Search

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]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

There are many real-life problems that, because of the need to involve a wide domain of knowledge, are beyond a single expert. This is especially true for complex problems. Therefore, it is usually necessary to allocate more than one expert to a decision process. In such situations, we can observe an increasing importance of uncertainty. In this paper, the Multi-Criteria Decision-Making (MCDM) method called the Characteristic Objects Method (COMET) is extended to solve problems for Multi-Criteria Group Decision-Making (MCGDM) in a hesitant fuzzy environment. It is a completely new idea for solving problems of group decision-making under uncertainty. In this approach, we use L-R-type Generalized Fuzzy Numbers (GFNs) to get the degree of hesitancy for an alternative under a certain criterion. Therefore, the classical COMET method was adapted to work with GFNs in group decision-making problems. The proposed extension is presented in detail, along with the necessary background information. Finally, an illustrative numerical example is provided to elaborate the proposed method with respect to the support of a decision process. The presented extension of the COMET method, as opposed to others' group decision-making methods, is completely free of the rank reversal phenomenon, which is identified as one of the most important MCDM challenges. [ABSTRACT FROM AUTHOR]

The paper introduces the modular approach in the Characteristic Objects method for the reduction of the rules base and thereby avoiding the curse of dimensionality. In this way, the required number of comparisons, between characteristic objects, is highly reduced. The modular approach decomposes a decisional model to related submodels, where each submodel aggregates correlated criteria. In the result, the modular solution consists of several fuzzy modules, which create a hierarchical structure of the considered problem. The proposed approach is compared with the conventional approach by using two exemplary decision functions. For this purpose, three and six-dimensional reference functions are used. Performed experiments enabled the comparison of an accuracy a proposed approach. [ABSTRACT FROM AUTHOR]

This paper introduces the Characteristic Objects Method (COMET) as a useful multi-criteria decision-making (MCDM) method for use in medical applications. The author presents an assessment of the risk of hard arteriosclerotic cardiovascular disease (ASCVD) events. First, an MCDM mini model will be obtained using the COMET, this mini model is the easiest to identify but has the lowest accuracy. The mini model uses only two values for each criterion as characteristic values. For the ASCVD problem, the following four criteria will be used: age, total cholesterol, HDL cholesterol and systolic blood pressure. The author assumes that a white, male patient who is nonsmoker and is free of diabetes or hypertension. The model will next be used to build a ranking for example patients. Finally, the obtained results will be verified using the statistical data (ACC/AHA model) to check the accuracy of the COMET procedure. [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]

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]

• Priority vector construction ways in BWM method under I2TL information are proposed. • Hamacher aggregation operations for I2TL are introduced. • MCGDM framework under I2TL information is proposed. Sometimes in the sense of intuitionist 2-tuple linguistic (I2TL) sets, experts may not be able to decide the most suitable criterion weight vector for multicriteria decision making (MCDM). To avoid this situation, the decision-makers (DMs) can use the Best-Worst method (BWM), in which DMs choose the best (most significant) criterion and the worst (least significant) criterion and then provide two preference vectors by comparing criteria best to other (BO) and other to worst (OW). In the Nonlinear Best-Worst Method (NBWM) it is more complicated to find the unique solution of the model. Therefore, the main goal of this study is to propose two approaches to BWM, namely, Linear Best-Worst Method (LBWM) and Euclidean Best-Worst method (EBWM) to achieve the best criteria priority vector for Multi-Criteria Group Decision Making (MCGDM) problems in the context of I2TL information. In the computational process of MCDM problems, we have to aggregate I2TL elements into a global one. Consequently, under certain critical properties, we are creating some operational laws for I2TL elements based on Hamacher operations. Also, the intuitionistic 2-tuple linguistic Hamacher weighted average (I2TLHWA), and the intuitionistic 2-tuple linguistic Hamacher weighted geometric (I2TLHWG) operators are introduced with the assistance of Hamacher operations and I2TL elements. Subsequently, we analyze some of the I2TLHWA operator's related properties and we propose MCGDM framework under I2TL information. Finally, we demonstrate the validity and efficiency of our method and operations. [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]

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]

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]

