Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship |
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Authors: | Wenyi Zeng Ping Guo |
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Affiliation: | College of Information Science and Technology, Beijing Normal University, Beijing 100875, PR China |
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Abstract: | In this paper, we introduce an axiomatic definition of an interval-valued fuzzy sets’ inclusion measure which is different from Bustince’s H. Bustince, Indicator of inclusion grade for interval-valued fuzzy sets, Applications to approximate reasoning based on interval-valued fuzzy sets, International Journal of Approximate Reasoning, 23 (2000) 137-209]. The relationship among the normalized distance, the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets is investigated in detail. Furthermore, six theorems are proposed showing how the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets can be deduced by the interval-valued fuzzy sets’ normalized distance based on their axiomatic definitions. Some formulas have also been put forward to calculate the similarity measure, the inclusion measure, and the entropy of interval-valued fuzzy sets. |
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Keywords: | Interval-valued fuzzy set Normalized distance Similarity measure Inclusion measure Entropy |
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