The use of fuzzy preference models in multiple criteria choice, ranking and sorting

This chapter presents several approaches to derive a recommendation from a fuzzy relational preference model. Depending on the specificities of the decision problem, the recommendation can be a selection of the best alternatives, a ranking of these alternatives or a classification. In many decision problems involving several criteria and/or several experts with possibly conflicting evaluations of the alternatives, deriving a clear prescription is not an easy task since the overall fuzzy preference model is usually neither transitive nor complete. In this chapter, we present methods that have been specially designed to face this difficulty. We first consider the problem of choosing from a fuzzy preference relation. The classical notions of non-dominated alternatives and core are introduced (§ 3.1). Then several choice functions based on the use of scores, covering relations and kernels respectively are presented in sections (§ 3.2-3.5). Finally, a brief survey of ranking and sorting procedures is proposed (§ 3.6).

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