Multi-Criteria Decision Analysis (MCDA) methods are widely applied in complex decision-making scenarios involving multiple, often conflicting criteria. While considerable research has focused on their performance under varying numbers of alternatives, the effect of changes in the number and importance of criteria, particularly in rank reversal-resistant methods, remains underexplored. This study investigates the stability of three rank reversal-resistant MCDA methods, namely the Reference Ideal Method (RIM), Stable Preference Ordering Towards Ideal Solution (SPOTIS), and the Characteristic Objects Method (COMET), under systematic changes in criteria inclusion. Through a series of 1,000 simulations with varying numbers of alternatives and criteria, the methods were tested for ranking consistency as criteria were removed in both ascending and descending order of importance. Results show that COMET was the most stable in high-dimensional problems, RIM performed best in mid-sized scenarios, and SPOTIS was more robust when more important criteria were removed. The findings provide valuable insights for selecting appropriate MCDA methods in dynamic decision environments and fulfill the study’s goal of assessing method sensitivity to criteria variation.

This paper investigates the impact of different relationship functions on the performance of the Ranking Comparison (RANCOM) method, a ranking-based approach to calculate criteria weights based on subjective preferences of decision-makers in the Multi-Criteria Decision Analysis (MCDA) field. Three relationship functions (three-value, ratio-based, and logarithmic ratio-based) were evaluated across varying decision contexts using simulated weights generated from Dirichlet distributions with different concentration parameters. The results indicate that no single function performs best in all scenarios. Instead, each excels under specific conditions of weight similarity. The ratio-based function performs best with diverse weights, the logarithmic ratio-based function is superior when weights are similar, and the three-value function remains robust under general conditions. These findings provide valuable guidelines for selecting relationship functions based on expected weight distributions. The study highlights the importance of aligning modeling techniques with decision context and opens avenues for further research into alternative relationship functions and their application in practical decision-making problems.

Decision-making involves various aspects of daily life, encompassing routine tasks, complex business strategies, and resource management. With problems often including multiple criteria, detailed analysis becomes imperative to ensure a reliable assessment. Consequently, diverse tools have emerged to aid decision-makers in making well-informed choices, with Multi-Criteria Decision Analysis (MCDA) methods standing out for structured evaluations and adaptable processes. MCDA methods accommodate both crisp and fuzzy data, handling uncertainties inherent in decision problems. However, the abundance of methods poses a challenge in selecting the most suitable approach. Comparative analyses underscore the variability in outcomes, emphasizing the importance of employing multiple techniques for robust decision-making. Within resource management, MCDA methods offer versatile solutions, integrating expert knowledge and fuzzy logic to enhance reliability. As technological advancements introduce novel tools, empirical validation becomes crucial. Fuzzy ranking emerges as a promising approach, offering comprehensive insights into decision stability and robustness. This study applies selected MCDA methods within an Intuitionistic Fuzzy (IF) environment to personnel selection, analyzing multiple criteria with the participation of decision-makers. Through Monte Carlo simulation and fuzzy ranking, the study validates the efficacy of fuzzy ranking in practical multi-criteria decision-making scenarios, offering insights into decision robustness and stability. The proposed research provides a comprehensive approach to personnel selection, producing reliable and robust recommendations under changing input conditions.

In the area of decision-making, where complexities often exceed experts’ analytical capabilities, this study addresses a critical gap by introducing a novel methodology for sensitivity analysis within the Multi-Criteria Decision Analysis (MCDA) problems. Current analytical frameworks struggle to comprehensively consider potential modifications to values within decision matrices, making it challenging to understand their impact in detail. To address this challenge, decision-makers need enhanced tools, and MCDA methods combined with systematic changes in selected elements of the decision matrix stand out as a promising approach. However, existing studies primarily focus on different criteria-weight scenarios, leaving an unexplored gap in the simultaneous modification of multiple values within the decision matrix. This paper integrates sensitivity analysis within the MCDA methods, extending its role in the comprehensive assessment of decision problems. Sensitivity analysis becomes crucial in offering decision-makers a broader perspective, aiding them in navigating the complexities of decision-making in dynamic environments. Recognizing the unexplored potential in sensitivity analysis, the study proposed a novel approach of simultaneous modification of multiple values in a decision matrix, offering an extension of conventional one-at-a-time modifications. As a Proof of Concept (PoC) research work, the study investigated whether the determined approach provides divergent preference scores compared to the traditional single-modification method across ten different MCDA techniques. The results showed that modifying multiple values simultaneously produced different preference scores of alternatives than in the case of a conventional single change, showing that additional insight knowledge could be extracted from this type of sensitivity analysis.

