A systematic review on multi-criteria group decision-making methods based on weights: analysis and classification scheme

Interest in group decision-making (GDM) has been increasing prominently over the last decade. Access to global databases, sophisticated sensors which can obtain multiple inputs or complex problems requiring opinions from several experts have driven interest in data aggregation. Consequently, the field has been widely studied from several viewpoints and multiple approaches have been proposed. Nevertheless, there is a lack of general framework. Moreover, this problem is exacerbated in the case of experts’ weighting methods, one of the most widely-used techniques to deal with multiple source aggregation. This lack of general classification scheme, or a guide to assist expert knowledge, leads to ambiguity or misreading for readers, who may be overwhelmed by the large amount of unclassified information currently available. To invert this situation, a general GDM framework is presented which divides and classifies all data aggregation techniques, focusing on and expanding the classification of experts’ weighting methods in terms of analysis type by carrying out an in-depth literature review. Results are not only classified but analysed and discussed regarding multiple characteristics, such as MCDMs in which they are applied, type of data used, ideal solutions considered or when they are applied. Furthermore, general requirements supplement this analysis such as initial influence, or component division considerations. As a result, this paper provides not only a general classification scheme and a detailed analysis of experts’ weighting methods but also a road map for researchers working on GDM topics or a guide for experts who use these methods. Furthermore, six significant contributions for future research pathways are provided in the conclusions.The first author acknowledges support from the Spanish Ministry of Universities [grant number FPU18/01471]. The second and third author wish to recognize their support from the Serra Hunter program. Finally, this work was supported by the Catalan agency AGAUR through its research group support program (2017SGR00227). This research is part of the R&D project IAQ4EDU, reference no. PID2020-117366RB-I00, funded by MCIN/AEI/10.13039/ 501100011033.Peer ReviewedPostprint (published version

Weight Analysis for Multiattribute Group Decision-Making with Interval Grey Numbers Based on Decision-Makers’ Psychological Criteria

open access articleTo address the problem of multiattribute group decision-making with interval grey numbers, decision matrices are adjusted using kernels of interval grey numbers to reduce the psychological effects of decision-makers. The comprehensive weights of attributes are obtained by aggregating the subjective weights with objective weights, which are calculated based on the accuracy and difference of attributes. Considering the consistent, best, and worst decision-making abilities of decision-makers, grey incidence models are established to obtain the consistency weights and individual bipolar weights of decision-makers; then, the comprehensive weights of decision-makers are determined. A clustering approach of interval grey numbers is presented, and overall evaluations are obtained. Finally, an example is provided and its validity is tested to verify the feasibility of the proposed method

The Optimization Ordering Model for Intuitionistic Fuzzy Preference Relations with Utility Functions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Intuitionistic fuzzy sets describe information from the three aspects of membership degree, non-membership degree and hesitation degree, which has more practical significance when uncertainty pervades qualitative decision problems. In this paper, we investigate the problem of ranking intuitionistic fuzzy preference relations (IFPRs) based on various non-linear utility functions. First, we transform IFPRs into their isomorphic interval-value fuzzy preference relations (IVFPRs), and utilise non-linear utility functions, such as parabolic, S-shaped, and hyperbolic absolute risk aversion, to fit the true value of a decision-maker's judgement. Ultimately, the optimization ordering models for the membership and non-membership of IVFPRs based on utility function are constructed, with objective function aiming at minimizing the distance deviation between the multiplicative consistency ideal judgment and the actual judgment, represented by utility function, subject to the decision-maker's utility constraints. The proposed models ensure that more factual and optimal ranking of alternative is acquired, avoiding information distortion caused by the operations of intervals. Second, by introducing a non-Archimedean infinitesimal, we establish the optimization ordering model for IFPRs with the priority of utility or deviation, which realises the goal of prioritising solutions under multi-objective programming. Subsequently, we verify that a close connection exists between the ranking for membership and non-membership degree IVFPRs. Comparison analyses with existing approaches are summarized to demonstrate that the proposed models have advantage in dealing with group decision making problems with IFPRs

