Generalized Choquet-like aggregation functions for handling bipolar scales

Generalized Choquet-like aggregation functions for handling bipolar scales

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Article ID: iaor20084029
Country: Netherlands
Volume: 172
Issue: 3
Start Page Number: 931
End Page Number: 955
Publication Date: Aug 2006
Journal: European Journal of Operational Research
Authors: ,
Keywords: programming: multiple criteria
Abstract:

We are interested in modeling interaction between criteria in multi-criteria decision making when underlying scales are bipolar. Interacting phenomena involving behavioral bias between attractive and repulsive values are in particular considered here. We show in an example that both the Choquet integral and the cumulative prospect theory (CPT) model fail to represent these interacting phenomena. Axioms that enable the construction of the preferences of the decision maker over each attribute, and the representation of his preferences about aggregation of criteria are introduced and justified. We show there is a unique aggregation operator that fits with these axioms. It is based on the notion of bi-capacity and generalizes both the Choquet integral and the CPT model.

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