کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
389247 | 661120 | 2015 | 14 صفحه PDF | دانلود رایگان |
We consider reciprocal matrices over an abelian linearly ordered group; in this way we provide a general framework including multiplicative, additive and fuzzy matrices. In a multi-criteria decision making context, a pairwise comparison matrix A=(aij)A=(aij) is a reciprocal matrix that represents a useful tool for determining a weighting vector w for a set X of decision elements; but, when A is inconsistent, the weighting vector, usually proposed in literature, may provide a ranking on X that does not agree with the expressed preference intensities aijaij, thus, it is unreliable. We analyze a condition of transitivity for a reciprocal matrix A=(aij)A=(aij) over an abelian linearly ordered group, that, whenever A is a pairwise comparison matrix, allows us to state a qualitative dominance ranking on X and obtain ordinal evaluation vectors; in this way, we get a first tool for checking the reliability of a weighting vector. We also provide tools to check the transitivity.
Journal: Fuzzy Sets and Systems - Volume 266, 1 May 2015, Pages 33–46