The relationship between similarity measure and entropy of intuitionistic fuzzy sets

  • Authors:

  • Jinquan Li;Guannan Deng;Hongxing Li;Wenyi Zeng

  • Affiliations:

  • School of Applied Mathematics, Research Center of Fuzzy Systems, Beijing Normal University, Zhuhai, Guangdong 519087, PR China;School of Sciences, Northeast Dianli University, Jilin, 132012, PR China;School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, PR China;College of Information Science and Technology, Beijing Normal University, Beijing 100875, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2012

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Abstract

In this paper, we introduce an axiomatic definition of the similarity measure of intuitionistic fuzzy sets (IFS) that differs from the definition of Li [15]. The relationship between the similarity measure and the entropy of IFS is investigated in detail. Six theorems on how the similarity measure could be transformed into the entropy for IFS and vice versa are proposed based on their axiomatic definitions. Some formulas have been proposed to calculate the similarity measure and the entropy of IFS. Finally, sufficient conditions to transform the similarity measures to the entropy for IFS and vice versa are given.