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.

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

In literature, several consistency indices are proposed for estimating the deviation of preferences from a fully consistent form. Finding that some indices are dependent on each other is very important in the process of inconsistency estimation. In this article, we look for functional relations and correlations among nine consistency indices.

Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision-making methods. Since several types of pairwise comparison matrices (e.g., multiplicative, additive, fuzzy) are proposed in literature, in this paper, we investigate, for which type of matrix, decision-makers are more coherent when they express their subjective preferences. By performing an experiment, we found that the additive approach provides the worst level of coherence.