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Ensuring reliability of the weighting vector: Weak consistent pairwise comparison matrices

机译：确保加权向量的可靠性：弱一致的成对比较矩阵

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摘要

In the context of Pairwise Comparison Matrices (PCMs) defined over abelian linearly ordered group, circle dot-consistency and circle dot-transitivity represent a full coherence of the Decision Maker (DM) and the minimal logical requirement that DM's preferences should satisfy, respectively. Moreover, the circle dot-mean vector w(m circle dot) is proposed as weighting vector for the decision elements related to the PCM. In this paper, we investigate the effects of circle dot-inconsistency of a circle dot-transitive PCM on w(m circle dot) and, in order to ensure its reliability as weighting vector, we provide the notion of weak circle dot-consistency; it is weaker than circle dot-consistency and stronger than circle dot-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 circle dot-mean vector w(m circle dot) 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 circle dot-consistency is satisfied; the simple order allows us to easily determine the actual ranking on the set of related decision elements. (C) 2015 Elsevier B.V. All rights reserved.
机译：在阿贝尔线性有序组上定义的成对比较矩阵（PCM）的背景下，圆点一致性和圆点传递性分别表示决策者（DM）的完整一致性和DM偏好应满足的最小逻辑要求。此外，提出了圆点均值向量w（m个圆点）作为与PCM相关的决策元素的加权向量。在本文中，我们研究了圆点传递PCM的圆点不一致性对w（m圆点）的影响，为了确保其作为加权矢量的可靠性，我们提供了弱圆点一致性的概念。它比圆点一致性弱，比圆点传递性强，并且通过严格增加的合成功能，确保与PCM相关的向量对于在相关决策元素集上分配优先级顺序是可靠的。圆点均值向量w（m圆点）通过这些功能之一与PCM关联。最后，我们在PCM的行上引入一个顺序关系，当且仅当满足弱圆点一致性的条件时，这是一个简单的顺序。简单的顺序使我们可以轻松地确定一组相关决策元素的实际排名。 （C）2015 Elsevier B.V.保留所有权利。

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