In multidimensional scaling (MDS) carried out on the basis of a metric data matrix (interval, ratio), the main decision problems relate to the selection of the method of normalization of the values of the variables, the selection of distance measure and the selection of MDS model. The article proposes a solution that allows choosing the optimal multidimensional scaling procedure according to the normalization methods, distance measures and MDS model applied. The study includes 18 normalization methods, 5 distance measures and 3 types of MDS models (ratio, interval and spline). It uses two criteria for selecting the optimal multidimensional scaling procedure: Kruskal's Stress-1 fit measure and Hirschman-Herfindahl HHI index calculated based on Stress per point values. The results are illustrated by an empirical example.

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The article evaluates, based on ordinal data simulated with cluster.Gen function of clusterSim package working in R environment, some cluster analysis procedures containing GDM distance for ordinal data (see [4,18,19]), nine clustering methods and eight internal cluster quality indices for determining the number of clusters. Seventy two clustering procedures are evaluated based on simulated data originating from a variety of models. Models contain the known structure of clusters and differ in the number of true dimensions, the number of categories for each variable, the density and shape of clusters, the number of true clusters, the number of noisy variables. Each clustering result was compared with the known cluster structure from models applying Hubert and Arabie's [2] corrected Rand index.

Customer loyalty to a destination and accommodation services constitutes a frequent object of research; however, customer loyalty to travel agencies is rarely analyzed. The presented article is an attempt to fill in this research gap. Its purpose is to construct and verify the model covering the impact of the selected factors on the loyalty level of customers of travel agencies operating in Poland. The conceptualization of the loyalty model of travel agency customers (based on the European path-based EPSI model) proposed in the article was first used to illustrate the existing correlations in customer behavior to analyze and explain the development of the loyalty phenomenon vis-a-vis travel agency customers. The aforementioned assumptions—having applied the structural equation modelling (SEM)—were reflected in the development of the theoretical model of travel agencies customer loyalty, the empirical verification of which (N = 1151) allowed us to determine the impacts of selected factors (i.e., the perceived quality of the travel agency’s offers, its image and the satisfaction with its service buyers) on the loyalty level of travel agency customers. It has been shown that two major factors have positive impacts on the loyalty of travel agency customers: (i) the perceived quality of travel agency offers, and (ii) its image. Furthermore, the conducted analysis highlights the positive influence of the perceived value of travel agency offers on the loyalty of customers.

The TOPSIS method (Technique for Order Preference by Similarity Ideal Solution) suggested by Hwang and Yoon [1981], belongs to the group of pattern linear ordering methods of multidimensional objects. A characteristic feature of this method is a way to evaluate a synthetic criterion's values, which takes into consideration the distance of an evaluated object from a positive-ideal solution as well as from a negative-ideal solution. The fuzzy TOPSIS method enables the linear ordering of objects described through linguistic variables, whose values are expressed in the form of triangular fuzzy numbers. In this article, a way of synthetic measurement estimation in environment R was presented, according to the assumptions of the fuzzy TOPSIS method proposed by Chen [2000]. Scripts, which are included in the article make the accomplishment of this particular method's stages possible.