In a Multicriteria Decision Making context, a pairwise comparison matrix $A=(a_{ij})$ is a helpful tool to determine the weighted ranking on a set $X$ of alternatives or criteria. The entry $a_{ij}$ of the matrix can assume different meanings: $a_{ij}$ can be a preference ratio (multiplicative case) or a preference difference (additive case) or $a_{ij}$ belongs to $[0,1]$ and measures the distance from the indifference that is expressed by 0.5 (fuzzy case). For the multiplicative case, a consistency index for the matrix $A$ has been provided by T.L. Saaty in terms of maximum eigenvalue. We consider pairwise comparison matrices over an abelian linearly ordered group and, in this way, we provide a general framework including the mentioned cases. By introducing a more general notion of metric, we provide a consistency index that has a natural meaning and it is easy to compute in the additive and multiplicative cases; in the other cases, it can be computed easily starting from a suitable additive or multiplicative matrix

The Pairwise Comparison Matrices (PCMs) over an abelian linearly ordered (alo)-group G = (G, ⊙, ≤) have been introduced in order to gener- alize multiplicative, additive and fuzzy ones and remove some consistency drawbacks. Under the assumption of divisibility of G, for each PCM A = (aij), a ⊙-mean vector wm(A) can be associated to A and a consis- tency measure IG(A), expressed in terms of ⊙-mean of G-distances, can be provided. In this paper, we focus on the consistency index IG(A). By using the notion of rational power and the related properties, we establish a link between wm(A) and IG(A). The relevance of this link is twofold because it gives more validity to IG(A) and more meaning to wm(A); in fact, it ensures that if IG(A) is close to the identity element then, from a side A is close to be a consistent PCM and from the other side wm(A) is close to be a consistent vector; thus, it can be chosen as a priority vector for the alternatives

Run-time binding is an important and useful feature of Service Oriented Architectures (SOA), which aims at selecting, among functionally equivalent services, the ones that optimize some QoS objective of the overall application. To this aim, it is particularly relevant to forecast the QoS a service will likely exhibit in future invocations.\ud \ud This paper presents an empirical study aimed at comparing different approaches for QoS forecasting, namely the use of average and current values, linear models, and models based on time series. The study is performed on QoS data obtained by monitoring the execution of 10 real services for 4 months.\ud \ud Results show that, overall, the use of time series forecasting has the best compromise in ensuring a good prediction error, being sensible to outliers, and being able to predict likely violations of QoS constraints

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