5<X, R> Models of Multicriteria Decision‐Making and Their Analysis

In this chapter, we present an introduction to preference modeling realized in terms of binary fuzzy relations. In dealing with <X, R> models, which serve for multiattribute decision‐making, a fundamental question arises of how can one construct fuzzy preference relations? In practice, a decision‐maker (DM) can directly assess fuzzy preference relations. The corresponding techniques are considered. A natural and convincing approach to constructing fuzzy preference relations based on the ordering of fuzzy quantities is discussed as well. Since any involved expert or any included criterion may require different formats for representing preferences (five main types of preference format are considered in this chapter), the questions of their conversion into fuzzy preference relations on the basis of so‐called transformation functions are considered. We discuss methods used to analyze problems of multicriteria evaluation, comparison, choice, prioritization, and/or ordering of alternatives. Two types of situation exist that give rise to these problems. The first one is related to the direct statement of multiattribute decision‐making problems when the consequences associated with solutions to problems cannot be estimated with a single criterion. The second class is related to problems that may be solved on the basis of a single criterion or several criteria; however, if the uncertainty of information does not permit ...

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