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Vagueness in scientific studies poses a challenge. Intuitionistic Fuzzy Set (IFS) theory has emerged as a powerful and flexible tool to counter such challenge. So, there is a need to develop such measures which can not only measure the vagueness but also quantify the differences in underlying IFSs. The aim of this communication is to introduce one such divergence measure called Intuitionistic Fuzzy Jensen-Tsalli Divergence measure in the settings of IFS theory. The presence of parameters makes the proposed divergence measure flexible and competent for applications. Besides discussing some of its major properties, the findings are applied in pattern recognition problem and in medical diagnosis of some diseases with same set of symptoms. The performance of the proposed measure is genuinely compared with some other existing measures in literature through numerical examples based on medical diagnosis and pattern recognition. [ABSTRACT FROM AUTHOR]

Many researchers have put forward lots of entropy and distance measures for intuitionistic fuzzy sets (IFSs). This paper firstly reviews some basic concepts for IFSs and several widely used distance measures between IFSs. And then a series of distance measures are presented on the basis of above widely used distance measures. Based on such distance measures and intuitionistic index, a set of entropies for IFSs are proposed and proved to meet the axiomatic requirements given by Szmidt and Kacprzyk in 2001. Besides, two numerical examples are demonstrated to verify the efficiency of the proposed entropies for IFSs. Finally, the paper concludes with suggestions for future research. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy (IF) rough sets are the generalization of traditional rough sets obtained by combining the IF set theory and the rough set theory. The existing research on IF rough sets mainly concentrates on the establishment of lower and upper approximation operators using constructive and axiomatic approaches. Less effort has been put on the attribute reduction of databases based on IF rough sets. This paper systematically studies attribute reduction based on IF rough sets. Firstly, attribute reduction with traditional rough sets and some concepts of IF rough sets are reviewed. Then, we introduce some concepts and theorems of attribute reduction with IF rough sets, and completely investigate the structure of attribute reduction. Employing the discernibility matrix approach, an algorithm to find all attribute reductions is also presented. Finally, an example is proposed to illustrate our idea and method. Altogether, these findings lay a solid theoretical foundation for attribute reduction based on IF rough sets. [ABSTRACT FROM AUTHOR]

In a recent paper [International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems 8:611–618], Yager & Kreinovich characterize a certain proportional division rule in terms of the three axioms (1) symmetry, (2) participant mergability, and (3) continuity. This technical note tightens their characterization: The proportional division rule is already fully characterized by the first two axioms (1) symmetry and (2) participant mergability. [ABSTRACT FROM AUTHOR]