A similarity measure of intuitionistic fuzzy sets based on the Sugeno integral with its application to pattern recognition

  • Authors:

  • Chao-Ming Hwang;Miin-Shen Yang;Wen-Liang Hung;Ming-Gay Lee

  • Affiliations:

  • Department of Applied Mathematics, Chinese Culture University, Yangminshan, Taipei, Taiwan;Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taiwan;Department of Applied Mathematics, National Hsinchu University of Education, Hsinchu, Taiwan;Department of Applied Mathematics, Chinese Culture University, Yangminshan, Taipei, Taiwan

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

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Abstract

Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although several similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, no one has considered the use of the Sugeno integral to define them. Since the Sugeno integral provides an expected-value-like operation, it can be a useful tool in defining the expected total similarity degree between two intuitionistic fuzzy sets. In this paper, we propose a new similarity measure formula for intuitionistic fuzzy sets induced by the Sugeno integral. Some examples are illustrated to compare the proposed method with several existing methods. Numerical results show that the proposed similarity measure is more reasonable than those existing methods. On the other hand, measuring the similarity between intuitionistic fuzzy sets is also important in pattern recognition. Finally, the proposed similarity measure uses a robust clustering method to recognize the patterns of intuitionistic fuzzy sets.