Paper:
Language: English:

Cardinal-Probabilistic Interaction Indices and their Applications: A Survey

Katsushige Fujimoto

Faculty of Economics, Fukushima University, 1, Kanayagawa, Fukushima 960-1296, Japan

Received: January 31, 2003

Accepted: February 24, 2003

Keywords: k-monotonicity, marginal interaction, cardinal-probabilistic interaction indices, balanced interaction indices

Journal ref: Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.7, No.2 pp. 79-85, 2003

Abstract

The class of cardinal probabilistic interaction indices obtained as expected marginal interactions includes the Shapley, Banzhaf, and chaining interaction indices and the Möbius and co-Möbius transform so. We will survey cardinal-probabilistic interaction indices and their applications, focusing on axiomatic characterization of the class of cardinal-probabilistic interaction indices. We show that these typical cardinal-probabilistic interaction indices can be represented as the Stieltjes integrals with respect to choice-probability measures on [0,1]. We introduce a method for hierarchical decomposition of systems represented by the Choquet integral using interaction indices.

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