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Probabilistic bipartition interaction index of multiple decision criteria associated with the nonadditivity of fuzzy measures

journal contribution
posted on 2019-02-01, 00:00 authored by J Z Wu, Gleb BeliakovGleb Beliakov
The probabilistic simultaneous interaction index has been widely adopted to measure the interaction among the decision criteria. However, this type of indices sometimes fails to reflect the kind of interaction associated with the nonadditivity of a fuzzy measure (capacity). For example, any simultaneous interaction index of the universal set of criteria w.r.t. a strictly superadditive capacity is not always positive. The main reason is that the simultaneous interaction index generalizes the notion of value by replacing the marginal contribution of a single criterion with the marginal simultaneous interaction of criteria subset. In this paper, we reform the generalization process and replace the marginal contribution with the marginal bipartition interaction, which can better reflect the kind of interaction associated with the nonadditivity, for example, superadditivity, subadditivity, strict-superadditivity, or strict-subadditivity. We construct a family of probabilistic bipartition interaction indices of subsets of criteria and study its properties. We discuss the issue of capacity identification based on the bipartition interaction index and demonstrate that the new type of interaction index can be adopted as a feasible alternative to describing the interaction phenomenon among the decision criteria.

History

Journal

International journal of intelligent systems

Volume

34

Issue

2

Pagination

247 - 270

Publisher

Wiley

Location

Chichester, Eng.

ISSN

0884-8173

eISSN

1098-111X

Language

Eng

Publication classification

C1 Refereed article in a scholarly journal

Copyright notice

2018 Wiley Periodicals, Inc.