Multiple Criteria Group Decision Research Articles

A Choquet integral-based hesitant fuzzy gained and lost dominance score method for multi-criteria group decision making considering the risk preferences of experts: Case study of higher business education evaluation

With the rapid development of higher business education, higher business education evaluation has attracted considerable attention of researchers and practitioners. The higher business education evaluation is an essential part of the development of a business school, which has a direct impact on its resource distribution. The higher business education evaluation can be considered as a multiple criteria group decision making (MCGDM) problem that involves a group of experts. Due to the complexity of the decision-making problem, decision criteria are not fully independent to each other, and the assumption of complete rationality of experts is usually invalid in many situations. In this paper, we propose a Choquet integral-based hesitant fuzzy gained and lost dominance score method to address the two important issues regarding the interactions among criteria and the behavior preference characteristics of experts in MCGDM problems. Firstly, a comprehensive distance measure of hesitant fuzzy sets is introduced by considering the relative importance of two separations. Then, a Choquet integral-based hesitant fuzzy gained and lost dominance score method based on the prospect theory is proposed to address the MCGDM problems in which experts make decision with the risk preference psychology. Finally, an illustrative example of higher business education evaluation is provided to demonstrate the applicability of the proposed method, and the sensitivity and comparative analysis are also completed to verify the validity of the proposed method.

A Minimum Trust Discount Coefficient Model for Incomplete Information in Group Decision Making with Intuitionistic Fuzzy Soft Set

This article proposes a framework to deal with incomplete information in multiple criteria group decision making with intuitionistic fuzzy soft set. To do that, the weighted sum method for choice values and simple mathematical expectation method are extended to the case of obtained fuzzy soft set, and they are proved to have the same result in estimating the incomplete information. In order to reduce the system error in the estimating process cause by multiple decision information, a minimum trust discount coefficient model is established according to the relevant methods of evidence theory. Then, a new definition of entropy for intuitionistic fuzzy sets is introduced to determine the weights of group experts. Therefore, individual decision-making matrices are integrated into a comprehensive decision-making matrix by the integration operation formula of intuitionistic fuzzy soft matrix. The decision making is realized according to the difference of the score values of objects. Finally, the steps of this method are concluded, and one example is given to explain the application of this method.

Rough-Number-Based Multiple-Criteria Group Decision-Making Method by Combining the BWM and Prospect Theory

Multicriteria group decision-making (MCGDM) problems have been a research hotspot in recent years, and prospect theory is introduced to cope with the risk and imprecision in the process of decision-making. To guarantee the effectiveness of information aggregation and extend the feasibility of prospect theory, this paper proposes a novel decision-making approach based on rough numbers and prospect theory to solve risky and uncertain MCGDM problems. Firstly by combining rough numbers and the best-worst method (BWM), we construct a linear programming model to calculate rough criteria weights, which are defined by lower limitations and upper limitations. Then for the imprecision of value function and weighting function in prospect theory, we propose a novel method with the aid of combining rough numbers and prospect theory to handle the risk in decision-making problems. Finally, a numerical example involving investment is introduced to illustrate the application and validity of the proposed method.

Multiple criteria group decision making based on group satisfaction

To generate solutions to multiple criteria group decision-making (MCGDM) problems that are satisfactory to the decision makers, this paper proposes a new method. To examine whether a group solution is satisfactory to the decision makers, group satisfaction is constructed from alternative assessment and ranking differences between the decision makers and the group. The difference between a decision maker's assessment and a group's assessment is designed based on differences in assessment grades, whose normalization is theoretically proven to construct alternative assessment differences. Inspired by Spearman's rank correlation coefficient, the expected utilities of decision makers’ and the group's assessments are used to construct alternative ranking differences. An abstract two-variable function with specific properties is designed to relate alternative assessment difference to alternative ranking difference to form group satisfaction. From the constructed group satisfaction, the process of generating group-satisfactory solutions to MCGDM problems is presented. The problem of selecting engineering project management software is analyzed by using the proposed method to demonstrate its applicability. To highlight the importance of group satisfaction in MCGDM, relationships and differences between group satisfaction and group consensus are analyzed through the problem and simulation experiments.

