Two approaches to importance indices of fuzzy measures on restricted domains

Abstract

The Shapley value has been proposed as an important index of fuzzy measures. The Shapley value can be interpreted as the following two representations: 1) an expected marginal contributions and 2) an cumulative value of dividends. In ordinary cases, these different two interpretations lead to the same notion, i.e., the Shapley value, while in some restricted domains, to different notions. In this paper, we show notions/indices which are led by two approaches based on above interpretations. Moreover, we suggest how and in what situations these indices should be applied.