This paper provides a comparative analysis of three selected Multi-Criteria Decision Analysis (MCDA) methods in a practical decision problem to examine the robustness of the obtained results. The Complex Proportional Assessment (COPRAS), Preference Ranking Organization METHod for Enrichment of Evaluations (PROMEHTEE) II, and Evaluation based on Distance from Average Solution (EDAS) methods were utilized for the evaluation purposes, while the Ranking Comparison (RANCOM) method was applied to determine criteria weights. The application was directed toward sustainable development management in selected European countries considering different energy sources in the consumption share per capita. The obtained results showed, that depending on the used MCDA method, the ranking of countries differed, thus showing that the evaluation process is sensitive to changing assessment methods.

This paper presents a comparative analysis of selected distance metrics within the intuitionistic fuzzy environment in Multi-Criteria Decision Analysis (MCDA). The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, combined with intuitionistic fuzzy sets (IFS), was employed to investigate how different distance metrics influence decision-making outcomes. The study examines the sensitivity of the obtained recommendations to the variation in the calculation formula used to determine the distance between two IFS. The practical problem of selecting a site for a large-scale rooftop photovoltaic project served as the case study for this comparison. The results indicated that using different distance metrics within the IF-TOPSIS method led to varying preference score ranges and differing rankings, particularly in the middle portions of the rankings. The findings underscore the sensitivity of MCDA methods to the choice of distance metrics used in the calculation process.

In today's world, addressing multi-criteria decision problems presents a considerable challenge due to their inherent complexity. Decision-makers face diverse and often conflicting factors that exceed their analytical capabilities and complicate the identification of the best solutions. Within this intricate field, Multi-Criteria Decision Analysis (MCDA) serves as an important decision support tool. The complex nature of these problems introduces numerous variables that influence the final choice. This complexity requires sensitivity analysis as an indispensable part of the assessment process. It allows for an examination of how changes in input data can affect the outcomes, providing valuable insights into the stability and reliability of the decision-making process. Based on the state-of-the-art, this study identifies a gap in sensitivity analysis, particularly in assessing the impact of modifications to the decision matrix. Although one-at-a-time (OAT) modification is efficient, simultaneously changing multiple elements provides nuanced insights into decision-matrix interdependencies. Therefore, this research introduces a novel sensitivity analysis method, the COMprehensive Sensitivity Analysis Method (COMSAM), which systematically modifies multiple values within the decision matrix. The COMSAM allows for a detailed problem space exploration, providing insights into alterations across criteria values. Furthermore, the method represents the preferences obtained from the evaluations as interval numbers, offering decision makers additional knowledge about the uncertainty of the analyzed problem. This study advances the field of sensitivity analysis, providing a new perspective on changes in multiple values' simultaneous influence on the robustness of the MCDA result.

In recent years, complex networks have gained significant attention for their practical potential in data analysis and decision-making.However, assessing node relevance in complex networks poses challenges, including subjectivity and difficulty reproducing criteria relationships.To address these issues, we propose MLP-COMET.This novel approach combines the Multi-Layer Perceptron (MLP) with the Characteristic Objects Method (COMET) in Multi-Criteria Decision Analysis (MCDA).MLP-COMET aims to re-identify decision models using MLP to evaluate characteristic objects.We evaluate the approach to assessing the complex network and demonstrate its effectiveness in evaluating without heavy reliance on domain experts.The MLP-COMET performance is evaluated through ranking comparisons, showing a strong correlation with reference expert rankings.We also analyze the impact of training sample size and number of characteristic objects on ranking similarity, observing high stability and similarity using the rw metric.MLP-COMET offers an effective and reliable tool for evaluating complex networks and facilitating decision-making processes.

We encounter uncertainty in many areas.In decision-making, it is an aspect that allows for better modeling of real-world problems.However, many methods rely on crisp numbers in their calculations.It makes it necessary to use techniques that perform this conversion.In this paper, we address the problem of score functions assessment regarding their effectiveness and usefulness in the decision-making field.The selected methods were used to convert the intuitionistic fuzzy set matrix into crisp data, then used in the multi-criteria assessment.Managing the theoretical problem showed that the used techniques provide high similarity values.Moreover, they proved to be helpful when dealing with intuitionistic fuzzy sets in the decision-making area.

Using fuzzy logic in multi-criteria problems allows real-world problems to be modeled with greater accuracy. In addition, it is possible to solve problems in which all data are incomplete. The difficulty may be the choice of an appropriate technique leading to a ranking calculation. Methods fully integrated with fuzzy logic can be used. It is also possible to convert fuzzy data to crisp values and then apply traditional MCDA methods. In this paper, the performance of the TOPSIS method in a crisp and fuzzy environment was analyzed. The approaches of operating fully on uncertain data when calculating preference values were compared with converting data to crisp values using selected membership functions. The research has shown that significant differences and discrepancies in how the alternatives are classified are noticeable in the rankings.

The practical capabilities of decision support systems are beneficial in many complex problems. They aim to equip the decision-maker with knowledge about the preferred choices from the set under consideration. Often, there are minor differences between the alternatives analyzed, making it necessary to determine whether changes in the parameters characterizing them can influence their final position. For this purpose, a sensitivity analysis of the solutions can be used to examine the resistance of the results to changes. In this paper, we address the problem of performing the sensitivity analysis using MCDA methods. Most studies focus on testing the sensitivity of rankings of popular methods. However, their main disadvantage is their susceptibility to the phenomenon of ranking reversal. It may distort the results obtained in a sensitivity analysis. Therefore, it is worth using methods resistant to the ranking reversal phenomenon for this purpose. The SPOTIS and COMET methods were used in a theoretical multi-criteria problem, where the calculated results were then subjected to sensitivity analysis. The study showed that the SPOTIS method tends to be more robust to the computed results.

Multi-Criteria Decision Analysis (MCDA) methods enable a comprehensive analysis of decision options to identify the most preferred values. However, the abundance of these techniques, using different transformations in the calculations, can cause a divergence of results. However, the resulting rankings should be as consistent and reliable as possible. In this paper, we used the TOPSIS, COPRAS, SPOTIS, and COMET methods to examine the consistency of their results in the practical problem of laptop evaluation. The rankings were then compared with the reference ranking. The research showed that among the methods listed, the COPRAS method's results differed the most from the others. In turn, this technique ensured a ranking in line with the reference ranking. Based on the results, it can be established that the methods used are characterized by high consistency of results.

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.

Multi-Criteria Decision Analysis methods are readily used in decision support models. However, many methods in this group of methods cause a problem with choosing an appropriate method for a given problem. One of such methods is COMET (Characteristic Objects Method), which compares pairs of Characteristic Objects (COs) when calculating preference values of alternatives. In this paper, the COMET method was used to create a model that evaluates swimming athletes regarding their predisposition to compete in freestyle sprint events. Besides, to reduce the complexity of the problem, a division of the initial structure was applied, which made it possible to reduce the number of comparisons to 0.7e-8 % of their initial number. To verify the obtained results, it was decided to use selected MCDA methods to solve the same problem. The correlation between the rankings was examined using the Pearson correlation coefficient and the WS similarity coefficient. Based on the results obtained, it can be concluded that the proposed model gives results that guarantee a high correlation with the results from the other methods. Moreover, it can be useful in evaluating and selecting swimming athletes for participation in given events.

Solving logic puzzles using selected algorithms is an interesting problem in which the efficiency of the methods is essential. One such task is solving nonograms, where board fields should be filled to meet the conditions for rows and columns, respectively. The number of methods possible to use opens the possibility to compare their efficiency and quality of operation. In this paper, we decided to analyze two algorithms belonging to different groups of methods to determine their effectiveness. A modified Depth-First Search (DFS) method and a soft computing method based on permutations generation were chosen and used to solve selected nonograms. The research was conducted on four board sizes, and the results showed that the effectiveness of the used methods mainly depends on the level of nonogram complexity. The algorithm results with permutations were stable, while in contrast to the DFS method, it did not always guarantee a complete solution.

