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In this study we propose a measure of the entropy of the norm (R, S) for q-row orthopair fuzzy sets (qROFS). The proposed entropy measure is validated both theoretically and practically to ensure validity. We also propose a simple methodology for the purpose of solving a multi-criteria decision-analysis problems using the introduced entropy measure. This method takes into account different circumstances of criteria weights, such as unknown weights, as well as other cases when the weights are not fully known. Finally, a demonstration with numerical examples for the proposed entropy has been provided to show how to apply the novel methodologies. [ABSTRACT FROM AUTHOR]

The alternative sources of energy have significantly improved quality and are more prevalent in recent years. Solar panels as one of these energy sources continue to be chosen for commercial and private usage. One of the more complex decisions is to choose components to installed in the solar system. All of the public available solar panels have eight important characteristics related to electricity efficiency and dimensions. However, there are many possible alternatives, so it is hard to say which one will be the most proper choice. MCDA methods can make this complex decision problem. This work presents an assessment of solar panels obtained by two popular MCDA methods, i.e., the COMET and TOPSIS techniques. Both methods are distance-based MCDA methods which are using characteristic points idea. However, the COMET method is the rank reversal phenomenon free method and return more accurate results. Next, we present a comparison to find the most rational solar panel from the defined set of alternatives considered their criteria. For this purpose, the weights vector is determined by using three methods. Therefore, results are determined based not only on the used MCDA method but also on the applied weights of the criteria. [ABSTRACT FROM AUTHOR]

Decision-making processes increasingly use models based on various methods to ensure professional analysis and evaluation of the considered alternatives. However, the abundance of these methods makes it difficult to choose the proper method to solve a given problem. Also, it is worth noting whether different results can be obtained using different methods within a single decision problem. In this paper, we used three selected Multi-Criteria Decision Analysis (MCDA) methods called COMET, TOPSIS, and SPOTIS in order to examine how the obtained rankings vary. The selection of material suppliers was taken into consideration. The equal weights, entropy and standard deviation methods were used to determine the weights for criteria. Final preferences values were then compared with the WS similarity coefficient and weighted Spearman correlation coefficient to check the similarity of the received rankings. It was noticed that in the given problem, all of the methods provide highly correlated results, and the obtained positional rankings are not significantly different. However, practical conclusions indicate the need to look for improved solutions in the correct and accurate assessment of suppliers in a given period. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Actual existing multi-criteria decision-making (MCDM) methods yield results that may be questionable and unreliable. These methods very often ignore the issue of uncertainty and rank reversal paradox, which are fundamental and important challenges of MCDM methods. In response to these challenges, the Characteristic Objects Method (COMET) was developed. Despite it being immune to the rank reversal paradox, classical COMET is not designed for uncertain, decisional problems. In this paper, we propose to extend COMET using hesitant fuzzy set (HFS) theory. Hesitant fuzzy set theory is a powerful tool to express the uncertainty that derives from an expert comparing characteristic objects and identifying membership functions for each criterion domain. We present the theoretical foundations and principles of COMET, and we provide an illustrative example to show how COMET handles uncertain decision problems both practically and effectively. [ABSTRACT FROM AUTHOR]