Many scientific papers are devoted to solving multi-criteria problems. Researchers solve these problems, usually using methods that find discrete solutions and with the collaboration of domain experts. In both symmetrical and asymmetrical problems, the challenge is when new decision-making variants emerge. Unfortunately, discreet identification of preferences makes it impossible to determine the preferences for new alternatives. In this work, we propose a new approach to identifying a multi-criteria decision model to address this challenge. Our proposal is based on stochastic optimization techniques and the characteristic objects method (COMET). An extensive work comparing the use of hill-climbing, simulated annealing, and particle swarm optimization algorithms are presented in this paper. The paper also contains preliminary studies on initial conditions. Finally, our approach has been demonstrated using a simple numerical example. [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 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]

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]

In this paper, the characterization of Γ-convergence for the first countable topological spaces, characterization of convergence in supremum metric in general setting and some mutual relation between these convergences are discussed. The Γ-convergence is defined as the Kuratowaski-Painlevé convergence of the endographs of the intuitionistic fuzzy sets. The supremum metric is the supremum of Hausdroff distance among the η-cuts of the intuitionistic fuzzy sets. To study these convergences is an important part of the theoretical fundamentals for intuitionistic fuzzy set theory. Some results are given as an application to variational analysis. [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]

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]

Sustainable transportation has a significant impact on factors related to urban development and economic development. Therefore, much research is being undertaken to select the best strategies to manage sustainable transportation. Transportation requires a carefully designed method to manage the development of mobility modes in terms of the pollution they produce or the use of renewable energy sources. However, due to numerous preferences of decision-makers and data uncertainty problems, it is challenging to select the optimal strategy. In this paper, we focus on creating a framework for determining the best strategy for sustainable transportation management. For this purpose, T-spherical fuzzy graphs will be used, which, together with the combination of Laplacian Energy, can accurately represent decision-makers' preferences in an uncertain environment. Due to the lack of limitations of T-spherical fuzzy graphs and its numerous membership functions, decision-makers can decide which factor seems most important for selecting the optimal sustainable transportation strategy. Additionally, due to the applicability, the SFS TOPSIS approach has been used in this approach. The obtained results demonstrate the high performance of the proposed approach and the applicability of the approach in management and sustainable transport problems. [ABSTRACT FROM AUTHOR]

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. [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]

A graph is a tool for designing a system's required interconnection network. The topology of such networks determines their compatibility. For the first time, in this work we construct subdivided η ζ network S (η ζ Γ) and discussed their topology. In graph theory, there are a variety of invariants to study the topology of a network, but topological indices are designed in such a way that these may transform the graph into a numeric value. In this work, we study S (η ζ Γ) via Zagreb connection indices. Due to their predictive potential for enthalpy, entropy, and acentric factor, these indices gain value in the field of chemical graph theory in a very short time. η ζ Γ formed by ζ time repeated process which consists η ζ copies of graph Γ along with η 2 | V (Γ) | ζ η ζ − 1 edges which used to join these η ζ copies of Γ. The free hand to choose the initial graph Γ for desired network S (η ζ Γ) and its relation with chemical networks along with the repute of Zagreb connection indices enhance the worth of this study. These computations are theoretically innovative and aid topological characterization of S (η ζ Γ) . [ABSTRACT FROM AUTHOR]

In many physical models, internal energy will run out without external energy sources. Therefore, finding optimal energy sources and studying their behavior are essential issues. In this article, we study the following variational problem: G ϵ ∗ = sup ∫ Ω G (u) ϵ q (x) d x : ∥ ∇ u ∥ L p (.) ≤ ϵ , u = 0   on   ∂ Ω , with the help of Γ -convergence, where G : R → R is upper semicontinuous, non zero in the L 1 sense, 0 ≤ G (u) ≤ c | u | q (.) , Ω is a bounded open subset of R n , n ≥ 3 , 1 < p (.) < n , and p (.) ≤ q (.) ≤ p ∗ (.) . For special choices of G, we can study Bernoulli's free-boundary and plasma problems in variable exponent Lebesgue spaces. [ABSTRACT FROM AUTHOR]

The paper presents a hybrid model for decision-making support based on D numbers, the FUCOM method and fuzzified RAFSI method, used for solving the selection of the group of construction machines for enabling mobility. By applying D numbers, the input parameters for the calculation of the weight coefficients of the criteria were provided. The calculation of the weight coefficients of the criteria was performed using the FUCOM method. The best alternative was selected using the fuzzified method, which was conditioned by the specificity of the issue so that in this case, the selection of the best alternative was made using the fuzzified RAFSI method. [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 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]