A SPHERICAL FUZZY BASED DECISION MAKING FRAMEWORK WITH EINSTEIN AGGREGATION FOR COMPARING PREPAREDNESS OF SMEs IN QUALITY 4.0

Researchers work hard to embrace technological changes and redefine the quality management as Quality 4.0 (Q 4.0). In this context, the purpose of the current work is twofold. First, it aims to compare the preparedness of the small and medium enterprises (SMEs) for sustaining in Q4. Second, it intends to propose a novel hybrid spherical fuzzy based multi-criteria group decision-making (MAGDM) framework with Einstein aggregation (EA). A real-life case study on six SMEs is carried out with the help of three experts. For aggregating the individual responses (using spherical fuzzy numbers or SFNs), EA is used. Then two very recent models such as Simple Ranking Process (SRP) and Symmetry Point of Criterion (SPC) are extended using SFN to rank the SMEs. Finally, the validation tests and sensitivity analysis are carried out. It is noted that the application of analytical tools, knowledge management and use of technology under the support and mentorship of visionary leadership are the key criteria for building up the capability to embrace Q 4.0. Interestingly, it is noted that medium scale firms are better prepared than small-scale enterprises. This work is apparently a first of its kind that focuses on SMEs for assessing their quality management practices in Industry 4.0 era

Credit risk management of property investments through multi-criteria indicators

The economic crisis of 2008 has highlighted the ineffectiveness of the banks in their disbursement of mortgages which caused the spread of Non-Performing Loans (NPLs) with underlying real estate. With the methods stated by the Basel III agreements, aimed at improving the capital requirements of banks and determining an adequate regulatory capital, the banks without the skills required have difficulties in applying the rigid weighting coefficients structures. The aim of the work is to identify a synthetic risk index through the participatory process, in order to support the restructuring debt operations to benefit smaller banks and small and medium-sized enterprises (SME), by analyzing the real estate credit risk. The proposed synthetic risk index aims at overcoming the complexity of Basel III methodologies through the implementation of three different multi-criteria techniques. In particular, the integration of objective financial variables with subjective expert judgments into a participatory process is not that common in the reference literature and brings its benefits for reaching more approved and shared results in the debt restructuring operations procedure. Moreover, the main findings derived by the application to a real case study have demonstrated how important it is for the credit manager to have an adequate synthetic index that could lead to the avoidance of risky scenarios where several modalities to repair the credit debt occur

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

The Applicability of Multiple MCDM Techniques for Implementation in the Priority of Road Maintenance

Priority of road maintenance can be viewed as a process influenced by decision-makers with varying decision-making power. Each decision-maker may have their view and judgment depending on their function and responsibilities. Therefore, determining the priority of road maintenance can be thought of as a process of MCDM. Regarding the priority of road maintenance, this is a difficult MCDM problem involving uncertainty, qualitative criteria, and possible causal relationships between choice criteria. This paper aims to examine the applicability of multiple MCDM techniques, which are used for assessing the priority of road maintenance, by adapting them to this sector. Priority of road maintenance problems subject to internal uncertainty caused by imprecise human judgments will be reviewed and investigated, as well as the most popular theories and methods in group MCDM for presenting uncertain information, creating weights for decision criteria, examining causal relationships, and ranking alternatives. The study concluded that through the strengths and weaknesses reached, fuzzy set theory is the most appropriate and best used in modeling uncertain information. In addition, the methods that are employed the most common in the literature that has been done to explore the correlations between decision criteria have been examined, and it is concluded that the fuzzy best-worst method may be utilized in this research. The Fuzzy VIKOR approach is most likely the best method for ranking the decision alternatives.