The correlation between two different variables possesses an important place in the field of statistics. Correlation is used to estimate the change in one variable associated with another variable. The concept of correlation is well known but it is not used within intuitionistic 2-tuple fuzzy linguistic (I2TFL) information. To investigate the best alternative among different alternatives in multi-criteria group decision-making (MCGDM) problems, our aim is to propose a formula for the correlation coefficient based on I2TFL information. A new type of information energy for I2TFL element is defined first and then the correlation coefficient between I2TFL information are discussed based on this information energy. In addition, considering that different I2TFL elements may have different criteria weights, the weighted correlation coefficients are further investigated. Some of the properties of the proposed correlation coefficient are also mentioned and verified. Furthermore, best-worst method (BWM) is expanded to uncertain situations like I2TFL BWM, where the data is expressed in I2TFL form. Utilizing the idea of BWM, linearly constrained optimization problems are framed to acquire weights of criteria in the context of I2TFL environment. Two numerical illustrations are described to confirm the effectiveness of the proposed work in the cases where the criteria weights are either known or unknown. Finally, comparative discussions between the proposed approach and existing practices are taken to reveal the importance of our work. • Multi-criteria group decision-making based on the correlation coefficient. • Intuitionistic 2-tuple fuzzy linguistic environment (I2TFL). • Correlation coefficient between I2TFL. • Best-Worst method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new intuitionistic entropy measurement for multi-criteria decision-making (MCDM) problems. The entropy of an intuitionistic fuzzy set (IFS) measures uncertainty related to the data modelling as IFS. The entropy of fuzzy sets is widely used in decision support methods, where dealing with uncertain data grows in importance. The Complex Proportional Assessment (COPRAS) method identifies the preferences and ranking of decisional variants. It also allows for a more comprehensive analysis of complex decision-making problems, where many opposite criteria are observed. This approach allows us to minimize cost and maximize profit in the finally chosen decision (alternative). This paper presents a new entropy measurement for fuzzy intuitionistic sets and an application example using the IFS COPRAS method. The new entropy method was used in the decision-making process to calculate the objective weights. In addition, other entropy methods determining objective weights were also compared with the proposed approach. The presented results allow us to conclude that the new entropy measure can be applied to decision problems in uncertain data environments since the proposed entropy measure is stable and unambiguous. [ABSTRACT FROM AUTHOR]

The necessity of making reliable decisions is exceptionally important in the field of sustainable development, particularly when evaluating the management of renewable energy sources. A thorough analysis becomes imperative in complex decision problems where various factors influence outcomes. Multi-Criteria Decision Analysis (MCDA) methods have emerged as valuable tools for addressing such challenges, enabling decision-makers to navigate through conflicting criteria and make informed choices. Combined with sensitivity analysis approaches, comprehensive assessments can be achieved, ensuring the robustness of decision-making processes. To increase the reliability of the results, different aspects of input data fluctuations should be examined to provide a broader view of the stability of the results. This paper proposes a comprehensive multi-dimensional sensitivity analysis approach to assess the robustness of renewable energy source (RES) development in selected European countries. By evaluating RES management in terms of electricity and energy consumption and generation, the study addresses key components of sustainable development. It offers a holistic perspective on result reliability and stability by analyzing five sensitivity dimensions: a comparative analysis of four MCDA methods, varying criteria weights scenarios, probabilistic modifications, criteria relevance identification, and ranking stability. This approach enhances decision-making in sustainable energy development, providing valuable insights for policymakers on prioritizing sustainable technologies. The provided open-source implementation promotes transparency and accessibility in decision support systems. • Novel sensitivity analysis for robust RES in Europe. • Advances decision-making in sustainable energy. • Guides policy with insights & open-source framework. [ABSTRACT FROM AUTHOR]

The paper undertakes the problem of proper structuring of multi-criteria decision support models. To achieve that, a methodological framework is proposed. The authors' framework is the basis for the relevance analysis of individual criteria in any considered decision model. The formal foundations of the authors' approach provide a reference set of Multi-Criteria Decision Analysis (MCDA) methods (TOPSIS, VIKOR, COMET) along with their similarity coefficients (Spearman correlation coefficients and WS coefficient). In the empirical research, a practical MCDA-based wind farm location problem was studied. Reference rankings of the decision variants were obtained, followed by a set of rankings in which particular criteria were excluded. This was the basis for testing the similarity of the obtained solutions sets, as well as for recommendations in terms of both indicating the high significance and the possible elimination of individual criteria in the original model. When carrying out the analyzes, both the positions in the final rankings, as well as the corresponding values of utility functions of the decision variants were studied. As a result of the detailed analysis of the obtained results, recommendations were presented in the field of reference criteria set for the considered decision problem, thus demonstrating the practical usefulness of the authors' proposed approach. It should be pointed out that the presented study of criteria relevance is an important factor for objectification of the multi-criteria decision support processes. [ABSTRACT FROM AUTHOR]

