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JACIII Vol.7 No.2 pp. 79-85
doi: 10.20965/jaciii.2003.p0079
(2003)

Paper:

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
Published:
June 20, 2003
Keywords:
k-monotonicity, marginal interaction, cardinal-probabilistic interaction indices, balanced interaction indices
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.

Cite this article as:
Katsushige Fujimoto, “Cardinal-Probabilistic Interaction Indices and their Applications: A Survey,” J. Adv. Comput. Intell. Intell. Inform., Vol.7, No.2, pp. 79-85, 2003.
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