Journal
FUZZY OPTIMIZATION AND DECISION MAKING
Volume 15, Issue 1, Pages 75-101Publisher
SPRINGER
DOI: 10.1007/s10700-015-9215-7
Keywords
Pattern recognition; Multi-criteria decision making; Atannasov's interval-valued intuitionistic fuzzy set; Entropy; Similarity measure
Funding
- State Key Program of National Natural Science of China [71431006]
- Funds for Creative Research Groups of China [71221061]
- Projects of Major International Cooperation NSFC [71210003]
- National Natural Science Foundation of China [71201089, 71271217, 71201110, 71271029]
- National Science Foundation for Post-doctoral Scientists of China [2014M560655]
- Program for New Century Excellent Talents in University of China [NCET-12-0541]
- Qingdao Technology Plan Foundation [KJZD-13-31-JCH]
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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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