A generic framework to include belief functions in preference handling and multi-criteria decision

Abstract

Modelling the preferences of a decision maker about alternatives having multiple criteria usually starts by collecting preference information (comparisons of alternatives, importance of criteria, . . . ), which are then used to fit a preference model issued from some set of hypothesis (weighted average, CP-net, lexicographic orderings, . . . ). In practice, this process may often lead to inconsistencies that may be due to inaccurate information provided by the decision maker, who can be unsure about the provided information, or to a poor choice of hypothesis set, which can be too restrictive or not well adapted to the decision process. In this paper, we propose to use belief functions as a way to quantify and resolve such inconsistencies, notably by allowing the decision maker to express her/his certainty about the provided preferential information. Our framework is generic, in the sense that it does not assume a given set of hypothesis a priori, and is consistent with precise methods, in the sense that in the absence of uncertainty and inconsistencies in the information, precise models are ultimately retrieved.

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