A Method Based on Bivariate Almost Stochastic Dominance for Multiple Criteria Group Decision Making With Probabilistic Dual Hesitant Fuzzy Information

Probabilistic dual hesitant fuzzy sets (PDHFSs) are sound information granules to describe decision maker's aleatory and epistemic uncertainty in multiple criteria group decision making (MCGDM) process. In this paper, a bivariate almost stochastic dominance-based PROMETHEE-II method is presented to solve probabilistic dual hesitant fuzzy MCGDM problems which consider correlation averse behavior of decision makers. First, probabilistic dual hesitant fuzzy power Bonferroni mean (PDHFPBM) operator and probabilistic dual hesitant fuzzy power geometric Bonferroni mean (PDHFPGBM) operator are proposed to acquire collective preference information of decision makers. Second, based on the defined bivariate almost stochastic dominance (BASD) and BASD degree, qualitative and quantitative relationships between two probabilistic dual hesitant fuzzy elements (PDHFEs) with corresponding to all criteria are obtained. Third, distance-based correlation coefficient method for computing combined weight with respect to all criteria is proposed. Finally, a BASD-based PROMETHEE-II method is developed to determine the ranking results. Three illustrative examples followed by comparative analysis are included to show the practicality and effectiveness of the proposed method.

Multi-criteria group decision making with Pythagorean fuzzy soft topology

Pythagorean fuzzy set (PFS) introduced by Yager (2013) is the extension of intuitionistic fuzzy set (IFS) introduced by Atanassov (1983). PFS is also known as IFS of type-2. Pythagorean fuzzy soft set (PFSS), introduced by Peng et al. (2015) and later studied by Guleria and Bajaj (2019) and Naeem et al. (2019), are very helpful in representing vague information that occurs in real world circumstances. In this article, we introduce the notion of Pythagorean fuzzy soft topology (PFS-topology) defined on Pythagorean fuzzy soft set (PFSS). We define PFS-basis, PFS-subspace, PFS-interior, PFS-closure and boundary of PFSS. We introduce Pythagorean fuzzy soft separation axioms, Pythagorean fuzzy soft regular and normal spaces. Furthermore, we present an application of PFSSs to multiple criteria group decision making (MCGDM) using choice value method in the real world problems which yields the optimum results for investment in the stock exchange. We also render an application of PFS-topology in medical diagnosis using TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution). The applications are accompanied by Algorithms, flow charts and statistical diagrams.

A multi-criteria decision-making method based on triangular interval-valued fuzzy numbers and the VIKOR method

In many cases, complex problems cannot be accurately described by precise numerical values. Fuzzy theory provides a suitable tool for solving these problems. However, if decision makers cannot reach an agreement on the method for defining linguistic variables based on fuzzy sets, TIVFNs (triangular interval-valued fuzzy numbers) can provide more accurate modeling. Therefore, solving fuzzy MCGDM (multiple criteria group decision-making) problem with an unknown expert weight and criterion weight in TIVFNs has become an important research direction. In this paper, TIVF-VIKOR (triangular interval-valued fuzzy VIKOR) method, which is suitable for the environment of TIVFNs, is proposed to solve the problem of fuzzy MCGDM. To achieve this goal, the TIVF-VIKOR method is innovatively adopted similarity and coefficient of variation are combined to calculate expert weight, and deviation maximization method based on divergence matrix is used to calculate criterion weight. VIKOR method is used to find the compromise solutions, which are converted into the form of binary connection number, and the optimal compromise solution is obtained after ranking. The proposed method is applied to the problem of machine fault detection, and the validity and feasibility of the method are illustrated. Compared with the TOPSIS∖ELECTRE method, the ranking results of the three methods are equivalent, and the fluctuation of the TIVF-VIKOR method is more distinct.

CREATING A NEW CULTURAL TOURISM PRODUCT RELATED TO LOCAL POST-INDUSTRIAL HERITAGE AS A MULTIPLE CRITERIA DECISION AIDING PROBLEM

Creating local cultural tourism products (CTPs) requires the involvement of many entities, e.g., local government units, culture and tourism institutions, non-government organisations, etc., as well as organisational, technical, financial, and human resources. When deciding on a future product venture, it is important to establish visions, goals, or the product’s desired functions common to all these actors. Then, the alternative instances of such CTP need to be designed and examined from the viewpoint of these goals, which may be mutually exclusive due to the various preferences of the actors. Furthermore, despite their importance, these criteria may conflict with, e.g., the tourism policy of local authorities. The issues mentioned above make the decisions regarding creating CTPs very complex and have behavioural, group multiple criteria character. This paper aims to identify the structural elements of creating the best possible CTP promoting local post-industrial heritage in the Czeladź Commune. The specific assumptions, conditions, and criteria are defined to formulate the problem for further consideration using multiple criteria group decision-making (GDM) approaches. Keywords: multiple criteria decision making, group decision-making, multiple criteria problems in cultural tourism, decisions on new cultural tourism products.