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]

To answer the question stated in the title, we present and compare two approaches: first, a standard approach for solving dual fuzzy nonlinear systems (DFN-systems) based on Newton's method, which uses 2D FN representation and second, the new approach, based on multidimensional fuzzy arithmetic (MF-arithmetic). We use a numerical example to explain how the proposed MF-arithmetic solves the DFN-system. To analyze results from the standard and the new approaches, we introduce an imprecision measure. We discuss the reasons why imprecision varies between both methods. The imprecision of the standard approach results (roots) is significant, which means that many possible values are excluded. [ABSTRACT FROM AUTHOR]

The identification of the criteria relevance from the expert in the multi-criteria problem could be a challenging task. It is important to provide simple and intuitive techniques that reflect the expert knowledge effectively. When the problem includes many criteria, it is possible to occur some probability of error in determining the criteria relevance. However, most subjective weighting methods perform correctly when the experts do not hesitate, are repeatable, and are very precise. Consequently, there is interest in improving the currently used approaches to handle expert hesitation more effectively. To fill this gap, we propose the RANking COMparison (RANCOM) method, which can be used to determine criteria weights based on expert knowledge. Its performance is based on defining the criteria ranking order to obtain the weights vector. The illustrative example and a comparative analysis of the selected subjective weighting methods show that the proposed approach provides reliable results, highly correlated with the existing approaches. However, it offers a simple manner of use, adjusted for less and more experienced users. The comparison of the RANCOM and AHP methods shows that when a slight probability of error in expert judgments occurs, the RANCOM method proves to be a more suitable solution to handle the expert inaccuracies for the problems with 5 or more criteria. Performed experiments showed that the RANCOM method is a repeatable and more consistent method regarding possible judgment errors. The obtained results showed that the RANCOM method guarantees more repeatable results than the AHP method, especially for a greater number of criteria. [ABSTRACT FROM AUTHOR]

Nowadays, in the modern digital era, the use of computer technologies such as smartphones, tablets and the Internet, as well as the enormous quantity of confidential information being converted into digital form have resulted in raised security issues. This, in turn, has led to rapid developments in cryptography, due to the imminent need for system security. Low-dimensional chaotic systems have low complexity and key space, yet they achieve high encryption speed. An image encryption scheme is proposed that, without compromising the security, uses reasonable resources. We introduced a chaotic dynamic state variables selection procedure (CDSVSP) to use all state variables of a hyper-chaotic four-dimensional dynamical system. As a result, less iterations of the dynamical system are required, and resources are saved, thus making the algorithm fast and suitable for practical use. The simulation results of security and other miscellaneous tests demonstrate that the suggested algorithm excels at robustness, security and high speed encryption. [ABSTRACT FROM AUTHOR]

The classical matrix theory is deficient to express the vagueness of the real life. The fuzzy set theory has been successfully applied to bridge this gap. Much work has already been done on a two-person zero sum matrix game with fuzzy goals. In continuation, this paper is dedicated to define and study a multi-criteria two-person zero sum game with intuitionistic fuzzy goals. It is shown that solving such games is equivalent to solving two crisp multi object linear programming problems. Our work generalizes the previous study on a multi-criteria game with fuzzy goals by adopting the approach of linear programming with intuitionistic fuzzy sets. Finally, an illustrative numerical example is provided to elaborate the proposed approach. [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]

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]

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]

Graph theory can be used to optimize interconnection network systems. The compatibility of such networks mainly depends on their topology. Topological indices may characterize the topology of such networks. In this work, we studied a symmetric network θ ϕ formed by ϕ time repetition of the process of joining θ copies of a selected graph Ω in such a way that corresponding vertices of Ω in all the copies are joined with each other by a new edge. The symmetry of θ ϕ is ensured by the involvement of complete graph K θ in the construction process. The free hand to choose an initial graph Ω and formation of chemical graphs using θ ϕ Ω enhance its importance as a family of graphs which covers all the pre-defined graphs, along with space for new graphs, possibly formed in this way. We used Zagreb connection indices for the characterization of θ ϕ Ω . These indices have gained worth in the field of chemical graph theory in very small duration due to their predictive power for enthalpy, entropy, and acentric factor. These computations are mathematically novel and assist in topological characterization of θ ϕ Ω to enable its emerging use. [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]