Multi-criteria methods are used in systems designed to support decision-making or for prediction. One of these methods is the Characteristic Objects Method (COMET), which uses expert knowledge to calculate preference values when creating a rule base. The number of Characteristic Objects (COs) pairs necessary to perform comparisons depends on the model’s structure, the number of criteria and characteristic values. In this paper, it was decided to build a complex MCDM model based on the COMET method, which was used to predict the chances of overtaking during pit stops in Formula 1 races. To improve the performance of the model and reduce the necessary pairwise comparisons of COs, it was decided to split the structure into submodels aggregating criteria with similar characteristics to reduce the complexity of the problem. Additionally, the influence of each criterion on the obtained preference values and the final result was examined. By restructuring the model, it was possible to reduce the number of comparisons while maintaining the designed model’s correct operation.

Multi-criteria methods are an important element used in developing decision support systems aimed at helping the decision-maker choose the optimal decision. It is necessary to define weights for the criteria for which appropriate methods are used. However, it is important to check whether the results obtained by these methods are correlated with each other. In this paper, the energy-efficient material selection problem addressed by Bhomwik and Gangwar was used, where TOPSIS and entropy methods were used by researchers. COMET, VIKOR, PROMETHEE II, SPOTIS and COPRAS methods were selected in combination with entropy, equal weights and standard deviation methods to investigate the correlation with other weighting methods and MCDA methods, which provided a comprehensive results comparison. It was noted that although there were similarities between the rankings, they were not significant enough for the weighting methods to be used equally without changes in the final rankings occurring.

Multi-Criteria Decision Analysis (MCDA) methods are becoming more popular as the complexity of decisions is rising. As more people are trying to apply such a method, the mistakes are often made and duplicated through numerous use cases. In this paper, the discussion on a given topic is made. We highlight mistakes made on real-life examples and show how to make sure none of them is made in the future. Moreover, the Characteristic Object’s Method (COMET) is shown as an alternative to so popular Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method. The results were then compared using selected similarity coefficients to emphasize the correlation of the resulting rankings. The research showed that every single step of the decision-making method is needed to be correctly made to make sure that received results are reasonable.

Our decisions are usually influenced by many factors, which makes it challenging to choose the optimal solution. The problem may be to determine which aspects should be taken into account and how they influence the final result. Multi-criteria decision analysis (MCDA) methods are helpful in this case, and they allow to evaluate defined alternatives despite the lack of precise expert knowledge. In this paper, the COMET (Characteristic Objects Method) method was used to create a multi-criteria model to assess the progression of swimmers over the season. Presented alternatives were divided into two groups of players, and after obtaining preference values from the model, they were compared with each other using statistical values. The research has shown that in the proposed model created based on expert knowledge, the size of the progress combined with the best FINA (Fédération Internationale de Natation) score can be an effective indicator of the swimmers’ progress.

Many decisions made in different areas of life require a certain number of criteria to be taken into account to help find the optimal solution. The problem may be to determine whether the way in which we represent the input has an impact on the final result. It means whether or not the normalization affects the results achieved by using multi-criteria decision analysis (MCDA) methods. In this paper, we examine the influence of normalization on the results obtained by the VIKOR method. This issue will be addressed based on the training management problem. First, we prepare the raw decision matrix and its forms after normalizations. According to the VIKOR method, we use a calculating procedure for all cases and compare the obtained rankings using selected similarity coefficients, which showed to what extent these rankings are similar. The results obtained as a result of the conducted research show that the presentation of the input data has an impact on the final obtained rankings.

The methods of multi-criteria decision making are more and more willingly used as assistance in finding an optimal solution to the problem. As the family of these methods grows, choosing the appropriate technique and whether the use of multiple methods for one problem will provide a similar final result may be a problem. In this paper, extensions of the classic TOPSIS method have been used to show one decision problem results. We used the Interval TOPSIS, Bag-Based TOPSIS, and Fuzzy TOPSIS methods to examine the influence of used methods to final rankings. They solved the theoretical problem of selecting a high-protein supplement for persons in power training. The results were then compared using selected similarity coefficients to emphasize the correlation between the resulting rankings. The research showed that the method used has an impact on the final ranking, which was confirmed by the indicators obtained through the similarity coefficients.