The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...

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...

In the present communication, the existing measures of fuzzy entropy are reviewed. A generalized parametric exponential fuzzy entropy is defined.Our study of the four essential and some other properties of the proposed measure, clearly establishes the validity of the measure as an entropy. Keywords—fuzzy sets, fuzzy entropy, exponential entropy, exponential fuzzy entropy.

Study about fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Unlike fuzzy set, IFSs contains uncertainty named hesistancy, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of ununified entropy definition. By considering different fuzzy entropy definitions, fuzzy entropy is designed and...

In this paper, we propose a new entropy measure with geometrical interpretation of intuitionistic fuzzy sets. Compared with the entropy measure provided by Szmidt and Kacprzyk, the new entropy formula in this paper can measure both fuzziness and intuitionism for intuitionistic fuzzy sets. According to the relationship between entropy and similarity measure, we construct a new similarity measure...

In this paper we study the relations among similarity measure, subsethood measure and fuzzy entropy and present several propositions that similarity measure, subsethood measure and fuzzy entropy can be transformed by each other based on their axiomatic definitions. Some new formulae to calculate similarity measure, subsethood measure and fuzzy entropy are proposed.

Several types of entropy of fuzzy variables or fuzzy sets have been given in the literature in order to measure the degree of uncertainty. In order to measure the degree of uncertainty of fuzzy vectors, a new definition of entropy of fuzzy vectors is proposed. Some properties are then investigated and the relations between the entropy of fuzzy variables and fuzzy vectors are discussed.

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...

As a measure of information shared between two fuzzy pattern vectors, the fuzzy information proximity measure (FIPM) plays an important part in fuzzy pattern recognition, fuzzy clustering analysis and fuzzy approximate reasoning. In this paper, two novel FIPMs are set up. Firstly, an axiom theory about the FIPM is given, and different expressions of the FIPM are discussed. A new FIPM is then pr...

Measuring uncertainty for fuzzy sets has been carried out by calculating fuzzy entropy. Fuzzy entropy of fuzzy set is derived with the help of distance measure. The distance proportional value between the fuzzy set and the corresponding crisp set is designed as the fuzzy entropy. The usefulness is verified by proving the proposed entropy. Generally, fuzzy entropy contains the complementary char...