Journal
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
Volume 31, Issue 3, Pages 303-329Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/03081070290018047
Keywords
fuzzy measures; entropy; Dempster-Shafer; cardinality index
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We briefly introduce the fuzzy measure and then discuss its use in representing information about uncertain variables. A relationship between the fuzzy measure and the Dempster-Shafer belief structure is discussed and a method for generating the family of fuzzy measures associated with a belief structure is described. We discuss the use of the Shapley index as a means for introducing an extension of the concept of entropy to fuzzy measures called the Shapley entropy. It is shown that all fuzzy measures generated from a given Dempster-Shafer belief structure have the same value for their Shapley entropy. We introduce the cardinality index of a fuzzy measure and use it to define the attitudinal character of a fuzzy measure. A semantics for this attitudinal character in the framework of using fuzzy measures to represent information about uncertain variables is suggested.
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