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\(k\)-order additive discrete fuzzy measures and their representation. (English) Zbl 0927.28014

Summary: In order to face with the complexity of discrete fuzzy measures, we propose the concept of \(k\)-order additive fuzzy measure, including usual additive measures and fuzzy measures. Every discrete fuzzy measure is a \(k\)-order additive fuzzy measure for a unique \(k\). A related topic of the paper is to introduce an alternative representation of fuzzy measures, called the interaction representation, which sets and extends in a common framework the Shaply value and the interaction index proposed by Murofushi and Soneda.

MSC:

28E10 Fuzzy measure theory
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