How to improve acts: an alternative representation of the importance of criteria in MCDM

Abstract : The intepretation of aggregation functions in multicriteria decision making is often based on indices such as importance indices that measure the importance of one criterion. For instance, for the Choquet integral, the importance index is the so-called Shapley value. The use of an index must always be limited to the specific context it has been designed for. Here, we are interested in determining on which criteria acts should be improved if we want their global evaluation to increase as much as possible. The Shapley value is not suited for describing this. So, we introduce a new index of importance which represents the mean worth for acts to reach higher scores in a set of criteria. This index is defined for general aggregation functions with the help of several axioms. This importance index is then applied to the Choquet integral. In particular, we computer the worth to reach higher levels in one attribute, and in a couple of attributes. Interestingly, this leads to quantities that are closely related to the Shapley and interaction indices.
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Michel Grabisch, Christophe Labreuche. How to improve acts: an alternative representation of the importance of criteria in MCDM. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, World Scientific Publishing, 2001, 9 (2), pp.145-157. 〈10.1142/S0218488501000697〉. 〈hal-01185823〉

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