On paired prioritizations of criteria in the perspective of digraphs

Abstract

It is not usually independent among criteria in multi-criteria decision making (MCDM), and various dependences of criteria greatly influence the results of decision making. If an exact decision is desired, we must make clear the role of the dependences of criteria. Prioritizations, a new kind of dependences of criteria proposed recently, imply that the importance weights of criteria with lower priority for an alternative rely on whether the alternative satisfies the decision maker under criteria with higher priority. It has been validated that there exist lots of relevant applications in our daily activities. However, most existing literatures focus on how to deal with the problems of MCDM with ordered prioritizations among criteria (a special form of prioritizations). The characteristics of prioritizations are not dug deep. This paper constructs a new form of prioritizations, called paired prioritizations, so as to reduce or even avoid imperfect rationality of decision makers hidden in the ordered prioritizations. We first represent binary paired prioritizations as a digraph, based on which we discover two kinds of imperfect rationality (inconsistency and incompleteness) produced in the period that the decision maker supplies the binary paired prioritizations. After the given paired prioritizations are consistent and complete, we develop an approach to transform the paired prioritizations to ordered prioritizations. The latter can be used to handle prioritized MCDM problems. Moreover, uncertainty, another kind of imperfect rationality, is considered when the decision maker provides the fuzzy paired prioritizations based on a set of linguistic labels. We construct a fuzzy digraph whose fuzzy relations are just the fuzzy paired prioritizations. The ordered prioritizations can then be derived with the aid of the fuzzy digraph. Two use cases are taken to show the process of transformations from binary/fuzzy paired prioritizations to ordered prioritizations.

Keywords

Paired prioritization / ordered prioritization / criteria / digraph / fuzzy digraph

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