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Contribution of individual judgments toward inconsistency in pairwise comparisons. (English) Zbl 1341.90073

Summary: Pairwise comparison (PC) is a well-established method to assist decision makers in estimating their preferences. In PCs, the acquired judgments are used to construct a PC matrix (PCM) that is used to check whether the inconsistency in judgments is acceptable or requires revision. The use of Consistency Ratio (CR) – a widely used measure for inconsistency – has been widely debated and the literature survey has identified a need for a more appropriate measure. Considering this need, a new measure, termed congruence, is proposed in this paper. The measure is shown to be useful in finding the contribution of individual judgments toward overall inconsistency of a PCM and, therefore, can be used to detect and correct cardinally inconsistent judgments. The proposed measure is applicable to incomplete sets of PC judgments without modification, unlike CR which requires a complete set of PC judgments. To address ordinal inconsistency, another measure termed dissonance, is proposed as a supplement to the congruence measure. The two measures appear useful in detecting both outliers and the phenomenon of consistency deadlock where all judgments equally contribute toward the overall inconsistency.

MSC:

90B50 Management decision making, including multiple objectives
62J15 Paired and multiple comparisons; multiple testing
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