Similarity of intuitionistic fuzzy sets (IFSs) is an important measure to indicate the similarity degree between IFSs. Recently, Ye (2011) proposed a similarity measure between IFSs based on the cosine concept. Although this cosine similarity measure has good concept and merit, the measure is not satisfied the definition of a similarity between IFSs and not presented well for analyzing IFS data...

Entropy of an intuitionistic fuzzy set (IFS) is used to indicate the degree of fuzziness for IFSs. In this paper we deal with entropies of IFSs. We first review some existing entropies of IFSs and then propose a new entropy measure based on exponential operations for an IFS. Finally, comparisons are made with some existing entropies to show the effectiveness of our proposed one.

In this paper we develop a measure for calculating the association coe±cient between Atanassov's intuitionistic fuzzy sets (A-IFSs), and show its desirable axiomatic properties. Then we present an algorithm for clustering A-IFSs. The algorithm ̄rst utilizes the association coe±cient of A-IFSs to construct an association matrix, and then calculates the -cutting matrix of the association matrix no...

Non-linear Iterated Function Systems (IFSs) are very powerful mathematical objects related to fractal theory, that can be used in order to generate (or model) very irregular shapes. We investigate in this paper how Genetic Programming techniques can be efficiently exploited in order to generate randomly or interactively artistic “fractal” 2D shapes. Two applications are presented for different ...

An axiomatic definition of divergence measure for intuitionistic fuzzy sets (IFSs, for short) is presented in this work, as a particular case of dissimilarity between IFSs. As the concept of divergence measure is more restrictive, it has particular properties which are studied. Furthermore, the relationships among IF-divergences, dissimilarities and distances are studied. We also provide some m...

In this article we exploit the concept of probability for defining the fuzzy entropy of intuitionistic fuzzy sets ~IFSs!. We then propose two families of entropy measures for IFSs and also construct the axiom definition and properties. Two definitions of entropy for IFSs proposed by Burillo and Bustince in 1996 and Szmidt and Kacprzyk in 2001 are used. The first one allows us to measure the deg...

The aim of this paper is to point out and correct some errors of two theorems for IFSs in Atanassov (Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 2000) and bring forward a new theorem for IFSs. In the end, some elementary, but non-standard equalities between IFSs were formulated.

In this paper, we revisit the notion of inclusion for intuitionistic fuzzy sets (IFSs). Applying the extended modal logic operators Dα over IFSs, we construct a new class of two–valued inclusion indicators; we compare it to the original proposal from [1]; and finally we exploit it to define an intuitively meaningful notion of graded inclusion indicators over IFSs, parallelling and clarifying ea...

Study of fuzzy entropy on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Built in uncertainty in IFSs, it is named as hesitance. It is contained in fuzzy membership function in itself by definition. Hence, designing fuzzy entropy is not easy because there is no general entropy definition about IFSs. By considering existing fuzzy entropy definitions, fuzzy entropy on IFSs is desig...