## $$k$$-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:

 2.8e+11 Fuzzy measure theory
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### References:

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