This paper aims to present an innovative approach based on two newly developed Multi-Criteria Decision-Making (MCDM) methods: COMET combined with TOPSIS and SPOTIS, which could be the basis for a decision support system (DSS) in the problem of selecting solar panels. Solar energy is one of the most promising and environmentally friendly energy sources because of the enormous potential of directly converting available solar radiation everywhere into electricity. Furthermore, ever-lower prices for photovoltaic systems make solar electricity more competitive with power from conventional energy sources, increasing interest in solar panels among companies and households. This fact generates the need for a user-friendly, objective, fully automated DSS to support the multi-criteria selection of solar panels. Both MCDM methods chosen for this purpose are rank-reversal-free and precise. First, the objective entropy weighting method was applied for determining criteria weights. Final rankings were compared by two ranking correlation coefficients: symmetrical r w and asymmetrical W S . Then the sensitivity analysis providing local weights of alternatives for decision criteria was performed. The obtained results prove the adequacy and practical usefulness of the presented approach in solving the problem of solar panels selection. [ABSTRACT FROM AUTHOR]

A high monetary value of the construction projects is one of the reasons of frequent disputes between a general contractor (GC) and a client. A construction site is a unique, one-time, and single-product factory with many parties involved and dependent on each other. The organizational dependencies and their complexity make any fault or mistake propagate and influence the final result (delays, cost overruns). The constant will of the parties involved results in completing a construction object. The cost increase, over the expected level, may cause settlements between parties difficult and lead to disputes that often finish in a court. Such decision of taking a client to a court may influence the future relations with a client, the trademark of the GC, as well as, its finance. To ascertain the correctness of the decision of this kind, the machine learning tools as decision trees (DT) and artificial neural networks (ANN) are applied to predict the result of a dispute. The dataset of about 10 projects completed by an undisclosed contractor is analyzed. Based on that, a much bigger database is simulated for automated classifications onto the following two classes: a dispute won or lost. The accuracy of over 93% is achieved, and the reasoning based on results from DT and ANN is presented and analyzed. The novelty of the article is the usage of in-company data as the independent variables what makes the model tailored for a specific GC. Secondly, the calculation of the risk of wrong decisions based on machine learning tools predictions is introduced and discussed. [ABSTRACT FROM AUTHOR]

The multi-criteria decision-making (MCDM) problem has a solution whose quality can be affected by the experts' inclinations. Under essential conditions, the fuzzy MCDM method can provide more acceptable and efficient outcomes to select the best alternatives. This work consists of a consensus-based technique for selecting and evaluating suppliers in an incomplete fuzzy preference relations (IFPRs) environment utilizing T L -transitivity (Lukasiewicz transitivity). The suggested method is developed based on the criteria of the Analytical Hierarchy Process (AHP) Fframework, and the decision matrix is construtced using consistent fuzzy preference relations (FPRs). We use the symmetrical decisional matrix approach. A variety of numerical explanations and an analysis of quantitative results illustrate the suggested methodology's logic and effectiveness. [ABSTRACT FROM AUTHOR]

Background and objectives: Machine learning approaches using random forest have been effectively used to provide decision support in health and medical informatics. This is especially true when predicting variables associated with Medicare reimbursements. However, more work is needed to analyze and predict data associated with reimbursements through Medicare and Medicaid services for physical therapy practices in the United States. The key objective of this study is to analyze different machine learning models to predict key variables associated with Medicare standardized payments for physical therapy practices in the United States. Materials and Methods: This study employs five methods, namely, multiple linear regression, decision tree regression, random forest regression, K-nearest neighbors, and linear generalized additive model, (GAM) to predict key variables associated with Medicare payments for physical therapy practices in the United States. Results: The study described in this article adds to the body of knowledge on the effective use of random forest regression and linear generalized additive model in predicting Medicare Standardized payment. It turns out that random forest regression may have any edge over other methods employed for this purpose. Conclusions: The study provides a useful insight into comparing the performance of the aforementioned methods, while identifying a few intricate details associated with predicting Medicare costs while also ascertaining that linear generalized additive model and random forest regression as the most suitable machine learning models for predicting key variables associated with standardized Medicare payments. [ABSTRACT FROM AUTHOR]