Monotonicity is a major property of entropy measures. In this paper, we focus on measures for intuitionistic fuzzy sets and interval-valued sets. We consider their polar representation which provides an easy interpretation monotonicity several introduced in the literature. Moreover, enables us to propose two new kinds such entropies, that offer more understandable way explain differences entrop...

The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results re...

The concept of duality, stating that something can or must coexist with its opposite, makes fuzzy logic seem natural, even inevitable. In fact, there are infinite degrees of uncertainty between the certainty of being and not being. This imperfection inherent to information represented in natural language has been treated mathematically using the theory of fuzzy sets. Thus, fuzzy logic introduce...

Concepts of graph theory have applications in many areas of computer science including data mining, image segmentation, clustering, image capturing, networks, etc . An interval-valued fuzzy set is a generalization of the notion of a fuzzy set. Interval-valued fuzzy models give more precision, flexibility and compatibility to the system as compared to the fuzzy models. In this paper, we introduc...

Neutrosophic sets was defined by Smarandache, which is a generalized of fuzzy sets and intuitionistic fuzzy sets. A single valued neutrosophic set is an instance of neutrosophic sets defined by Wang et al. (2005). In this study, we introduce similarity measure on two single valued neutrosophic sets. We develop an entropy of single valued neutrosophic sets. Finally, we give an example which demo...

With the demand for knowledge-handling systems capable of dealing with and distinguishing between various facets of imprecision ever increasing, a clear and formal characterization of the mathematical models implementing such services is quintessential. In this paper, this task is undertaken simultaneously for the definition of implication within two settings: first, within intuitionistic fuzzy...