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.

In this paper, we research the relationship between entropy and similarity of interval valued intuitionistic fuzzy sets in detail and prove eight theorems that entropy and similarity of interval valued intuitionistic fuzzy sets can be transformed to each other based on their axiomatic definitions. Finally, we propose some formulaes to calculate entropy and similarity of interval valued intuitio...

Interval type-2 fuzzy sets, each of which is characterized by the footprint of uncertainty, are a very useful means to depict the linguistic information in the process of decision making. In this article, we investigate the group decision making problems in which all the linguistic information provided by the decision makers is expressed as interval type-2 fuzzy decision matrices where each of ...

Comparison and data analysis to the similarity measures and entropy for fuzzy sets are studied. The distance proportional value between the fuzzy set and the corresponding crisp set is represented as fuzzy entropy. We also verified that the sum of the similarity measure and the entropy between fuzzy set and the corresponding crisp set constitutes the total information. Finally, we derive a simi...

The paper deals with the well-known notion of similarity measures between fuzzy sets and proposes a variety of similarity measures for fuzzy sets. Moreover, the paper proves that the proposed measures satisfy the properties of the axiomatic definition for similarity measures and introduces several theorems. Several illustrative and practical examples from the areas of pattern recognition, decis...

Szmidt and Kacprzyk (Lecture Notes in Artificial Intelligence 3070:388– 393, 2004a) introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develo...

one concern about using transgenic plants is the genetic variation that occurred from theirs tissue culture and regeneration. molecular markers are an important element for efficient and effective determination of genetic variation. the present work was carried out to assess the genetic uniformity of transgenic cottons (bt and chitinase lines), using rapd, issr molecular markers and sds-page an...

AX B In the paper, a class of fuzzy matrix equations    B where A is an m × n crisp matrix and is an m × p arbitrary LR fuzzy numbers matrix, is investigated. We convert the fuzzy matrix equation into two crisp matrix equations. Then the fuzzy approximate solution of the fuzzy matrix equation is obtained by solving two crisp matrix equations. The existence condition of the strong LR fuzzy s...

This paper addresses the issue of similarity measures of intuitionistic fuzzy sets (IFSs). Many measures of similarity between IFSs proposed before did not consider the abstention group influence, which may lead to counter-intuitive results in some cases. In this paper, first, we analyze the limitations of the existing similarity measures. Then, a new similarity measure of intuitionistic fuzzy ...