Multi-Criteria Decision-Analysis (MCDA) methods are successfully applied in different fields and disciplines. However, in many studies, the problem of selecting the proper methods and parameters for the decision problems is raised. The paper undertakes an attempt to benchmark selected Multi-Criteria Decision Analysis (MCDA) methods. To achieve that, a set of feasible MCDA methods was identified. Based on reference literature guidelines, a simulation experiment was planned. The formal foundations of the authors' approach provide a reference set of MCDA methods (Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), Complex Proportional Assessment (COPRAS), and PROMETHEE II: Preference Ranking Organization Method for Enrichment of Evaluations) along with their similarity coefficients (Spearman correlation coefficients and WS coefficient). This allowed the generation of a set of models differentiated by the number of attributes and decision variants, as well as similarity research for the obtained rankings sets. As the authors aim to build a complex benchmarking model, additional dimensions were taken into account during the simulation experiments. The aspects of the performed analysis and benchmarking methods include various weighing methods (results obtained using entropy and standard deviation methods) and varied techniques of normalization of MCDA model input data. Comparative analyses showed the detailed influence of values of particular parameters on the final form and a similarity of the final rankings obtained by different MCDA methods. [ABSTRACT FROM AUTHOR]

Over the past few decades, several researchers and professionals have focused on the development and application of multi-criteria group decision making (MCGDM) methods under a fuzzy environment in different areas and disciplines. This complex research area has become one of the more popular topics, and it seems that this trend will be increasing. In this paper, we propose a new MCGDM approach combining intuitionistic fuzzy sets (IFSs) and the Characteristic Object Method (COMET) for solving the group decision making (GDM) problems. The COMET method is resistant to the rank reversal phenomenon, and at the same time it remains relatively simple and intuitive in practical problems. This method can be used for both symmetric and asymmetric information. The Triangular Intuitionistic Fuzzy Numbers (TIFNs) have been used to handle uncertain data. This concept can ensure the preference information about an alternative under specific criteria more comprehensively and allows for easy modelling of symmetrical or asymmetrical linguistic values. Each expert provides the membership and non-membership degree values of intuitionistic fuzzy numbers (IFNs). So this approach deals with a different kind of uncertainty than with hesitant fuzzy sets (HFSs). The proposed combination of COMET and IFSs required an adaptation of the matrix of expert judgment (MEJ) and allowed to capture the behaviour aspects of the decision makers (DMs). Therefore, we get more reliable solutions while solving MCGDM problems. Finally, the proposed method is presented in a simple academic example. [ABSTRACT FROM AUTHOR]

A significant challenge in the current trend in decision-making methods is the problem's class in which the decision-maker makes decisions based on partially incomplete data. Classic methods of multicriteria decision analysis are used to analyze alternatives described by using numerical values. At the same time, fuzzy set modifications are usually used to include uncertain data in the decision-making process. However, data incompleteness is something else. In this paper, we show two approaches to identify fuzzy models with partially incomplete data. The monolithic approach assumes creating one model that requires many queries to the expert. In the structured approach, the problem is decomposed into several interrelated models. The main aim of the work is to compare their accuracy empirically and to determine the sensitivity of the obtained model to the used criteria. For this purpose, a study case will be presented. In order to compare the proposed approaches and analyze the significance of the decision criteria, we use two ranking similarity coefficients, i.e., symmetric r w and asymmetric W S . In this work, the limitations of each approach are presented, and the results show great similarity despite the use of two structurally different approaches. Finally, we show an example of calculations performed for alternatives with partially incomplete data. [ABSTRACT FROM AUTHOR]