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Entropy and similarity measure for Atannasov’s interval-valued intuitionistic fuzzy sets and their application

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Abstract

In this study, we first point out the problem of the similarity measure in the literature and then define a new entropy and similarity measure. In order to explore the inter-dependent or interactive characteristics between elements in a set, several Shapley-weighted similarity measures of Atannasov’s interval-valued intuitionistic fuzzy sets are defined by using the well-known Shapley function, which can be seen as an extension of the associated weighted similarity measures. Moreover, if the information about the weights is completely unknown or partially known, models for the optimal fuzzy measures are established, by which the optimal weight vector can be obtained. Finally, an approach to pattern recognition and multi-criteria decision making is developed, and the associated numerical examples are provided to verify the developed methods and demonstrate their practicality and feasibility.

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Authors and Affiliations

  1. Business School, Central South University, Changsha, 410083, China

    Fanyong Meng & Xiaohong Chen

  2. School of Management, Qingdao Technological University, Qingdao, 266520, China

    Fanyong Meng

Authors
  1. Fanyong Meng
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  2. Xiaohong Chen
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Correspondence to Fanyong Meng.

Additional information

This work was supported by the State Key Program of National Natural Science of China (No. 71431006), the Funds for Creative Research Groups of China (No. 71221061), the Projects of Major International Cooperation NSFC (No. 71210003), the National Natural Science Foundation of China (Nos. 71201089, 71271217, 71201110 and 71271029), the National Science Foundation for Post-doctoral Scientists of China (2014M560655), the Program for New Century Excellent Talents in University of China (No. NCET-12-0541), and the Qingdao Technology Plan Foundation (KJZD- 13-31-JCH).

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Meng, F., Chen, X. Entropy and similarity measure for Atannasov’s interval-valued intuitionistic fuzzy sets and their application. Fuzzy Optim Decis Making 15, 75–101 (2016). https://doi.org/10.1007/s10700-015-9215-7

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  • DOI: https://doi.org/10.1007/s10700-015-9215-7

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