In this paper, at first, we provide some results on the group of vectors with components in a divisible Abelian linearly ordered group, the related subgroup of ⊙ -normal vectors, the relation of ⊙ -proportionality and the corresponding quotient group. Then, we apply the achieved results to the groups of reciprocal and consistent matrices over divisible Abelian linearly ordered groups; this allows us to deal with the problem of deriving a weighted ranking for the alternatives from a pairwise comparison matrix. The proposed weighting vector has several advantages; it satisfies, for instance, the independence of scale-inversion condition.
Deriving weights from a pairwise comparison matrix over an alo-group / Cavallo, Bice; D'Apuzzo, Livia. - In: SOFT COMPUTING. - ISSN 1432-7643. - 16:(2012), pp. 353-366. [10.1007/s00500-011-0746-8]
Deriving weights from a pairwise comparison matrix over an alo-group
CAVALLO, BICE
;D'APUZZO, LIVIA
2012
Abstract
In this paper, at first, we provide some results on the group of vectors with components in a divisible Abelian linearly ordered group, the related subgroup of ⊙ -normal vectors, the relation of ⊙ -proportionality and the corresponding quotient group. Then, we apply the achieved results to the groups of reciprocal and consistent matrices over divisible Abelian linearly ordered groups; this allows us to deal with the problem of deriving a weighted ranking for the alternatives from a pairwise comparison matrix. The proposed weighting vector has several advantages; it satisfies, for instance, the independence of scale-inversion condition.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.