nel [27] introduced the notion of a topological universe which implies concrete quasitopos [1]. Every topological universe satisfies all the properties of a topos except one condition on the subobj...

The notion of fuzzy function based on many-valued equivalence relations (many-valued similarity relations (equalities) [17, 18, 19], fuzzy equivalence relations [4, 6, 7, 21, 22, 26], similarity relations [1, 2, 3, 15, 28], indistinguishability operators [27], etc.) has been introduced by several authors, and applied to category theory [5], approximate reasoning and fuzzy control theory [8, 10,...

Aggregation of fuzzy relations on alternatives with the help of aggregation operators is considered in two cases: – the weighted coefficients of the criteria are not present in the mathematical formula of the aggregation operators; – a fuzzy preference relation between the criteria importance is given. The main result consists in proving the properties of the aggregated relation in dependence w...

In (Fuzzy Sets and Systems 97 (1998) 33), we presented a fuzzy multipurpose decision making model integrating di4erent preference representations based on additive reciprocal fuzzy preference relations. The main aim of this paper is to complete the decision model studying conditions under which reciprocity property is maintained when aggregating preference relations using an OWA operator guided...

$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...

Spatial relations have key point importance in image analysis and computer vision. Numerous technics have been developed to study these relations especially directional relations. Modern digital computers give rise to quantitative methods and among them fuzzy methods have core importance due to handling imprecise knowledge information and vagueness. In most fuzzy methods external directional re...

Concept of combined extraction of topological and directional relations information developed by J. Malki et al. [1] by employing the Allen’s temporal relations in 1D spatial domain was improved by Matsakis and Nikitenko [2]. This latter algorithm has high computational complexity due to its limitations of object approximation and segment fuzzification. In this paper, fuzzy Allen relations are ...

The aim of this paper is the study of a covering of a max-mingeneral fuzzy automaton by another, admissible relations, admissiblepartitions of a max-min general fuzzy automaton,$tilde{delta}$-orthogonality of admissible partitions, irreduciblemax-min general fuzzy automata. Then we obtain the relationshipsbetween them.  

In this paper, the notion of generalized regular fuzzy irresolute, generalized regular fuzzy irresolute open  and generalized regular fuzzy irresolute closed maps in fuzzy  topological spaces are introduced and studied. Moreover, some separation axioms and $r$-GRF-separated sets are established. Also, the relations between generalized regular fuzzy continuous maps and generalized regular fuzzy ...

This paper introduces a new approach for decision support. It is characterized by a collaborative decision making process relying on the implicit sharing of preferences and experience between di erent individuals facing similar decision problems. A recommendation principle is described, based on fuzzy ltering methods de ned from individual fuzzy preference relations and fuzzy similarity relatio...