Article ID Journal Published Year Pages File Type
389141 Fuzzy Sets and Systems 2016 14 Pages PDF
Abstract

In the context of Pairwise Comparison Matrices (PCMs) defined over abelian linearly ordered group, ⊙-consistency and ⊙-transitivity represent a full coherence of the Decision Maker (DM) and the minimal logical requirement that DM's preferences should satisfy, respectively. Moreover, the ⊙-mean vector wm⊙wm⊙ is proposed as weighting vector for the decision elements related to the PCM. In this paper, we investigate the effects of ⊙-inconsistency of a ⊙-transitive PCM on wm⊙wm⊙ and, in order to ensure its reliability as weighting vector, we provide the notion of weak ⊙-consistency; it is weaker than ⊙-consistency and stronger than ⊙-transitivity, and ensures that vectors associated with a PCM, by means of a strictly increasing synthesis functional, are reliable for assigning a preference order on the set of related decision elements. The ⊙-mean vector wm⊙wm⊙ is associated with a PCM by means of one of these functionals. Finally, we introduce an order relation on the rows of the PCM, that is a simple order if and only if the condition of weak ⊙-consistency is satisfied; the simple order allows us to easily determine the actual ranking on the set of related decision elements.

Related Topics
Physical Sciences and Engineering Computer Science Artificial Intelligence
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