Abstract
In some multi-criteria decision-making problems, it is more convenient to express the decision maker (DM) preferences in bipolar scales. In such cases, the bipolar Choquet integral with respect to bi-capacities was introduced as a versatile tool to model these kind of preferences. However, this aggregation function is useful in practice only if its parameters can be set up easily. To this end, elicitation techniques aim at finding the parameters values that best fit some given examples. In this paper, we address the problem of eliciting a bipolar Choquet integral with respect to a 2-additive bi-capacity. We present several techniques based on solving an optimization problem, taking into account the possible interaction, or not, with the DM. We deal with possible inconsistencies in the observed preferences and we also discuss the parsimonious character of the different models to favor simple models when several solutions exist.
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Notes
Grabisch and Labreuche (Grabisch and Labreuche 2003, 2005a, b) proposed a definition of the Möbius transform of a BC different to the one given in Fujimoto (2004). However, there is a one-to-one correspondence between the two Möbius transform definitions. This equivalence was established in Fujimoto and Murofushi (2005).
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Rolland, A., Ah-Pine, J. & Mayag, B. Elicitation of 2-additive bi-capacity parameters. EURO J Decis Process 3, 5–28 (2015). https://doi.org/10.1007/s40070-015-0043-3
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DOI: https://doi.org/10.1007/s40070-015-0043-3