We introduce a fuzzy metric on the set of probability measures on a fuzzy metric space. The construction is an analogue, in the realm of fuzzy metric spaces, of the Prokhorov metric on the set of probability measures on compact metric spaces. © 2011 Elsevier B.V. All rights reserved.

A hesitant fuzzy set, allowing the membership of an element to be a set of several possible values, is very useful to express people’s hesitancy in daily life. In this paper, we define the distance and correlation measures for hesitant fuzzy information and then discuss their properties in detail. These measures are all defined under the assumption that the values in all hesitant fuzzy elements...

We consider some existing similarity measures for Atanassov’s intuitionistic fuzzy sets (A-IFSs, for short). We show that neither similarity measures treating an A-IF as a simple interval values fuzzy set, nor straightforward generalizations of the similarity measures well-known for the classic fuzzy sets work under reasonable circumstances. Next, expanding upon our previous works, we consider ...

1 Ronei Marcos de Moraes, Department of Statistics, Federal University of Paraíba, Cidade Universitária s/n CEP 58.051-900 João Pessoa – PB Brazil, [email protected] 2 Liliane dos Santos Machado, Department of Informatics, Federal University of Paraíba, Cidade Universitária s/n CEP 58.051-900 João Pessoa – PB Brazil, [email protected] Abstract  This paper presents a methodology of evaluation o...

The paper deals with the aggregation of classification rules by means of fuzzy integrals, in particular with the fuzzy measures employed in that aggregation. It points out that the kinds of fuzzy measures commonly encountered in this context do not take into account the diversity of classification rules. As a remedy, a new kind of fuzzy measures is proposed, called similarity-aware measures, an...

An approach is developed to MR brain images segmentation, based on pixel classification using Fuzzy Rule Based system and Fuzzy Similarity measures. The cerebral images are segmented into gray matter, white matter, and cerebrospinal fluid (CSF). Image preprocessing was first done to improve the quality of brain MR images and reducing artifacts. The feature vector was selected to be the pixel an...

Background: Science relies on experimentation to find truth. It demands that conditions remain unchanged for each repetition of an experiment. Thus, medicine relies on ‘probability theory’ based statistics and large double blind controlled randomized clinical trials. The purpose of this study is to discover measures that account for different and changing conditions of individual patients. Thes...

In this paper, we investigate the properties of some recently pro-posed fuzzy distance measures. We find out some shortcomings for these dis-tances and then the obtained results are illustrated by solving several examplesand compared with the other fuzzy distances.

This paper studies some relationships between fuzzy relations, fuzzy graphs and fuzzy measure. It is shown that a fundamental theorem of Discrete Convex Analysis is derived from the theory of fuzzy measures and the Choquet integral.

In this paper we study a large class of renormalization transformations of measures on lattices. An image of a Gibbs measure under such transformation is called a fuzzy Gibbs measure. Transformations of this type and fuzzy Gibbs measures appear naturally in many fields. Examples include the hidden Markov processes (HMP), memoryless channels in information theory, continuous block factors of sym...