Cardinal-Probabilistic Interaction Indices and their Applications: A Survey
Faculty of Economics, Fukushima University, 1, Kanayagawa, Fukushima 960-1296, Japan
Received:January 31, 2003Accepted:February 24, 2003Published:June 20, 2003
Keywords:k-monotonicity, marginal interaction, cardinal-probabilistic interaction indices, balanced interaction indices
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:K. Fujimoto, “Cardinal-Probabilistic Interaction Indices and their Applications: A Survey,” J. Adv. Comput. Intell. Intell. Inform., Vol.7 No.2, pp. 79-85, 2003.Data files: