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Correlation is considered the most important factor in analyzing the data in statistics. It is used to measure the movement of two different variables linearly. The concept of correlation is well-known and used in different fields to measure the association between two variables. The hesitant 2-tuple fuzzy linguistic set (H2FLS) comes out to be valuable in addressing people's reluctant subjective data. The purpose of this paper is to analyze new correlation measures between H2FLSs and apply them in the decision-making process. First and foremost, the ideas of mean and variance of hesitant 2-tuple fuzzy linguistic elements (H2FLEs) are introduced. Then, a new correlation coefficient between H2FLSs is established. In addition, considering that different H2FLEs may have different criteria weights, the weighted correlation coefficient and ordered weighted correlation coefficient are further investigated. A practical example concerning the detailed procedure of solving problems is exemplified to feature the reasonableness and attainability of the proposed technique in situations where the criteria weights are either known or unknown. When the weight vector is unknown, the best-worst method (BWM) is used to acquire the criteria weights in the context of a hesitant 2-tuple fuzzy linguistic environment. Furthermore, a comparative study is undertaken with current techniques to provide a vision into the design decision-making process. Finally, it is verified that the proposed correlation coefficient between H2FLSs is more satisfactory than the extant ones, and the correlation coefficient with the weights of criteria being either known or unknown is applicable., Competing Interests: The authors have declared that no competing interests exist.

A fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a significant problem in its uses, i.e., considerable data loss. The probabilistic hesitant fuzzy set (PHFS) has been proposed to improve the HFS. It provides probability values to the HFS and has the ability to retain more information than the HFS. Previously, fuzzy regression models such as the fuzzy linear regression model (FLRM) and hesitant fuzzy linear regression model were used for decision making; however, these models do not provide information about the distribution. To address this issue, we proposed a probabilistic hesitant fuzzy linear regression model (PHFLRM) that incorporates distribution information to account for multi-criteria decision-making (MCDM) problems. The PHFLRM observes the input-output (IPOP) variables as probabilistic hesitant fuzzy elements (PHFEs) and uses a linear programming model (LPM) to estimate the parameters. A case study is used to illustrate the proposed methodology. Additionally, an MCDM technique called the technique for order preference by similarity to ideal solution (TOPSIS) is employed to compare the PHFLRM findings with those obtained using TOPSIS. Lastly, Spearman's rank correlation test assesses the statistical significance of two rankings sets.

The Pythagorean fuzzy sets conveniently capture unreliable, ambiguous, and uncertain information, especially in problems involving multiple and opposing criteria. Pythagorean fuzzy sets are one of the popular generalizations of the intuitionistic fuzzy sets. They are instrumental in expressing and managing hesitant under uncertain environments, so they have been involved extensively in a diversity of scientific fields. This paper proposes a new Pythagorean entropy for Multi-Criteria Decision-Analysis (MCDA) problems. The entropy measures the fuzziness of two fuzzy sets and has an influential position in fuzzy functions. The more comprehensive the entropy, the more inadequate the ambiguity, so the decision-making established on entropy is beneficial. The COmplex PRoportional ASsessment (COPRAS) method is used to tackle uncertainty issues in MCDA and considers the singularity of one alternative over the rest of them. This can be enforced to maximize and minimize relevant criteria in an assessment where multiple opposing criteria are considered. Using the Pythagorean sets, we represent a decisional problem solution by using the COPRAS approach and the new Entropy measure.

The extension of intuitionistic fuzzy sets (IFS) to Pythagorean fuzzy sets (PFS) is a significant advancement, addressing the inherent limitations of IFS. This study introduces a novel entropy measure specifically designed for Pythagorean fuzzy sets, establishing its axiomatic definition and presenting key properties. Decision making guided by entropy is advantageous, as it effectively mitigates ambiguity with increasing entropy values. Furthermore, a numerical example is provided to facilitate a comparative assessment of our newly introduced entropy measure in contrast to existing PFS entropy measures. The validation of our findings is achieved through the application of the COPRAS method, which determines decision outcomes based on a multitude of influencing factors. Notably, the determination of weights in this method is underpinned by the utilization of our innovative entropy measure. [ABSTRACT FROM AUTHOR]

The ever-increasing demand for high-quality solutions drives research toward more sophisticated decision-making solutions. In the field of decision making, the ability to solve complex real-world problems is of paramount importance. To this end, fuzzy sets are used, which offer the possibility of incorporating uncertainty into the values describing decision options. This study focuses on Pythagorean fuzzy sets, an extension of classical fuzzy sets, providing even more tools for modeling real-world problems by presenting a distance measure for these specific sets. A verification of the characteristics of the proposed distance measure has been carried out, proving its validity. The proposed measure is characterized by a more straightforward formula and thus simplifies the calculations. Furthermore, to confirm its usability, a multi-criteria decision-making methodology is presented, the results of which are compared with two multi-criteria decision-making methods, namely, PF-TOPSIS and PF-VIKOR, and another distance measure previously presented in the literature. The comparative analysis highlights lower variability in terms of preference values calculated using the proposed distance measure, which confirms the stability and reliability of the newly proposed distance measure while maintaining low computational complexity. Moreover, a high correlation with rankings calculated using PF-TOPSIS ensures its utility in terms of decision making. [ABSTRACT FROM AUTHOR]

One of the main challenges in the Multi-Criteria Decision Analysis (MCDA) field is how we can identify criteria weights correctly. However, some MCDA methods do not use an explicitly defined vector of criterion weights, leaving the decision-maker lacking knowledge in this area. This is the motivation for our research because, in that case, a decision-maker cannot indicate a detailed justification for the proposed results. In this paper, we focus on the problem of identifying criterion weights in multi-criteria problems. Based on the proposed Characteristic Object Method (COMET) model, we used linear regression to determine the global and local criterion weights in the given situation. The work was directed toward a practical problem, i.e., evaluating Formula One drivers' performances in races in the 2021 season. The use of the linear regression model allowed for identifying the criterion weights. Thanks to that, the expert using the system based on the COMET method can be equipped with the missing knowledge about the significance of the criteria. The local identification allowed us to establish how small input parameter changes affect the final result. However, the local weights are still highly correlated with global weights. The proposed approach to identifying weights proved to be an effective tool that can be used to fill in the missing knowledge that the expert can use to justify the results in detail. Moreover, weights identified in that way seem to be more reliable than in the classical approach, where we know only global weights. From the research it can be concluded, that the identified global and local weights importance provide highly similar results, while the former one provides more detailed information for the expert. Furthermore, the proposed approach can be used as a support tool in the practical problem as it guarantees additional data for the decision-maker. [ABSTRACT FROM AUTHOR]

In recent years, multi-criteria decision support methods have become widely used research tools by both scientists and practitioners. Theoretical works involving new multi-criteria methods and developments of existing methods immediately find applications in areas of business practice. This paper attempts to sort out the areas of application of MCDA methods. For this purpose, the relevant literature from 2018–2023 was reviewed. The inclusion selection criteria were defined as addressing multi-criteria practical issues, open accessibility, comprehensive research methodology and findings, and the use of an MCDA method in the evaluation process. Detailed research identified that the main areas of use of MCDA methods are healthcare, energy management, supplier selection, and transportation. Due to the timeliness and importance of the problem, a detailed study of the use of MCDA methods in sustainability issues was separated. The paper contributes contributions to both theory and economic practice. The article provides a series of recommendations both on the methodological side of the problems to be solved and shows the practical prism of individual decision models, offering ready-to-use decision models, and providing a comprehensive review of recent MCDA advancements, fostering informed and reliable decision-making. Additionally, this review sheds light on the latest developments in MCDA, emphasizing trends in Decision Support Systems (DSS) and prominent application areas in contemporary research. [ABSTRACT FROM AUTHOR]

The subject of electric vehicles (EVs) is constantly relevant from the perspective of climate change and sustainability. Multi-Criteria Decision Analysis (MCDA) methods can be successfully used to evaluate models of such vehicles. In many cases, the MCDA methods are modified to account for uncertainty in the data. There are many ways to express uncertainty, including more advanced ones, such as fuzzy sets, for example, but expressing attributes in terms of interval numbers remains a popular method because it is an easy-to-implement and easy-to-understand technique. This study focuses on interval extensions of the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method. It aims to compare the most popular extension proposed by Jahanshahloo and the proposed new modification, which returns the result in an interval form. Certain inconsistencies of the Jahanshahloo extension are discussed, and it is explained how the new extension avoids them. Both extensions are applied to an EV evaluation problem taken from the literature as an example for sustainable assessment. The results are then analyzed, and the question of whether the input data of the interval should receive an evaluation in the form of interval results is addressed. [ABSTRACT FROM AUTHOR]

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]

This paper proposes some operations on the cubic intuitionistic set along with useful properties. We propose the internal cubic intuitionistic set (ICIS), the external cubic intuitionistic set (ECIS), P-order, R-order order (P-(R-) order), P-union, R-union (P-(R-) union), P-intersection, and R-intersection (P-(R-) intersection). We further investigate several properties of the P-(R-) union and P-(R-) intersection of ICISs and ECISs, and present some examples in this context. Some important theorems related to ICISs and ECISs are also presented with proof. Finally, an application example is given to measure the effectiveness and significance of the proposed operations by solving a multi-criteria decision-making (MCDM) problem. [ABSTRACT FROM AUTHOR]

The notion of soft matrix plays a vital role in many engineering applications and socio-economic and financial problems. A picture fuzzy set has been used to handle uncertainty data in modeling human opinion. In this work, we recall the picture fuzzy soft matrix concept and its different subsequent classes. Also, different kinds of binary operations over the proposed matrices have been provided. The main contribution of this paper is that using the concept of choice matrix and its weighted form and the score matrix, a new algorithm for decision-making has been outlined by considering the picture of fuzzy soft matrices. The current challenge In the decision-making problems is that many qualitative and quantitative criteria are involved. Hence, the dimensionality reduction technique plays an essential role in simplicity and broader applicability in the decision-making processes. We present an algorithm for the reduction process using the proposed definitions of the object and parameter-oriented picture fuzzy soft matrix and the technique to find the threshold value for the provided information. Then, illustrative numerical examples have also been provided for each proposed algorithm. A detailed comparative study of the proposed techniques has also been carried out in contrast with other existing techniques. [ABSTRACT FROM AUTHOR]

As a new conception of IFS (Intuitionistic Fuzzy Sets), Pythagorean Fuzzy Sets can manage conflicted details more fexibly in decision-making. This extension has been used repeatedly for decision making. This is an important trend in decision making that is worth further study in combination with the study of entropy properties. This paper proposes a new entropy for the Pythagorean Fuzzy Sets and an application measure using the TOPSIS method. The new entropy approach was used to estimate the objective weights in the decision-making procedure. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) technique is presumed that the optimum alternative has the least distance from the positive and farthest from the negative ideal solution. This approach has been widely adopted to solve MCDM issues in multiple fields. We present a simple study case where we use TOPSIS and new entropy to solve the group decision-making problem. [ABSTRACT FROM AUTHOR]

Operational research is a scientific discipline related to the decision theory that allows determining solutions for specific problems related to, for example, widely understood transport. Increasingly popular in this field are issues related to the domain of the green urban transport. In order to support the decision-making process in this area, methods of multi-criteria decision analysis (MCDA) are used more and more often. However, if we solve a specific problem using different MCDA methods, we get different rankings, as each method has a different methodological basis. Therefore, the challenge is how to make a reliable decision. This paper presents a numerical example from the green urban transport domain, which is solved by six different MCDA methods that return a complete ranking. We measure the similarity of these rankings using coefficients rw and WS, and then we propose a simple way of determining a compromise solution. The obtained compromise ranking is guaranteed to be the best match to the selected MCDA methods' rankings, which is proved in the paper. Finally, possible directions for further development work are identified. [ABSTRACT FROM AUTHOR]

Chess is a very demanding sport as it requires advanced planning and strategic thinking skills. The degree of difficulty of the game also depends on the time allotted for a game, which can range from a few minutes to several tens of minutes. For this reason, the games are divided into several categories: standard, blitz, and bullet. However, as many chess players specialize in only some of the categories, it is difficult to determine the best chess player. It is very important to keep a proper ranking of the players. One way to recognize their achievements is the FIDE (Fédération Internationale des Échecs) titles awarded to the best players. However, there is still the problem of how to determine the best among the Grandmasters. There are many very talented players competing in chess. Creating a single ranking for all types of chess, regardless of the time allotted for the game, is a difficult challenge, as many undeniably outstanding chess players do not specialize in all types. Creating a ranking for only one type would not accurately describe the level of players. Therefore, a ranking was created based on all of them using the COMET method, which belongs to the multi-criteria decision-making methods (MCDA). It is based on fuzzy logic and uses characteristic objects for the assessment of alternatives, which guarantees immunity to the paradox of reversal rankings. Expert opinion was used for correct evaluation. This article presents the ranking of chess players regardless of the type of game they specialize in, to prove that it should be possible to identify the single best chess player. [ABSTRACT FROM AUTHOR]

Multi-criteria decision-making methods aim to solve complex problems under many factors. These methods each day are more frequently applied and improved. Many researchers try to find a reliable solution for a specific problem or group of problems. More and more often, new methods are created that certain target requirements. That is why solving the specific problem can be executed on multiple methods. In this paper, we provide three new solutions for the problem presented in the referenced paper. For this purpose, the Characteristic Object's Method (COMET), the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method and the Stable Preference Ordering Towards Ideal Solution (SPOTIS) method were used. The results were then compared using selected similarity coefficients to emphasize the correlation of the resulting rankings. The research showed that choosing a method will have an impact on results and should be considered with caution. [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]

In the field of Multi-Criteria Decision Analysis (MCDA), the deployment of sensitivity analysis has become a fundamental approach to testing the robustness and reliability of the results obtained. Its importance lies in its ability to gain additional insight into potential changes that affect the desirability of the decision variants being evaluated. Through different methodologies, it reveals the vulnerability of results to changes in the underlying data, thus offering valuable information to support decision making. This research paper highlights a compendium of 250 researches involving the application of sensitivity analysis in a multi-criteria context. Using a structured approach of the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology, this study provides a comprehensive review process. The main objectives are to identify and categorize common sensitivity analysis techniques explained in the literature and to describe a selected framework that facilitates the execution of these techniques. The research demonstrates the importance of sensitivity analysis to enhance the credibility of MCDA outcomes and contributes to the field of decision support. • Extensive review on comprehensive analysis of sensitivity analysis in MCDA. • Identifies main categories of sensitivity analysis methods in MCDA. • Review on techniques reveal stability of rankings. • Review on techniques reveal changes in alternatives' preferences. • Frameworks for conducting sensitivity analysis in MCDA. [ABSTRACT FROM AUTHOR]

Human activity is moving steadily to virtual reality. More and more, people from all over the world are keen on growing fascination with e-sport. In practice, e-sport is a type of sport in which players compete using computer games. The competitions in games, like FIFA, Dota2, the League of Legends, and Counter-Strike, are prestigious tournaments with a global reach and a budget of millions of dollars. On the other hand, reliable player ranking is a critical issue in both classic and e-sport. For example, the "Golden Ball" is the most valuable prize for an individual football player in the whole football history. Moreover, the entire players' world wants to know who the best player is. The position of each player in the ranking depends on the assessment of his skills and predispositions. In this paper, we studied identification of players evaluation and ranking obtained using the multiple-criteria decision-making based method called Characteristic Objects METhod (COMET) on the example of the popular game Counter-Strike: Global Offensive (CS: GO). We present a range of advantages of the player evaluation model created using the COMET method and, therefore, prove the practicality of using multi-criteria decision analysis (MCDA) methods to build multi-criteria assessment models in emerging areas of eSports. Thus, we provide a methodical and practical background for building a decision support system engine for the evaluation of players in several eSports. [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]

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. [ABSTRACT FROM AUTHOR]

In multi-criteria decision support methods a significant participation of the decision maker is required. The obtained assessment is subjective, and the decision-making process is usually difficult to automate. Limiting interaction with the decision-maker, while maintaining the characteristics of multi-criteria analysis seems to be a desirable direction of methodological research. One of the solutions going in this direction is the original multi-criteria PVM method. The applicability of the method has been verified in the context of research on the assessment of EU countries in terms of ensuring healthy living conditions. [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]

Effective evaluation of cities' and communities' sustainability is important for sustainable development. From a methodological point of view, Multi-Criteria Decision Analysis (MCDA) methods proved their usability in the sustainability evaluation domain. Nevertheless, the process of building a model in the classical MCDA paradigm is based on a single set of input data. Therefore, it may lead to oversimplification, especially in the domain of sustainability. Moreover, in addition to the current assessment, it is also important to know the dynamics of sustainability change over time. Therefore, this paper proposes an innovative sustainability assessment method that integrates the MCDA approach with the variability of the alternatives' performance measurement called Data vARIability Assessment Technique for Order of Preference by Similarity to Ideal Solution (the DARIA-TOPSIS method). This method was used to assess sustainable cities and communities in 26 European countries. Time-based analyses conducted using the DARIA-TOPSIS method for aggregated data (countries), individual sustainability dimensions, and alternatives proved our new approach's usefulness, suitability, and effectiveness in sustainable cities and society domain. [Display omitted] • A new MCDA method named the DARIA-TOPSIS. • A DARIA-TOPSIS based framework for sustainable cities and communities assessment. • The practical problem of sustainable cities and communities assessment. [ABSTRACT FROM AUTHOR]

Multi-criteria decision-making (MCDM) methods are associated with the ranking of alternatives based on expert judgments made using a number of criteria. In the MCDM field, the distance-based approach is one popular method for receiving a final ranking. One of the newest MCDM method, which uses the distance-based approach, is the Characteristic Objects Method (COMET). In this method, the preferences of each alternative are obtained on the basis of the distance from the nearest characteristic objects and their values. For this purpose, the domain and fuzzy numbers set for all the considered criteria are determined. The characteristic objects are obtained as the combination of the crisp values of all the fuzzy numbers. The preference values of all the characteristic object are determined based on the tournament method and the principle of indifference. Finally, the fuzzy model is constructed and is used to calculate preference values of the alternatives. In this way, a multi-criteria model is created and it is free of rank reversal phenomenon. In this approach, the matrix of expert judgment is necessary to create. For this purpose, an expert has to compare all the characteristic objects with each other. The number of necessary comparisons depends squarely to the number of objects. This study proposes the improvement of the COMET method by using the transitivity of pairwise comparisons. Three numerical examples are used to illustrate the efficiency of the proposed improvement with respect to results from the original approach. The proposed improvement reduces significantly the number of necessary comparisons to create the matrix of expert judgment. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods. [ABSTRACT FROM AUTHOR]

An expert may experience difficulties in decision making when evaluating alternatives through a single assessment value in a hesitant environment. A fuzzy linear regression model (FLRM) is used for decision-making purposes, but this model is entirely unreasonable in the presence of hesitant fuzzy information. In order to overcome this issue, in this paper, we define a hesitant fuzzy linear regression model (HFLRM) to account for multicriteria decision-making (MCDM) problems in a hesitant environment. The HFLRM provides an alternative approach to statistical regression for modelling situations where input–output variables are observed as hesitant fuzzy elements (HFEs). The parameters of HFLRM are symmetric triangular fuzzy numbers (STFNs) estimated through solving the linear programming (LP) model. An application example is presented to measure the effectiveness and significance of our proposed methodology by solving a MCDM problem. Moreover, the results obtained employing HFLRM are compared with the MCDM tool called technique for order preference by similarity to ideal solution (TOPSIS). Finally, Spearman's rank correlation test is used to measure the significance for two sets of ranking. [ABSTRACT FROM AUTHOR]

Decision support systems (DSS) are currently developing rapidly and are increasingly used in various fields. More often, those systems are inseparable from information-based systems and computer systems. Therefore, from a methodical point of view, the algorithms implemented in the DSS play a critical role. In this aspect, multi-criteria decision support (MCDA) methods are widely used. As research progresses, many MCDA methods and algorithms for the objective identification of the significance of individual criteria of the MCDA models were developed. In this paper, an analysis of available objective methods for criteria weighting is presented. Additionally, the authors presented the implementation of the system that provides easy and accessible weight calculations for any decision matrix with the possibility of comparing results of different weighting methods. The results of weighting methods were compared using carefully selected similarity coefficients to emphasise the correlation of the resulting weights. The performed research shows that every method should provide distinctive weights considering input data, emphasising the importance of choosing the correct method for a given multi-criteria decision support model and DSS. [ABSTRACT FROM AUTHOR]

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work. [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]

Decision support systems often involve taking into account many factors that influence the choice of existing options. Besides, given the expert's uncertainty on how to express the relationships between the collected data, it is not easy to define how to choose optimal solutions. Such problems also arise in sport, where coaches or players have many variants to choose from when conducting training or selecting the composition of players for competitions. In this paper, an objective fuzzy inference system based on fuzzy logic to evaluate players in team sports is proposed on the example of football. Based on the Characteristic Objects Method (COMET), a multi-criteria model has been developed to evaluate players on the positions of forwards based on their match statistics. The study has shown that this method can be used effectively in assessing players based on their performance. The COMET method was chosen because of its unique properties. It is one of the few methods that allow identifying the model without giving weightings of decision criteria. Symmetrical and asymmetrical fuzzy triangular numbers were used in model identification. Using the calculated derivatives in the point, it turned out that the criteria weights change in the problem state space. This prevents the use of other multi-criteria decision analysis (MCDA) methods. However, we compare the obtained model with the Technique of Order Preference Similarity (TOPSIS) method in order to better show the advantage of the proposed approach. The results from the objectified COMET model were compared with subjective rankings such as Golden Ball and player value. [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]

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]

A q-rung orthopair fuzzy set (q-ROFS), an extension of the Pythagorean fuzzy set (PFS) and intuitionistic fuzzy set (IFS), is very helpful in representing vague information that occurs in real-world circumstances. The intention of this article is to introduce several aggregation operators in the framework of q-rung orthopair fuzzy numbers (q-ROFNs). The key feature of q-ROFNs is to deal with the situation when the sum of the qth powers of membership and non-membership grades of each alternative in the universe is less than one. The Einstein operators with their operational laws have excellent flexibility. Due to the flexible nature of these Einstein operational laws, we introduce the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator, q-rung orthopair fuzzy Einstein ordered weighted averaging (q-ROFEOWA) operator, q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator, and q-rung orthopair fuzzy Einstein ordered weighted geometric (q-ROFEOWG) operator. We discuss certain properties of these operators, inclusive of their ability that the aggregated value of a set of q-ROFNs is a unique q-ROFN. By utilizing the proposed Einstein operators, this article describes a robust multi-criteria decision making (MCDM) technique for solving real-world problems. Finally, a numerical example related to integrated energy modeling and sustainable energy planning is presented to justify the validity and feasibility of the proposed technique. [ABSTRACT FROM AUTHOR]

Multi-criteria decision-making (MCDM) plays a vibrant role in decision-making, and the characteristic object method (COMET) acts as a powerful tool for decision-making of complex problems. COMET technique allows using both symmetrical and asymmetrical triangular fuzzy numbers. The COMET technique is immune to the pivotal challenge of rank reversal paradox and is proficient at handling vagueness and hesitancy. Classical COMET is not designed for handling uncertainty data when the expert has a problem with the identification of the membership function. In this paper, symmetrical and asymmetrical normalized interval-valued triangular fuzzy numbers (NIVTFNs) are used for decision-making as the solution of the identified challenge. A new MCDM method based on the COMET method is developed by using the concept of NIVTFNs. A simple problem of MCDM in the form of an illustrative example is given to demonstrate the calculation procedure and accuracy of the proposed approach. Furthermore, we compare the solution of the proposed method, as interval preference, with the results obtained in the Technique for Order of Preference by Similarity to Ideal solution (TOPSIS) method (a certain preference number). [ABSTRACT FROM AUTHOR]

