The method of pairwise comparisons is frequently applied for ranking purposes. This article aims to rank top women tennis players based on their win/lose ratios. Incomplete comparison matrices (PCMs) were constructed from data obtained the WTA (Women’s Tennis Association) homepage. database contains head-to-head results period between 1973 and 2022 28 who had position No. 1 in official rankings...

We describe a seriation algorithm for ranking a set of n items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a similarity matrix from pairwise comparisons, using seriation methods to reorder this matrix and construct a ranking. We first show that this spectral seriat...

Given a matrix of dissimilarities, it has been debated whether researchers should perform multidimensional scaling on this original matrix or on a new one derived by comparing rows in the original matrix. Careful comparison studies (Drasgow & Jones, 1979; Van der Kloot & Van Herk, 1991) in the context of sorting data indicated that most of the initial enthusiasm for the derivative approach was ...

We propose to extend the aggregation scheme of Saaty’s AHP, from the standard weighted averaging to the more general Choquet integration. In our model, a measure of inconsistency between criteria is derived from the main pairwise comparison matrix and it is used to construct a non-additive capacity, whose associated Choquet integral reduces to the standard weighted mean in the consistency case....

Pairwise clustering methods partition a dataset using pairwise similarity between data-points. The pairwise similarity matrix can be used to define a Markov random walk on the data points. This view forms a probabilistic interpretation of spectral clustering methods. We utilize this probabilistic model to define a novel clustering cost function that is based on maximizing the mutual information...

Interval AHP was proposed to express the decision maker’s vague evaluations on criteria by interval weights from a given pairwise comparison matrix. It has been extended to group decision problems. Three complementary approaches have been proposed: the perfect incorporation approach for counting out indubitably inferior alternatives and the common ground and partial incorporation approaches for...

This paper develops the spectral properties of pairwise comparison matrices (PCM) used in the multicriteria decision making method called analytic hierarchy process (AHP). Perturbed PCMs are introduced which may result in a reversal of the rank order of the decision alternatives. The analysis utilizes matrix theory to derive the principal eigenvector components of perturbed PCMs in explicit for...

Consistency retrieval from a biased relative preference table is an imperative task in decision theory This paper considers the least squares approximation of a pairwise comparison matrix by consistent matrices It is observed that the highly nonlinear manifold of consistent matrices can be changed into a linear subspace by the component wise logarithmic transformation A rst order optimality con...

The selection of the most suitable machining process for a given machining application is not straightforward and requires consideration of a number of techno-technological and economic criteria. Therefore is often viewed as a multi-criteria decision making (MCDM). This paper is focused on multi-criteria economic analysis of various machining processes by applying recently developed MCDM method...