Cardinal-Probabilistic Interaction Indices and their Applications: A Survey | Zendy

Katsushige Fujimoto | Zendy

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Cardinal-Probabilistic Interaction Indices and their Applications: A Survey

Author(s) -

Katsushige Fujimoto

Publication year - 2003

Publication title -

journal of advanced computational intelligence and intelligent informatics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.172

H-Index - 20

eISSN - 1343-0130

pISSN - 1883-8014

DOI - 10.20965/jaciii.2003.p0079

Subject(s) - probabilistic logic , class (philosophy) , chaining , axiom , computer science , choquet integral , decomposition , mathematics , artificial intelligence , fuzzy logic , psychology , ecology , geometry , psychotherapist , biology

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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