Generalized Choquet-like aggregation functions for handling bipolar scales |
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| Institution: | 1. Thales Research and Technology, Domaine de Corbeville, 91404 Orsay Cedex, France;2. Université Paris I Panthéon-Sorbonne LIP6, 8 rue du Capitaine Scott, 75015 Paris, France;1. Faculty of Education, and Faculty of Mathematics and Physics, University of Ljubljana, PO Box 2964, Ljubljana, 1001, Slovenia;2. Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Straße 25, A-1090 Wien, Austria;1. Paris School of Economics, University of Paris I, 106-112, Bd. de l’Hôpital, 75013 Paris, France;2. Department of Business and Economics and COHERE, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark;1. College of Mechanical and Electrical Engineering, Henan Agricultural University, Zhengzhou, Henan Province, China;2. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China;1. Mathematics Research Unit, FSTC, University of Luxembourg, 6, rue Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg;2. University of Liège, Department of Mathematics, Grande Traverse, 12 - B37, B-4000 Liège, Belgium |
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| 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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