Selecting the Best Project Using the Fuzzy ELECTRE Method

Selecting projects is often a difficult task. It is complicated because there is usually more than one dimension for measuring the impact of each project, especially when there is more than one decision maker. This paper is aimed to present the fuzzy ELECTRE approach for prioritizing the most effective projects to improve decision making. To begin with, the ELECTRE is one of most extensively used methods to solve multicriteria decision making (MCDM) problems. The ELECTRE evaluation method is widely recognized for high-performance policy analysis involving both qualitative and quantitative criteria. In this paper, we consider a real application of project selection using the opinion of experts to be applied into a model by one of the group decision makers, called the fuzzy ELECTRE method. A numerical example for project selection is given to clarify the main developed result in this paper

Using Pythagorean Fuzzy Sets (PFS) in Multiple Criteria Group Decision Making (MCGDM) Methods for Engineering Materials Selection Applications

The process of materials’ selection is very critical during the initial stages of designing manufactured products. Inefficient decision-making outcomes in the material selection process could result in poor quality of products and unnecessary costs. In the last century, numerous materials have been developed for manufacturing mechanical components in different industries. Many of these new materials are similar in their properties and performances, thus creating great challenges for designers and engineers to make accurate selections. Our main objective in this work is to assist decision makers (DMs) within the manufacturing field to evaluate materials alternatives and to select the best alternative for specific manufacturing purposes. In this research, new hybrid fuzzy Multiple Criteria Group Decision Making (MCGDM) methods are proposed for the material selection problem. The proposed methods tackle some challenges that are associated with the material selection decision making process, such as aggregating decision makers’ (DMs) decisions appropriately and modeling uncertainty. In the proposed hybrid models, a novel aggregation approach is developed to convert DMs crisp decisions to Pythagorean fuzzy sets (PFS). This approach gives more flexibility to DMs to express their opinions than the traditional fuzzy and intuitionistic sets (IFS). Then, the proposed aggregation approach is integrated with a ranking method to solve the Pythagorean Fuzzy Multi Criteria Decision Making (PFMCGDM) problem and rank the material alternatives. The ranking methods used in the hybrid models are the Pythagorean Fuzzy TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution) and Pythagorean Fuzzy COPRAS (COmplex PRoportional Assessment). TOPSIS and COPRAS are selected based on their effectiveness and practicality in dealing with the nature of material selection problems. In the aggregation approach, the Sugeno Fuzzy measure and the Shapley value are used to fairly distribute the DMs weight in the Pythagorean Fuzzy numbers. Additionally, new functions to calculate uncertainty from DMs recommendations are developed using the Takagai-Sugeno approach. The literature reveals some work on these methods, but to our knowledge, there are no published works that integrate the proposed aggregation approach with the selected MCDM ranking methods under the Pythagorean Fuzzy environment for the use in materials selection problems. Furthermore, the proposed methods might be applied, due to its novelty, to any MCDM problem in other areas. A practical validation of the proposed hybrid PFMCGDM methods is investigated through conducting a case study of material selection for high pressure turbine blades in jet engines. The main objectives of the case study were: 1) to investigate the new developed aggregation approach in converting real DMs crisp decisions into Pythagorean fuzzy numbers; 2) to test the applicability of both the hybrid PFMCGDM TOPSIS and the hybrid PFMCGDM COPRAS methods in the field of material selection. In this case study, a group of five DMs, faculty members and graduate students, from the Materials Science and Engineering Department at the University of Wisconsin-Milwaukee, were selected to participate as DMs. Their evaluations fulfilled the first objective of the case study. A computer application for material selection was developed to assist designers and engineers in real life problems. A comparative analysis was performed to compare the results of both hybrid MCGDM methods. A sensitivity analysis was conducted to show the robustness and reliability of the outcomes obtained from both methods. It is concluded that using the proposed hybrid PFMCGDM TOPSIS method is more effective and practical in the material selection process than the proposed hybrid PFMCGDM COPRAS method. Additionally, recommendations for further research are suggested