Effect of Criteria Range on the Similarity of Results in the COMET Method Andrii Shekhovtsov, Jakub Wi˛ eckowski, Bartlomiej Kizielewicz and Wojciech Salabun Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology West Pomeranian University of Technology in Szczecin ul. ˙ Zolnierska 49, 71-210 Szczecin, Poland Email: {andrii-shekhovtsov, jakub-wieckowski, bartlomiej-kizielewicz, wojciech.salabun}@zut.edu.pl Abstract—Defining input values in the decision-making process can be done with appropriate methods or based on expert knowledge. It is essential to ensure that the values are adequate for the problem to be solved in both cases. There may be situations where values are overestimated, and it should be checked whether this affects the final results. In this paper, the Characteristic Objects Method (COMET) was used to investigate the overestimation effect on the final rankings. The decision matrixes with a different number of alternatives and criteria were assessed The obtained results were compared using the WS similarity coefficient and Spearman’s weighted correlation coefficient. The study showed that overesti- mation has a significant effect on the rankings. A larger number of criteria has a positive effect on the correlation strength of the compared rankings. In contrast, a large overestimation of characteristic values has a negative effect on the similarity of the results. I. I NTRODUCTION In decision-making, expert knowledge is an important el- ement influencing the results obtained [1]. It is important in specifying the importance of criteria and the weighting of each criterion in the process of evaluating alternatives [2], [3]. These decisions directly translate into the obtained preference values guaranteed by the selected multi-criteria methods [4], [5], [6]. For some Multi-Criteria Decision-Making (MCDM) meth- ods to solve decision-making problems, the expert must define the algorithm’s input parameters based on his experience and knowledge [7], [8]. Some methods allow the use of methods that determine weights for criteria in a defined problem [9], [10]. In other cases, the data determined for the method’s oper- ation must be specified solely based on expert knowledge [11], [12]. Multi-Criteria Decision-Making methods are eagerly used in solving problems where many factors contribute to the final assessment [13]. The development of new techniques attracts the attention of a growing audience, who use them to solve medical problems [14], [15], [16], [17], for resource planning [18], [19], [20], or the selection of sustainable means of transport [21], [22], [23]. One of the multi-criteria methods is the Characteristic Ob- jects Method (COMET), which uses the rule-based approach when evaluating the quality of alternatives [24]. The expert’s task using this method to solve the problem is to determine the characteristic values, which will be used to assess the preference of alternatives in subsequent steps [25], [26]. The advantage of this method is that it is resistant to the phe- nomenon of ranking reversal when the number of alternatives in the analyzed set changes [8]. In this paper, based on the COMET method’s operation, an attempt has been made to determine the effect of over- estimation of characteristic values on the results depending on the number of alternatives and criteria. Different levels of overestimation were used to examine and compare the results obtained. The results were then compared using the WS similarity coefficient and the weighted Spearman correlation coefficient to analyze the resulting rankings’ correlation. The rest of the paper is organized as follows. Section 2 presents the preliminaries and main assumptions of the COMET method. Section 3 includes the study case descrip- tion, where the influence of the overestimation of characteristic values on the received results was examined. Finally, in Section 4 the summary and conclusions from the research are drawn. II. PRELIMINARIES A. Weighted Spearman’s Rank Coefficient Weighted Spearman’s rank coefficient is defined as (1), where N is a sample size, rank values for both rankings is named as x i and y i . In this approach, the positions at the top of both rankings are the most important. The weight of signif- icance is calculated for each alternative. It is the element that determines the main difference to Spearman’s rank correlation coefficient, which examines whether the differences appeared and not where they appeared [27]. r w =1 - 6 ∑ N i=1 (x i - y i ) 2 ((N - x i + 1) + (N - y i + 1)) N 4 + N 3 - N 2 - N (1) B. WS Rank Similarity Coefficient Rank Similarity Coefficient WS is defined as (2). Un- like r w , it is an asymmetric measure. The weight of a given comparison is determined based on the significance of the Proceedings of the 16 th Conference on Computer Science and Intelligence Systems pp. 453–457 DOI: 10.15439/2021F44 ISSN 2300-5963 ACSIS, Vol. 25 IEEE Catalog Number: CFP2185N-ART ©2021, PTI 453