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

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

Multi-Criteria Decision Making under Uncertain Evaluations

Multi-Criteria Decision Making (MCDM) is a branch of operation research that aims to empower decision makers (DMs) in complex decision problems, where merely depending on DMs judgment is insufficient. Conventional MCDM approaches assume that precise information is available to analyze decision problems. However, decision problems in many applications involve uncertain, imprecise, and subjective data. This manuscripts-based thesis aims to address a number of challenges within the context of MCDM under uncertain evaluations, where the available data is relatively small and information is poor. The first manuscript is intended to handle decision problems, where interdependencies exist among evaluation criteria, while subjective and objective uncertainty are involved. To this end, a new hybrid MCDM methodology is introduced, in which grey systems theory is integrated with a distinctive combination of MCDM approaches. The emergent ability of the new methodology should improve the evaluation space in such a complex decision problem. The overall evaluation of a MCDM problem is based on alternatives evaluations over the different criteria and the associated weights of each criterion. However, information on criteria weights might be unknown. In the second manuscripts, MCDM problems with completely unknown weight information is investigated, where evaluations are uncertain. At first, to estimate the unknown criteria weights a new optimization model is proposed, which combines the maximizing deviation method and the principles of grey systems theory. To evaluate potential alternatives under uncertain evaluations, the Preference Ranking Organization METHod for Enrichment Evaluations approach is extended using degrees of possibility. In many decision areas, information is collected at different periods. Conventional MCDM approaches are not suitable to handle such a dynamic decision problem. Accordingly, the third manuscript aims to address dynamic MCDM (DMCDM) problems with uncertain evaluations over different periods, while information on criteria weights and the influence of different time periods are unknown. A new DMCDM is developed in which three phases are involved: (1) establish priorities among evaluation criteria over different periods; (2) estimate the weight of vectors of different time periods, where the variabilities in the influence of evaluation criteria over the different periods are considered; (3) assess potential alternatives

Integrated Frameworks for Effective Multi-criteria Decision Making in Reliability Centred Maintenance of Industrial Machines

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An overview of fuzzy techniques in supply chain management: bibliometrics, methodologies, applications and future directions

Every practice in supply chain management (SCM) requires decision making. However, due to the complexity of evaluated objects and the cognitive limitations of individuals, the decision information given by experts is often fuzzy, which may make it difficult to make decisions. In this regard, many scholars applied fuzzy techniques to solve decision making problems in SCM. Although there were review papers about either fuzzy methods or SCM, most of them did not use bibliometrics methods or did not consider fuzzy sets theory-based techniques comprehensively in SCM. In this paper, for the purpose of analyzing the advances of fuzzy techniques in SCM, we review 301 relevant papers from 1998 to 2020. By the analyses in terms of bibliometrics, methodologies and applications, publication trends, popular methods such as fuzzy MCDM methods, and hot applications such as supplier selection, are found. Finally, we propose future directions regarding fuzzy techniques in SCM. It is hoped that this paper would be helpful for scholars and practitioners in the field of fuzzy decision making and SCM

Neutrosophic Multi-Criteria Decision Making

The notion of a neutrosophic quadruple BCK/BCI-number is considered in the first article (“Neutrosophic Quadruple BCK/BCI-Algebras”, by Young Bae Jun, Seok-Zun Song, Florentin Smarandache, and Hashem Bordbar), and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied. Given subsets A and B of a BCK/BCI-algebra, the set NQ(A,B), which consists of neutrosophic quadruple BCK/BCInumbers with a condition, is established. Conditions for the set NQ(A,B) to be a (positive implicative) ideal of a neutrosophic quadruple BCK-algebra are provided, and conditions for the set NQ(A,B) to be a (closed) ideal of a neutrosophic quadruple BCI-algebra are given. Techniques for the order of preference by similarity to ideal solution (TOPSIS) and elimination and choice translating reality (ELECTRE) are widely used methods to solve multicriteria decision-making problems. In the second research article (“Decision-Making with Bipolar Neutrosophic TOPSIS and Bipolar Neutrosophic ELECTRE-I”), Muhammad Akram, Shumaiza, and Florentin Smarandache present the bipolar neutrosophic TOPSIS method and the bipolar neutrosophic ELECTRE-I method to solve such problems. The authors use the revised closeness degree to rank the alternatives in the bipolar neutrosophic TOPSIS method. The researchers describe the bipolar neutrosophic TOPSIS method and the bipolar neutrosophic ELECTRE-I method by flow charts, also solving numerical examples by the proposed methods and providing a comparison of these methods. In the third article (“Interval Neutrosophic Sets with Applications in BCK/BCI-Algebra”, by Young Bae Jun, Seon Jeong Kim and Florentin Smarandache), the notion of (T(i,j),I(k,l),F(m,n))-interval neutrosophic subalgebra in BCK/BCI-algebra is introduced for i,j,k,l,m,n infoNumber 1,2,3,4, and properties and relations are investigated. The notion of interval neutrosophic length of an interval neutrosophic set is also introduced, and the related properties are investigated

A bi-objective score-variance based linear assignment method for group decision making with hesitant fuzzy linguistic term sets

open access articleDecision makers usually prefer to express their preferences by linguistic variables. Classic fuzzy sets allowed expressing these preferences using a single linguistic value. Considering inevitable hesitancy of decision makers, hesitant fuzzy linguistic term sets allowed them to express individual evaluation using several linguistic values. Therefore, these sets improve the ability of humans to determine believes using their own language. Considering this feature, in this paper a method upon linear assignment method is proposed to solve group decision making problems using this kind of information, when criteria weights are known or unknown. The performance of the proposed method is illustrated in a numerical example and the results are compared with other methods to delineate the models efficiency. Following a logical and well-known mathematical logic along with simplicity of execution are the main advantages of the proposed method

A bi-objective score-variance based linear assignment method for group decision making with hesitant fuzzy linguistic term sets

Decision makers usually prefer to express their preferences by linguistic variables. Classic fuzzy sets allowed expressing these preferences using a single linguistic value. Considering inevitable hesitancy of decision makers, hesitant fuzzy linguistic term sets allowed them to express individual evaluation using several linguistic values. Therefore, these sets improve the ability of humans to determine believes using their own language. Considering this feature, in this paper a method upon linear assignment method is proposed to solve group decision making problems using this kind of information, when criteria weights are known or unknown. The performance of the proposed method is illustrated in a numerical example and the results are compared with other methods to delineate the models efficiency. Following a logical and well-known mathematical logic along with simplicity of execution are the main advantages of the proposed method

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches