Journal
INFORMATION SCIENCES
Volume 178, Issue 5, Pages 1334-1342Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2007.10.007
Keywords
interval-valued fuzzy set; normalized distance; similarity measure; inclusion measure; entropy
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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. (C) 2007 Elsevier Inc. All rights reserved.
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