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Pairwise Comparisons Matrices on Alo-Groups in Decision-Making

In: Pairwise Comparisons Method

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  • Jaroslav Ramík

    (Silesian University in Opava)

Abstract

This chapter deals with PC matrices on alo-groups in decision-making. We consider pairwise comparisons matrices over abelian linearly (totally) ordered groups briefly called alo-groups, and, in this way, we provide a general framework for three important cases: multiplicative, additive, and fuzzy ones. By introducing the more general setting, we provide an optimization method for generating priority vectors satisfying appropriate conditions. Then we deal with the problem of measuring the inconsistency of the PC matrix with a natural meaning, which corresponds to the consistency indexes presented in the previous chapter. We consider PC matrices with some missing elements, particularly two important cases of PCMs with some missing elements where the expert evaluates at least $$n-1$$ pairwise comparisons of the alternatives. Here, we present several interesting results concerning this problem.

Suggested Citation

  • Jaroslav Ramík, 2020. "Pairwise Comparisons Matrices on Alo-Groups in Decision-Making," Lecture Notes in Economics and Mathematical Systems, in: Pairwise Comparisons Method, chapter 0, pages 67-123, Springer.
    • Handle: RePEc:spr:lnechp:978-3-030-39891-0_3
    DOI: 10.1007/978-3-030-39891-0_3
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