in this paper, some results of the chebyshev type integral inequality for the pseudo-integral are proven. the obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. finally, we applied our results  to the case of comonotone functions.

We discuss the use of the fuzzy measure for representing information about uncertain variables. We describe the relationship between the fuzzy measure and the Dempster-Shafer belief structure. A method for generating the fuzzy measures associated with a D-S belief structure is described. We discuss the use of the Shapley index as a means for providing an entropy for fuzzy measures. We introduce...

In this paper, we present a revised similarity measure based onChen-and-Chen's similarity measure for fuzzy risk analysis. The revisedsimilarity measure uses the corrected formulae to calculate the centre ofgravity points, therefore it is more  effective than the Chen-and-Chen'smethod. The revised similarity measure can overcome the drawbacks of theexisting methods. We have also proposed a new ...

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 ...