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An Innovative Drastic Metric for Ranking Similarity in Decision-Making Problems

Sałabun Wojciech, Shekhovtsov Andrii

Annals of Computer Science and Information Systems

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2023

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Vol. 35

731--738

EN

In this paper, we propose a novel approach to distance measurement for rankings, introducing a new metric that exhibits exceptional properties. Our proposed distance metric is defined within the interval of 0 to 1, ensuring a compact and standardized representation. Importantly, we demonstrate that this distance metric satisfies all the essential criteria to be classified as a true metric. By adhering to properties such as non-negativity, identity of indiscernibles, symmetry, and the crucial triangle inequality, our proposed distance metric provides a robust and reliable approach for comparing rankings in a rigorous and mathematically sound manner. Finally, we compare our new metric with distances such as Hamming distance, Canberra distance, Bray-Curtis distance, Euclidean distance, Manhattan distance, and Chebyshev distance. By conducting simple experiments, we assess the performance and advantages of our proposed metric in comparison to these established distance measures. Through these comparisons, we demonstrate the superior properties and capabilities of our new drastic weighted similarity distance for accurately capturing the dissimilarities and similarities between rankings in the decision-making domain.

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A novel iterative approach to determining compromise rankings

Kizielewicz Bartłomiej, Shekhovtsov Andrii, Sałabun Wojciech

Annals of Computer Science and Information Systems

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2022

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Vol. 30

783--787

EN

In many cases involving multi-criteria decision-making, we need compromise solutions. This is a crucial aspect due to the specific characteristics of decision problems. However, the proposed trade-off approaches are often complex to verify to what extent they are reliable. Therefore, this paper proposes a new iterative approach based on decision option evaluations from selected multi-criteria decision-making methods, i.e., TOPSIS, VIKOR, and SPOTIS. The obtained results have high similarity among each other, which was measured by Spearman's weighted correlation coefficient and WS ranking similarity coefficient. Furthermore, the proposed approach showed high efficiency and adaptability of the generated results.

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Effect of Criteria Range on the Similarity of Results in the COMET Method

Shekhovtsov Andrii, Więckowski Jakub, Kizielewicz Bartłomiej, Sałabun Wojciech

Annals of Computer Science and Information Systems

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2021

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Vol. 25

453--457

EN

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 overestimation 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.