This paper introduces a new V-COMET method for assessing the sustainable management of renewable energy sources (RES) in European countries. The proposed method belongs to the multi-criteria methods and is free of significant shortcomings occurring in most Multi-Criteria Decision Analysis (MCDA) methods. The paper shows that the V-COMET method is characterized by high accuracy and has very limited computational complexity. The practical contribution of the paper covers the use of the developed V-COMET method in RES assessment. The practical research domain covers the evaluation of 30 European countries in respect of criteria provided by Eurostat (the statistical office of the European Union). Three evaluation models with high criteria details for comparison were proposed: model with KTOE, percentage, and TOE per capita data. Due to the practical potential of the model with data in TOE per capita based on the V-COMET method, full robustness and sensitivity tests of the country rankings were carried out, showing the wide practical possibilities of the proposed approach. Additionally, a methodological evaluation of the proposed V-COMET method was performed. For this purpose, the uncertainty was investigated, and the developed V-COMET method was benchmarked with the set reference MCDA methods. The results allow concluding that the proposed method shows very high accuracy. [Display omitted] • Multi-criteria methods application in renewable energy sources (RES) evaluation domain is investigated. • A new multi-criteria method called V-COMET is proposed. • Based on the method developed a practical framework for sustainable RES evaluation is proposed. • The practical problem of sustainable RES assessment in European Union countries is investigated. [ABSTRACT FROM AUTHOR]

Sustainability research and practice decisions are the fields that address one of the most important challenges of today's world, which is frugal resource management. More people are adopting ethical, less polluting lifestyles and, thus, are seeking out companies that share their values. Multi-Criteria Decision Analysis (MCDA) is a suitable tool for comprehensively analyzing the available decision variants. However, the currently used frameworks are frequently based on crisp values, so the resulting ranking and ratings can only be regarded as initial recommendations. On the other hand, tools for solutions based on uncertain data are limited in practical usability, scalability, and flexibility for solutions based on uncertain data. In this paper, we propose a new comprehensive framework for sensitivity analysis based on interval arithmetic and the MCDA approach. The primary assessment gives initial recommendations, but only after thorough analysis can the ranking of alternatives be reliably treated. It means that thresholds for each criterion should be obtained, which informs us about the robustness of obtained alternative's order. It is very important information that allows accepting or rejecting the ranking received. The framework's performance is verified in sustainable development, where we evaluate the group of electric cars. The TOPSIS method for crisp and interval numbers is involved as the selected MCDA method. The results show that the proposed framework can be effectively used as a recommendation system for multi-criteria problems where input data can fluctuate. [ABSTRACT FROM AUTHOR]

[Display omitted] • We investigate Multi-Criteria Decision Analysis (MCDA) methods application in the renewable energy sources (RES) evaluation domain. • We propose a new MCDA method called CODAS-COMET. • We assess Green Electricity Generation in Poland using the method developed. The purpose of this paper is to present the new hybrid multi-criteria decision analysis (MCDA) method CODAS-COMET for evaluating sustainable electricity generation considering renewable energy sources (RES). The introduced approach combines the advantages of two known MCDA methods: Characteristic Object METhod (COMET) and COmbinative Distance-based ASsessment (CODAS). Due to the advantages of the COMET method, the proposed approach enables the identification of the whole domain model, is resistant to the rank reversal phenomenon, is easy to apply, and allows to obtain an objective and reliable recommendation based on the gathered data. Meanwhile, combining the COMET method with CODAS eliminates the limitations of COMET by automatizing and accelerating the characteristic object comparison procedure. The presented method's practical application includes evaluating Poland's sixteen voivodeships, considering the sustainable use of RES in the electricity generation domain. An additional contribution of this research is to investigate the impact on results of distance metrics other than the default distance metric used by the method that is the focus of this paper and demonstrate the design and practical application of a research framework for selecting the most appropriate metrics. A comparative analysis of the CODAS-COMET method with the TOPSIS-COMET reference approach was performed to confirm the results' reliability. The results showed a high correlation among all final rankings and confirmed the robustness of the CODAS-COMET approach to changing metrics in the algorithm. Furthermore, the results proved that our approach is a suitable and valuable tool for sustainability assessment in renewable energy domains and other complex issues requiring consideration of multiple criteria. [ABSTRACT FROM AUTHOR]