A Novel Pythagorean Fuzzy LINMAP-Based Compromising Approach for Multiple Criteria Group Decision-Making with Preference Over Alternatives

This paper presents a new compromising approach to multiple criteria group decision-making (MCGDM) for the treatment of uncertainty which is based on Pythagorean fuzzy (PF) sets. The present work intends to propose a novel linear programming technique for multidimensional analysis of preference (LINMAP) by way of some useful concepts related to PF dominance relations, individual consistency and inconsistency levels, and individual fit measurements. The concept of PF scalar function-based dominance measures is defined to conduct intracriterion comparisons concerning uncertain evaluation information based on Pythagorean fuzziness; moreover, several valuable properties are also investigated to demonstrate its effectiveness. For the assessment of overall dominance of alternatives, this paper provides a synthetic index, named a comprehensive dominance measure, which is the aggregation of the weighted dominance measures by combining unknown weight information and PF dominance measures of various criteria. For each decision-maker, this paper employs the proposed measures to evaluate the individual levels of rank consistency and rank inconsistency regarding the obtained overall dominance relations and the decision-maker’s preference comparisons over paired alternatives. In the framework of individual fit measurements, this paper constructs bi-objective mathematical programming models and then provides their corresponding parametric linear programming models for generating the best compromise alternative. Realistic applications with some comparative analyses concerning railway project investment are implemented to demonstrate the appropriateness and usefulness of the proposed methodology in addressing actual MCGDM problems.

Spherical Fuzzy Linear Assignment Method for Multiple Criteria Group Decision-Making Problems

Spherical fuzzy sets theory is useful and advantageous for handling uncertainty and imprecision in multiple attribute decision-making problems by considering membership, non-membership, and indeterminacy degrees. In this paper, by extending the classical linear assignment method, we propose a novel method called the spherical fuzzy linear assignment method (SF-LAM) to solve multiple criteria group decision-making problems in the spherical fuzzy environment. A ranking procedure consisting of aggregation functions, score functions, accuracy functions, weighted rank frequency, and a binary mathematical model are presented to determine the criterion-wise preferences and various alternatives’ priority order. The proposed method’s applicability and validity are shown through the selection problem among wind power farm locations. The proposed method helps managers to find the best location to construct the wind power plant based on the determined criteria. Finally, a comparative analysis is performed between the proposed spherical fuzzy linear assignment (SF-LAM) model and the spherical fuzzy analytic hierarchy process (SF-AHP) and spherical fuzzy WASPAS methods.

VIKOR method for multiple criteria group decision making under 2-tuple linguistic neutrosophic environment

In this article, the VIKOR method is proposed to solve the multiple criteria group decision making (MCGDM) with 2-tuple linguistic neutrosophic numbers (2TLNNs). Firstly, the fundamental concepts, operation formulas and distance calculating method of 2TLNNs are introduced. Then some aggregation operators of 2TLNNs are reviewed. Thereafter, the original VIKOR method is extended to 2TLNNs and the calculating steps of VIKOR method with 2TLNNs are proposed. In the proposed method, it’s more reasonable and scientific for considering the conflicting criteria. Furthermore, the VIKOR are extended to interval-valued 2-tuple linguistic neutrosophic numbers (IV2TLNNs). Moreover, a numerical example for green supplier selection has been given to illustrate the new method and some comparisons are also conducted to further illustrate advantages of the new method.

D-WASPAS: Addressing Social Cognition in Uncertain Decision-Making with an Application to a Sustainable Project Portfolio Problem

Decision-making is an interdisciplinary area that has roots in mathematics, economics, and social science. Multiple-criteria group decision-making (MCGDM) is one of the most applicable areas of decision-making. Social cognition is involved in group decision-making. Therefore, it is necessary to address how decision makers (DMs) process and apply judgments and information during the process. In recent years, many approaches have been applied to MCGDM. As an important aspect of this process, uncertainty has led to the application of fuzzy sets. However, utilizing various decision-making approaches can result in different results and confusion among DMs. Moreover, using classic fuzzy sets and expressing degrees of belonging by crisp values has proven to be inadequate for uncertain decision-making environments. This paper presents a novel MCGDM approach, double-weighted aggregated sum product assessment (D-WASPAS), under interval-valued Pythagorean fuzzy (IVPF) uncertainty. The proposed approach applies knowledge measures to address the objective weights of criteria. Then, subjective and objective weights of criteria are aggregated to create a more appropriate weight. This approach considers three decision-making methods. In the first, an IVPF-ARAS (additive ratio assessment) method is extended to rank the alternatives. In the second, an IVPF-EDAS (evaluation based on distance from average solution) method is developed to rank the alternatives. In the third, a novel IVPF-COADAP (complex adequate appraisal) method is utilized for a third ranking. To aggregate the results, two steps are carried out using the WASPAS method. First, the results of the ranking approaches are aggregated. This process starts with computing the objective weights of the ranking approaches and aggregating the outcome with the subjective weights of the approaches. Then, the WASPAS method is applied to aggregate the obtained rankings and obtain a set of rankings for each DM. The second aggregation is utilized to aggregate the results for the DMs and reach a final set of rankings. Similarly, the subjective and objective weights of the DMs are applied in the WASPAS to aggregate the results. It should be noted that since the WASPAS method is utilized twice to aggregate the results, this approach is called D-WASPAS. A case study of the application of the proposed method shows that it is applicable to many multiple-criteria analysis and decision-making processes. Moreover, the results are more reliable because various decision-making methods are taken into consideration, and it is a last-aggregation process. Double-weighted aggregated sum product assessment offers a novel decision-making framework that is applicable in real-world decision-making situations. The proposed method is based on interval-valued Pythagorean fuzzy sets (IVPFSs), which would be especially applicable to uncertain situations. Also, it would enhance calculations of the process by offering more flexibility in dealing with uncertainty. Consequently, introducing this new decision-making framework and applying extended fuzzy sets would make the proposed method more widely applicable. The last-aggregation nature of this method avoids loss of cognitive information and assigning weights to the DMs, and the different ranking methods address the social cognition that leads to the judgments expressed and the final decisions.

Contested energy futures, conflicted rewards? Examining low-carbon transition risks and governance dynamics in China's built environment

China's urbanisation has caused city populations to grow rapidly, boosting continuous development and scaling up the construction industry more intensely. The building sector is thus a key area to consider for climate change mitigation efforts. This study initially seeks to explore the development of a green transition pathway for the Chinese building sector, informed by national and local low-carbon policies and strategies, with specific references to Beijing and Shanghai. Acknowledging that the barriers and impacts of these policies have not been explored in depth and in consideration of the multiplicity of stakeholder views, we then set out to collect stakeholders’ perspectives of implementation and consequential risks associated with the envisaged transition and with the policies aiming to promote this transition. These concerns are evaluated in a multiple-criteria group decision making approach. By focusing on the resulting most critical implementation barriers, we then outline five plausible socioeconomic scenarios, against which we simulate the impacts of the considered policy strategies on the low-carbon transition of the Chinese built environment as well the extent of their key possible negative consequences, by means of fuzzy cognitive maps.

EDAS method for multiple criteria group decision making under 2-tuple linguistic neutrosophic environment

In this paper, we present 2-tuple linguistic neutrosophic EDAS model based on traditional EDAS (Evaluation based on Distance from Average Solution) model and some fundamental theories of 2-tuple linguistic neutrosophic information. Firstly, we brief

Approach to Multicriteria Group Decision Making with Z-Numbers Based on TOPSIS and Power Aggregation Operators

Decisions strongly rely on information, so the information must be reliable, yet most of the real-world information is imprecise and uncertain. The reliability of the information about decision analysis should be measured. Z-number, which incorporates a restraint of evaluation on investigated objects and the corresponding degree of confidence, is considered as a powerful tool to characterize this information. In this paper, we develop a novel approach based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method and the power aggregation operators for solving the multiple criteria group decision making (MCGDM) problem where the weight information for decision makers (DMs) and criteria is incomplete. In the MCGDM, the evaluation information made by DMs is represented in the form of linguistic terms and the following calculation is performed using Z-numbers. First, we establish an optimization model based on similarity measure to determine the weights of DMs and a linear programming model with partial weight information provided by DMs based on distance measure to determine the weights of criteria. Subsequently, decision matrices from all the DMs are aggregated into a comprehensive evaluation matrix utilizing the proposed ZWAPA operator or ZWGPA operator. Then, those considered alternatives are ranked in accordance with TOPSIS idea and the feature of Z-evaluation. Finally, a practical example about supplier selection is given to demonstrate the detailed implementation process of the proposed approach, and the feasibility and validity of the approach are verified by comparisons with some existing approaches.

