About a consistency index for pairwise comparison matrices over a divisible alo-group
✍ Scribed by B. Cavallo; L. D'Apuzzo; M. Squillante
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 170 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0884-8173
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✦ Synopsis
Pairwise comparison matrices (PCMs) over an Abelian linearly ordered (alo)-group G = (G, , ≤ ) have been introduced to generalize multiplicative, additive and fuzzy ones and remove some consistency drawbacks. Under the assumption of divisibility of G, for each PCM A = (a ij ), a -mean vector w m (A) can be associated with A and a consistency measure I G (A), expressed in terms of -mean of G-distances, can be provided. In this paper, we focus on the consistency index I G (A). By using the notion of rational power and the related properties, we establish a link between w m (A) and I G (A). The relevance of this link is twofold because it gives more validity to I G (A) and more meaning to w m (A); in fact, it ensures that if I G (A) is close to the identity element then, from a side A is close to be a consistent PCM and from the other side w m (A) is close to be a consistent vector; thus, it can be chosen as a priority vector for the alternatives.