International audience

Evaluating cities based on cost of living and quality of life can be a complex task without the support of a structured decision-making framework. To address this challenge, various methods from the Multi-Criteria Decision Analysis (MCDA) domain can be utilized to assist in solving such decision problems. In this paper, we propose a novel RANCOM-RAM (RANking COMparison - Root Assessment Method) framework, enhanced with a fuzzy ranking approach, to provide a robust tool for city evaluation in terms of living costs. To demonstrate the framework, we present a case study evaluating selected European Union capitals using criteria such as average prices of everyday goods, rent, and income levels. The results show that, under the identified weights, Luxembourg, Brussels, and Berlin occupy the top three positions in the ranking. However, the fuzzy ranking approach reveals that cities like Sofa or Budapest can achieve high rankings under alternative weighting scenarios, highlighting the flexibility of the proposed method.

Multiple-Criteria Model Analysis (MCMA) is the well established area of research, with rich collection of diverse methods and successful applications in science, and in model-based decision-making support in industry, economy, and policy-making. Solutions of multiple-criteria problems are objectively incomparable. Therefore, the solution choice depends on the preferences, and consequently, the MCMA research focused on methods based on the user preferences.However, scientific problem analysis should be objective, i.e., preference-free in terms of reaching a better goal for some criterion while compromising (necessary when a change of Pareto-efficient solution is considered) another goal. Hence, scientific MCMA requires a uniform representation of all Pareto-efficient solutions.The contribution discusses the novel method for effective generation of the Pareto-set representation, and shows its relations with the user-guided Pareto-front exploration methods. The presented method is illustrated by the model supporting technology choice for the liquid fuel production in China. The software implementation of the method is available under the GNU General Public License v2.0.

This paper is about the Compromise Ranking Problem (CRP), a well-known problem in the social choice theory. According to the famous Arrow’s theorem there is no voting method which is entirely satisfying and fairness if one accepts Arrow’s axioms. In this paper we formalize the problem as a minimisation problem in a discrete finite search space. We attempt to solve it based on the Least Squares (LS) approach thanks to some appealing metrics to get the optimal CRP solution. Surprisingly, we show that the optimal consensus (compromise) ranking solution disagrees with the commonsense solutions in four simple interesting examples. The search for an optimal solution in agreement with the commonsense appears to be an open very challenging question and our paper warns the users about the impossibility of the main current methods to provide acceptable solutions even for the rather simple examples considered in this work.

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.

In every decision-making problem which involves two or more criteria, there is to identify the relative importance of those criteria in order to make a proper decision. Very often, a decision-makers employee, for this purpose, subjective weighting methods, such as Analytic Hierarchy Process (AHP) or Ranking Comparison (RANCOM). However, there is no simple way to compare the quality of the weights identification using different methods. To address this issue, this paper proposes a simple but Efficient Weights Similarity Coefficient, which allows us to evaluate the relative performance of different subjective weighting methods. Furthermore, we propose a framework that utilizes the proposed coefficient in order to provide more complete comparison results. To demonstrate the applicability and effectiveness of the proposed framework, a case study is performed to compare two popular weighting methods: AHP and RANCOM. The results of the comparison prove that proposed coefficient with the combination of the proposed framework is an Efficient instrument for weighing methods comparison.

In this paper, we show the practical application of two recently proposed Multi-Criteria Decision Analysis (MCDA) methods, namely the Stable Preference Ordering Towards the Ideal Solution (SPOTIS) and the Reference Ideal Method (RIM) methods. Both of these methods can utilize the Expected Solution Point (ESP) concept, which allows it to easily reflect the decision-maker's or the customer's preferences and expectations. We show the comparison of those methods in the practical study case of laptop choice for the customer with specific needs and expectations for the hardware expressed using ESP. The comparison also includes rankings built toward an optimal solution to underline the necessity of such an approach as the Expected Solution Point. We also use the recently developed Ranking Comparison (RANCOM) method to identify criteria weights to include customer preferences in the weights. The paper also contains a broad discussion of the obtained results and limitations of the presented methods.

