On the cardinality index and attitudinal character of fuzzy measures

Ronald R. Yager

63 citations0/0 files storedInternational Journal of General Systems

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Multi-Criteria Decision Making Advanced Algebra and Logic Fuzzy and Soft Set Theory

Abstract

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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References

1988On ordered weighted averaging aggregation operators in multicriteria decisionmaking 1988A value for n -person games 2000On the entropy of fuzzy measures 1999A class of fuzzy measures generated from a Dempster-Shafer belief structure

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