The study of linearly compensated hybrid connectives H = λC +(1−λ)C̄, where C is a t-norm and C̄ represents the dual connective of C, to define aggregation operators for fuzzy classifications is a key point not only in fuzzy sets theory but also in learning processes. Although these operators are not associative, the fact that they can be decomposed into associative functions easily gives rise to...

In this paper, generalized fuzzy 2-norms are defined on a set of objects endowed with a structure of linear space. The relationships between these fuzzy 2-norms and fuzzy metrics and between these fuzzy 2-norms and the topological structures induced on a linear space are analyzed. Some open problems in this framework are mentioned. Mathematics Subject Classification: 46A19, 54A40

In this paper, first we give the definitions of various indicators of fuzzy relations and their basic properties. Then we investigate the relationships between these indicators, particularly between those of T-transitivity, negative S-transitivity, T–S-semitransitivity and T–S-Ferrers property. The investigation is divided into three parts: results in the general case, results under a condition...

This paper deals with multi-criteria decision making (MCDM) problems with multiple priorities, in which priority weights associated with the lower priority criteria are related to the satisfactions of the higher priority criteria. To do so, we first propose a prioritized weighted aggregation operator based on ordered weighted averaging (OWA) operator and triangular norms (t-norms). In order to ...

INTRODUCTION There have been a number of generalizations of metric spaces. One such generalization is Menger space introduced in 1942 by Menger[9] who used distribution functions instead of nonnegative real numbers as values of the metric. This space was expanded rapidly with the pioneering works of Schweizer and Sklar [11, 12]. Modifying the idea of Kramosil and Michalek [7], George and Veeram...

Fuzzy associative memories (FAMs) and, in particular, the class of implicative fuzzy associative memories (IFAMs) can be used to implement fuzzy rule-based systems. In this way, a variety of applications can be dealt with. Since there are infinitely many IFAM models, we are confronted with the problem of selecting the best IFAM model for a given application. In this paper, we restrict ourselves...

Fuzzy relational compositions have been extensively studied by many authors. Especially, we would like to highlight initial studies of the fuzzy relational compositions motivated by their applications to medical diagnosis by Willis Bandler and Ladislav Kohout. We revisit these types of compositions and introduce new definitions that directly employ generalized quantifiers. The motivation for th...

There are presented the basic operations on real intervals: pseudo-addition and pseudo multiplication which induce the semiring structure. Application of special pseudo-operations on the unit interval: t-norms and t-conorms, in the theory of fuzzy sets and fuzzy logics are given. Pseudo-convolution as a generalization of the classical convolution is given, with many important special cases. Fur...

Weighted aggregation of fuzzy preference relations on the set of alternatives by several criteria in decision-making problems is considered. Pairwise comparisons with respect to importance of the criteria are given in fuzzy preference relation as well. The aggregation procedure uses the composition between each two relations of the alternatives. The membership function of the newly constructed ...

The composition of fuzzy relations for their uniting in multicriteria decision making problems is considered. Some criteria evaluate a set of alternatives by fuzzy preference relations. The comparison between the criteria importance is given as a fuzzy preference relation too. Aggregation of these relations is made with the help of a composition of the couple of the relations by the criteria an...