SUBSET, written in the matrix language Gauss, is a program that identifies optimal subsets of means or proportions based on independent groups. All possible configurations of ordered subsets of groups are identified and the best model is selected using either the AIC or BIC information criterion. For means, both homogeneous and heterogeneous variance cases are considered. SUBSET offers an alter...

Pairwise comparison matrices are increasingly used in settings where some pairs missing. However, there exist few inconsistency indices for similar incomplete data sets and no reasonable measure has an associated threshold. This paper generalises the famous rule of thumb acceptable level inconsistency, proposed by Saaty, to pairwise matrices. The extension is based on choosing missing elements ...

Context. The pairwise comparison method is a component of several decision support methodologies such as the analytic hierarchy and network processes (AHP, ANP), PROMETHEE, TOPSIS other. This results in weight vector elements decision-making model based on inversely symmetrical matrices. evaluation carried out mainly by experts under conditions uncertainty. Therefore, modifications this have be...

We apply methods of tropical optimization to handle problems of rating alternatives on the basis of the log-Chebyshev approximation of pairwise comparison matrices. We derive a direct solution in a closed form, and investigate the obtained solution when it is not unique. Provided the approximation problem yields a set of score vectors, rather than a unique (up to a constant factor) one, the set...

In several methods of multiattribute decision making, pairwise comparison matrices are applied to derive implicit weights for a given set of decision alternatives. A class of the approaches is based on the approximation of the pairwise comparison matrix by a consistent matrix. In the paper this approximation problem is considered in the least-squares sense. In general, the problem is nonconvex ...

Pairwise comparison matrices play a prominent role in multiple-criteria decision-making, particularly the analytic hierarchy process (AHP). Another form of preference modeling, called an incomplete pairwise matrix, is considered when one or more elements are missing. In this paper, algorithm proposed for optimal completion matrix. Our intention to numerically minimize maximum eigenvalue functio...

The contribution of this paper to the space transportation system field is to select promising Reusable Launch Vehicle (RLV) concepts by using a formal evaluation procedure. The vehicle system is divided into design features. Every design feature can have alternative characteristics. All combinations of design features and characteristics are compared pairwise with each other. The innovation an...

Nonnegative matrix factorization NMF is a popular tool for analyzing the latent structure of nonnegative data. For a positive pairwise similarity matrix, symmetric NMF SNMF and weighted NMF WNMF can be used to cluster the data. However, both of them are not very efficient for the ill-structured pairwise similarity matrix. In this paper, a novel model, called relationship matrix nonnegative deco...