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Mathematical Problems in Engineering
Volume 2015, Article ID 563745, 13 pages
Research Article

Entropy Measures for Interval-Valued Intuitionistic Fuzzy Sets and Their Application in Group Decision-Making

1College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
2Institute of Operations Research, Qufu Normal University, Shandong, Rizhao 276826, China

Received 8 July 2014; Revised 3 December 2014; Accepted 16 December 2014

Academic Editor: Ricardo Femat

Copyright © 2015 Cuiping Wei and Yuzhong Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Entropy measure is an important topic in the fuzzy set theory and has been investigated by many researchers from different points of view. In this paper, two new entropy measures based on the cosine function are proposed for intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets. According to the features of the cosine function, the general forms of these two kinds of entropy measures are presented. Compared with the existing ones, the proposed entropy measures can overcome some shortcomings and be used to measure both fuzziness and intuitionism of these two fuzzy sets; as a result, the uncertain information of which can be described more sufficiently. These entropy measures have been applied to assess the experts’ weights and to solve multicriteria fuzzy group decision-making problems.