This study introduces an extension of the Characteristic Objects Method (COMET) by incorporating the Expected Solution Point (ESP) approach to enhance individual decision-making. By integrating the ESP methodology, we aim to simplify decision-making, particularly when facing a vast decision matrix concerning multiple criteria. We demonstrate the efficacy of the proposed ESP-COMET method by applying it with one or two ESPs, thereby examining its impact on ranking alternatives according to personal customer preferences. In order to provide a practical example, we use a dataset of used cars to show how the proposed method facilitates the selection of the most suitable vehicle based on individual needs. The main goal of this paper is to show how the ESP-COMET method can help to adapt decisions to individual needs and expectations. We also introduce a novel and efficient approach for determining characteristic values in personalized decision-making, which plays a crucial role in ensuring the higher accuracy of the ESP-COMET method. Additionally, we compare the proposed approach with such methods as Stable Preference Ordering Toward the Ideal Solution (SPOTIS) and Reference Ideal Method (RIM). This study addresses the research gap by introducing an easy way to define customer preferences within COMET, enabling responsible decision-making.

In many cases involving multi-criteria decisionmaking, we need compromise solutions.This is a crucial aspect due to the specific characteristics of decision problems.However, the proposed compromise 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.

Much effort in modern scientific work has been put into improving objective decision-making. However, very often, it turns out that some problems do not have objective solutions that ft everyone—for example, buying a cell phone or a car. If one model could meet the expectations of each user, then we would not have so much diversity in the market. This observation motivates to work on customization in the decision-making process. In this work, we show approaches that help customize the decision-making process for a specific customer. In addition to expert methods for determining importance weights, the characteristic object method or the SPOTIS method could be used for this purpose. The presented research shows how the Expected Solution Point (ESP) can be used to make individual decisions and thus facilitate the process of customization. For this reason, we compare the objective result obtained using Ideal Solution Point (ISP) and results for artificial decision-makers using simulated ESP vectors. Simulation studies on a real database demonstrate the usefulness of the ESP approach to expressing personalized preferences.

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.

It is common practice in the MCDA to use several multi-criteria decision methods and then compares obtained rankings with one or two different rank correlation coefficients. The problem is that different rank correlation coefficient gives different values for the same pair of rankings, and the number of studies which tries to investigate it is small. Studying the similarity of rankings is a very important challenge in multi-criteria decision support, and the coefficients themselves seem to be the most practical ways of evaluating rankings. This paper compares chosen rank correlation coefficients to show how much different they are. Spearman’s, Weighted Spearman’s, Kendall Tau and Rank similarity correlation coefficient are compared statistically. The paper confirms that the coefficients are closely related, and their dependence is graphically represented, which initiates research towards allows for their better selection in the future. In conclusions, directions of further development are indicated.

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.

The TOPSIS method is widely used to support multi-criteria decision-making processes. In this method, one of the most important challenges is to choose an appropriate method for standardizing the decision matrix. There is a problem with determining the impact of standardization on the final result. Additionally, a significant problem is how to identify the criterion weighting vector. In this paper, we present a solution to the problem taken from the literature using four different methods of normalization. Next, we present how to calculate the final ranking without identifying the weights using the COMET method. The most important contribution is to confirm that basically, each normalization method has returned a different ranking order. The real ranking order can only be one. So when it comes to the accuracy of the results, it is essential to compare the extent to which the ranking pairs are similar to each other. The obtained results were compared using three ranking similarity coefficients.

Multi-criteria decision-methods (MCDA) has a broad field of applications in various areas, such as engineering, logistic, health management, and others. Their main objective is to rank the decision variants, from the best to the worst. It is always essential to get a reliable solution to a decision problem. However, rankings obtained with different MCDA methods are often different, and that is why an interesting research gap is related to measuring the accuracy and reliability of MCDA methods. In this paper, we examine how much different can be rankings obtained using TOPSIS and VIKOR methods. For this purpose, we apply classical versions of TOPSIS and VIKOR methods to randomly generated decision matrices with different criteria and alternatives. Then, we compare the obtained ranking using three ranking similarity coefficients. The comparison results of conducted simulations are represented as boxplots, which contain the primary distribution of similarity of results calculated using the tested methods. The work is finished with a discussion and conclusions on the results in different classes of problems.