Maximization of the Choquet integral over a convex set and its application to resource allocation problems

Timonin, Mikhail

doi:10.1007/s10479-012-1147-9

Cited by 10 publications

(1 citation statement)

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“…, n} which guarantees that C v (x) cannot decrease as quantities x i increase. In many papers on multicriteria optimization with a Choquet integral, the capacity is assumed to be given [32,33,34,35]. This assumes that preference elicitation methods are available to determine the capacity that best fits DM's preferences.…”

Section: Discrete Choquet Integralsmentioning

confidence: 99%

Incremental elicitation of Choquet capacities for multicriteria choice, ranking and sorting problems

Benabbou

Perny

Viappiani

2017

Artificial Intelligence

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This paper proposes incremental preference elicitation methods for multicriteria decision making with a Choquet integral. The Choquet integral is an evaluation function that performs a weighted aggregation of criterion values using a capacity function assigning a weight to any coalition of criteria, thus enabling positive and/or negative interactions among them and covering an important range of possible decision behaviors. However, the specification of the capacity involves many parameters which raises challenging questions, both in terms of elicitation burden and guarantee on the quality of the final recommendation. In this paper, we investigate the incremental elicitation of the capacity through a sequence of preference queries (questions) selected one-by-one using a minimax regret strategy so as to progressively reduce the set of possible capacities until the regret (the worst-case "loss" due to reasoning with only partially specified capacities) is low enough. We propose a new approach designed to efficiently compute minimax regret for the Choquet model and we show how this approach can be used in different settings: 1) the problem of recommending a single alternative, 2) the problem of ranking alternatives from best to worst, and 3) sorting several alternatives into ordered categories. Numerical experiments are provided to demonstrate the practical efficiency of our approach for each of these situations.

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Section: Discrete Choquet Integralsmentioning

confidence: 99%