Journal
INFORMATION SCIENCES
Volume 177, Issue 23, Pages 5378-5393Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2007.07.012
Keywords
uncertainty measure; interval type-2 fuzzy set; centroid; cardinality; fuzziness; entropy; variance; skewness
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Fuzziness (entropy) is a commonly used measure of uncertainty for type-1 fuzzy sets. For interval type-2 fuzzy sets (IT2 FSs), centroid, cardinality, fuzziness, variance and skewness are all measures of uncertainties. The centroid of an IT2 FS has been defined by Karnik and Mendel. In this paper, the other four concepts are defined. All definitions use a Representation Theorem for IT2 FSs. Formulas for computing the cardinality, fuzziness, variance and skewness of an IT2 FS are derived. These definitions should be useful in IT2 fuzzy logic systems design using the principles of uncertainty, and in measuring the similarity between two IT2 FSs. (C) 2007 Elsevier Inc. All rights reserved.
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