An extended MULTIMOORA method for probabilistic linguistic multi-criteria group decision-making based on prospect theory

The development of social economy has rendered the decision-making environment more complex. To better adapt to the environment and solve practical decision-making problems, this study uses the probabilistic linguistic terms set (PLTS) to describe qualitative information, which can not only provide every possible evaluation value, but can also yield the weight or proportion of these values. Based on the PLTS, we propose a probabilistic linguistic-dependent weighted average (PLDWA) operator; then, we establish the prospect theory-based multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) method (PT-MULTIMOORA) and extend it to the probabilistic linguistic information (PLI) environment. Moreover, we propose a final value determination method for the PT-MULTIMOORA method. Based on the combination of the PLDWA operator and the PT-MULTIMOORA method, we develop a novel approach to solve multiple criteria group decision making (MCGDM) problems with PLI. Two practical cases are demonstrated to verify the feasibility and superiority of the proposed method.

A hybrid hierarchical soft computing approach for the technology selection problem in brick industry considering environmental competencies: A case study

Brick manufacturing is an important industry which produces some fundamental building materials. Since brick production industries have environmental adverse effects such as air pollution, excessive energy consumption as well as waste production, they have become more challenging to manage as they face increasing pressure to improve economic performance and the green and clean production concerns. Concerning these issues and taking into account the current state of the literature in this area, this paper, proposes a hybrid hierarchical fuzzy multiple-criteria group decision making (HH-FMCGDM) model based on a modified fuzzy analytic hierarchy process (MFAHP) to evaluate and rank the related alternative technologies based on various criteria including economic, environmental, market related, technical advantages, and so on. In the proposed method MFAHP is utilized to determine the weights of the criteria. Also, a new method is presented to assign a weight factor for each decision maker (DM) in the group decision-making process. Also, we propose a fuzzy extended version of TOPSIS method as an evaluation tool to calculate the local priority of candidates of brick manufacturing technologies. Afterward, in order to avoid the data loss of DMs’ judgments, the final rank of alternatives are obtained based on the proposed last aggregation approach. To illustrate the efficiency of the proposed approach, a real-life case study in a brick industry is done based on our approach. Then, a sensitivity analysis is done to assess the robustness and sensitiveness of the obtained results from the proposed approach. Finally, some managerial insights are suggested to increase the applicability of the proposed HH-FMCGDM approach for real cases.

Evaluation and selection of clustering methods using a hybrid group MCDM

Due to the lack of objective measures, the evaluation and prioritization of clustering methods is inherently challenging. Since their evaluation generally involves numerous criteria, it can be designed as a multiple criteria decision making (MCDM) problem and using multiple data sets, the problem can be formulated as a group MCDM modeling.In this paper, a MCDM-based framework is proposed to evaluate and rank a number of clustering methods. The proposed approach employs three group MCDM algorithms and a Borda count method which leads to a comprehensive, robust framework capable of evaluating and ranking multiple clustering models on manifold data sets (cases). Moreover, we introduce a hybrid data clustering algorithm which combines a particle swarm optimization (PSO) algorithm with a K-means clustering algorithm. Finally, a clustering comparison with regard to both external and internal evaluation indicators is another contribution of this paper.Six clustering methods are compared based on five evaluation measures. The results of comparative experiments on ten data sets indicate the effectiveness of the proposed hybrid clustering method. More importantly, the experimental results vividly demonstrate the effectiveness of the group MCDM-based evaluation on clustering model selection.

An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods

Green supply chain management, which considers both the environment and supply chain management, is becoming a hot topic in modern operations management. In a manufacturing enterprise, it is crucial for supply chain managers to select an appropriate supplier for their long-term development prospects to and to pursue the business strategy and remain in a competitive position. Green supplier selection (GSS) can be viewed as a multiple-criteria group decision-making (MCGDM) problem that involves many unmeasurable and conflicting criteria. Considering the advantage of interval type-2 fuzzy sets (IT2FSs) in modeling such complexity and uncertainty, this study provides an integrated methodology to address MCGDM problems based on the best-worst method (BWM) and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) technique in an interval type-2 fuzzy environment. First, we extend a new decision-making method called the BWM to IT2FSs. Unlike the BWM and fuzzy BWM, our IT2FSs stem from a questionnaire survey and related interval approaches. Second, we develop an integrated model based on interval type-2 fuzzy BWM and VIKOR to solve MCGDM problems. Finally, we present a GSS example to illustrate on the performance of our approach. We also provide sensitivity and comparative analyses and a discussion of the effectiveness and advantages of the proposed method.

An Extended VIKOR Method for Multiple Criteria Group Decision Making with Triangular Fuzzy Neutrosophic Numbers

An Extended VIKOR Method for Multiple Criteria Group Decision Making with Triangular Fuzzy Neutrosophic Numbers