Journal
KNOWLEDGE-BASED SYSTEMS
Volume 22, Issue 6, Pages 449-454Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.knosys.2009.06.007
Keywords
Interval-valued fuzzy sets; Entropy; Similarity measure; Intuitionistic fuzzy sets; Measures of information
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Funding
- National Natural Science Foundation of China [60673096, 60773174, 60703117]
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This article proposes a new axiomatic definition of entropy of interval-valued fuzzy sets (IVFSs) and discusses its relation with similarity measure. First, we propose an axiomatic definition of entropy for IVFS based on distance which is consistent with the axiomatic definition of entropy of a fuzzy set introduced by De Luca, Termini and Liu. Next, some formulae are derived to calculate this kind of entropy. Furthermore we investigate the relationship between entropy and similarity measure of IVFSs and prove that similarity measure can be transformed by entropy. Finally, a numerical example is given to show that the proposed entropy measures are more reasonable and reliable for representing the degree of fuzziness of an IVFS. (C) 2009 Elsevier B.V. All rights reserved.
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