This paper studies by means of reciprocal fuzzy binary relations the aggregation of preferences when individuals show their preferences gradually. We have characterized neutral aggregation rules through functions from powers of the unit interval in the unit interval. Furthermore, we have determined the neutral aggregation rules that are decomposable and anonymous. In this class of rules, the co...

Describing and modeling a complex system is very hard and time consuming, so, we propose to use a linguistic approach introduced by Zadeh. By taking a linguistic approach we can use linguistic variables and approximate rules to characterize approximately phenomenons which are too complex or too ill-defined to be done in numerical terms. Starting from the results obtained in our previous works, ...

In the last few years, the coevolutionary paradigm has shown an increasing interest thanks to its high ability to manage huge search spaces. Particularly, the cooperative interaction scheme is recommendable when the problem solution may be decomposable in subcomponents and there are strong interdependencies among them. The paper introduces a novel application of these algorithms to the learning...

The aim of this paper is to introduce two new types of fuzzy integrals, namely, ⊗-fuzzy integral and →-fuzzy integral, where ⊗ and → are the multiplication and residuum of a complete residuated lattice, respectively. The first integral is based on a fuzzy measure of L-fuzzy sets and the second one on a complementary fuzzy measure of L-fuzzy sets, where L is a complete residuated lattice. Some o...

This paper proposes a new fuzzy similarity measure to calculate the degree of similarity of generalized fuzzy numbers (GFN’s).The fuzzy similarity measure is developed by integrating the concept of centre of gravity (COG) points and fuzzy difference of distance of points of fuzzy numbers. A fuzzy description for difference of distances between fuzzy numbers in its turn exploits appropriate simi...

As Similarity measure for fuzzy sets is one of the important research topics of fuzzy set theory, there are several methods to measure similarity between two fuzzy sets (FS), Intuitionistic fuzzy sets (IFS) and Intuitionistic fuzzy multi sets (IFMS). In this paper, the Normalized Hamming Similarity measure of Intuitionistic Fuzzy Multi sets (IFMS) is introduced. This new measure for IFMS is bas...

In this paper, we survey the relationship between the similarity measure and dissimilarity measure for fuzzy sets. First, we design a similarity measure using a distance measure for fuzzy sets and prove its usefulness. From this result, we assert that the similarity between two complementary fuzzy sets satisfies the fuzzy entropy definition. We also show that the summation of the similarity and...

the main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. in this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

Uncertainty and fuzziness are involved in most of the real world problems. In present communication we have studied various advancements in fuzzy information theory and proposed a new measure of divergence between two fuzzy sets. Further, a measure of fuzzy directed divergence was developed based on the proposed divergence measure. Some properties of this fuzzy directed divergence measure were ...

In the present paper, based on the concept of fuzzy entropy, an exponential intuitionistic fuzzy entropy measure is proposed in the setting of Atanassov’s intuitionistic fuzzy set theory. This measure is a generalized version of exponential fuzzy entropy proposed by Pal and Pal. A connection between exponential fuzzy entropy and exponential intuitionistic fuzzy entropy is also established. Some...