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Comprehensive nonmodularity and interaction indices for decision analysis

Version 2 2024-06-06, 04:29
Version 1 2021-07-29, 11:13
journal contribution
posted on 2024-06-06, 04:29 authored by Jianzhang WuJianzhang Wu, Gleb BeliakovGleb Beliakov
Nonmodularity is a prominent property of capacity that deeply links to the internal interaction phenomenon of multiple decision criteria. Following the common architectures of the simultaneous interaction indices as well as of the bipartition interaction indices, in this paper, we construct and study the notion of probabilistic nonmodularity index and also its particular cases, such as Shapely and Banzhaf nonmodularity indices, which can be used to describe the comprehensive interaction situations of decision criteria. The connections and differences among three categories of interaction indices are also investigated and compared theoretically and empirically. It is shown that three types of interaction indices have the same roots in their first and second orders, but meanwhile the nonmodularity indices have involved less amount of subsets and can be adopted to describe the interaction phenomenon in decision analysis.

History

Journal

Journal of Intelligent and Fuzzy Systems

Volume

40

Pagination

10671-10685

Location

Amsterdam, The Netherlands

ISSN

1064-1246

eISSN

1875-8967

Language

English

Publication classification

C1 Refereed article in a scholarly journal

Issue

6

Publisher

IOS Press