Group Decision-making Model Research Articles

Group Decision-Making Model With Hesitant Multiplicative Preference Relations Based on Regression Method and Feedback Mechanism

The hesitant multiplicative preference relation (HMPR) was initially put forward in 2013. Utilizing the HMPR, the decision makers can give some possible preference values from the Saaty’s 1–9 scale for pairwise comparisons over alternatives. However, until now, there is little research on the consistency and consensus of HMPRs. In this paper, we focus on exploiting the regression method and the feedback mechanism to improve the consistency and consensus for HMPRs and developing an efficient group decision-making model with HMPRs. First, a regression method based on complete consistency is developed to reduce HMPRs to multiplicative preference relations (MPRs). After that, a novel consistency checking and revising method based on the threshold estimation method and the feedback mechanism is given to improve the consistency level of the reduced MPRs. Then, a group consensus index is put forward to calculate the deviation degree between the reduced MPR and the group MPR and it is utilized to develop a consensus reaching process based on the feedback mechanism to improve the group consensus level of the reduced MPRs. Next, a complete group decision-making model with HMPRs is developed to rank all the alternatives and select the best one. Finally, a numerical example with respect to the investment of shared bikes is presented to demonstrate the proposed group decision-making model and then we also compare our proposed model with the existing one.

A New Distance-Based Consensus Reaching Model for Multi-Attribute Group Decision-Making with Linguistic Distribution Assessments

This paper proposes a novel consensus reaching model for multi-attribute group decision making (MAGDM) with information represented by means of linguistic distribution assessments. Firstly, some drawbacks of the existing distance measures for linguistic distribution assessments are analyzed by using numerical counterexamples, and a new distance measure is proposed for linguistic distribution assessments in order to alleviate the limitations. Then, a novel consensus reaching model is developed for MAGDM with linguistic distribution assessment, in which a feedback mechanism is devised by combining an identification rule and an optimization-based model. In this consensus framework, the model allows experts who are identified to modify their preferences to provide additional preference information about linguistic distribution assessments in each iteration. Meanwhile, by solving an optimization model, the consensus reaching model can automatically generate preference adjustment suggestions for experts. Moreover, the optimization model solved in each iteration minimizes the deviation between the adjusted values and initial preferences, which in turn leads to the good performance of the proposed consensus reaching model in preserving the initial preference information. Finally, an illustrative example shows that the proposed consensus reaching model is feasible and effective, and a comparative analysis highlights the advantages and characteristics of the model.

A trust transitivity model for group decision making in social network with intuitionistic fuzzy information

Group decision-making problems within social relationships among experts are called SN-GDM problems and have been widely considered in many fields, such as management, social science, and natural science. In SN-GDM problems, the trust relationships among experts possess uncertainty and attenuation during propagation. However, few studies have focused on the two issues at the same time. This work aims to develop a trust transitivity model for SN-GDM with intuitionistic fuzzy (IF) information. First, to model the trust relationships among experts, we present an intuitionistic fuzzy trust transitivity model that contains a trust propagation operator and an aggregation operator. Second, some concepts of IF trust network centrality analysis are defined and applied to determine expert weights. Third, a new approach is proposed to solve SN-GDM problems with IF information. Finally, comparison analysis is conducted to highlight the advantages of the proposed approach. An example is also provided to show the validity of the proposed method.

Hesitant Probabilistic Fuzzy Preference Relations in Decision Making

Preference of an alternative over another alternative is a useful way to express the opinion of decision maker. In the process of group decision making, preference relations are used in preference modelling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty; in many scenarios of decision making probabilities of different events affect the decision making process directly. In order to deal with this issue, in this paper, hesitant probabilistic fuzzy preference relation (HPFPR) is defined. Furthermore, consistency of HPFPR and consensus among decision makers are studied in the hesitant probabilistic fuzzy environment. In this respect, many novel algorithms are developed to achieve consistency of HPFPRs and reasonable consensus between decision makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision making. Lastly, we present a case study with complete illustration of the proposed model and discussed the effects of probabilities on decision making validating the importance of the introduction of probability in hesitant fuzzy preference relation.

An ontology-based approach for modeling the heavy metals’ temporal and spatial variations in groundwater resources by using fuzzy multi-criteria group decision-making models and geographical information system

An ontology-based approach for modeling the heavy metals’ temporal and spatial variations in groundwater resources by using fuzzy multi-criteria group decision-making models and geographical information system

Generalized Pythagorean Fuzzy Maclaurin Symmetric Means and Its Application to Multiple Attribute SIR Group Decision Model

Pythagorean fuzzy sets, originally proposed by Yager (IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), pp 57–61, 2013), which are convenient to describe vagueness and impression in real-world problems, can be regarded as a novel extension of intuitionistic fuzzy sets. Generalized Maclaurin symmetric mean comes as an extension of classical Maclaurin symmetric mean. Their prominent feature is that they can both capture overall interrelationships and also focus on individual importance among the arguments. However, the generalized Maclaurin symmetric mean can only be considered for aggregating numeric information. In this paper, we investigate the generalized Maclaurin symmetric mean and further extend to Pythagorean fuzzy environment. We develop the Pythagorean fuzzy generalized Maclaurin symmetric mean (PFGMSM), the Pythagorean fuzzy weighted generalized Maclaurin symmetric mean (PFWGMSM), and discuss a variety of their desirable properties. To better understand the proposed parameterization operators, we provide an innovative way to extend the classical superiority and inferiority ranking (SIR) group decision model to Pythagorean fuzzy environment. Then, an approach formed with the aid of PFWGMSM and SIR to multiple attribute group decision-making with Pythagorean fuzzy information is developed. Finally, an illustrative example concerning supply chain financial risk decision-making is provided to verify the proposed method and demonstrate its effectiveness.

An interval type-2 fuzzy TOPSIS model for large scale group decision making problems with social network information

Large scale group decision making (LGDM) problems and social network analysis (SNA) methods are both attracting increasing attention, and SNA methods are useful for addressing LGDM problems. By considering social network information, a new interval type-2 fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) model is proposed to solve LGDM problems in complex and uncertain environments. First, a SNA community detection method is applied to reduce the complexity of large scale decision makers (DMs) according to the social connections among them. Then, interval type-2 fuzzy sets (IT2 FSs) and linguistic variables are employed to handle the uncertainties, and the TOPSIS method is improved using IT2 FSs to obtain an optimal alternative for a LGDM problem. Next, decision weights are computed based on the centrality of the SNA, and the decision information is aggregated by the interval type-2 fuzzy weighted average method. The procedure for solving LGDM problems is presented. Finally, an illustrative example is investigated to demonstrate the feasibility of the proposed solution for LGDM problems, and the results are compared with those of an existing method to verify the validity of the new proposed method.

Determining Truth Degrees of Input Places in Fuzzy Petri Nets

Fuzzy Petri net (FPN), as one type of high-level Petri nets, has attracted a lot of attention over the recent decade due to its adequacy for knowledge representation and logic reasoning. However, in the FPN literature, the truth degrees of input places are usually given directly or supposed by researchers. No or little research has been performed on the determination of initial marking vector for a specific FPN. In this correspondence paper, we introduce a group decision-making model using hesitant 2-tuple linguistic term sets to obtain the initial truth values of FPNs based on domain experts’ knowledge and gathered data. As is illustrated by the numerical example, the proposed framework can well capture domain experts’ diversity judgements and derive initial truth degrees for an FPN under different types of uncertainties.

An interval-valued 2-tuple linguistic group decision-making model based on the Choquet integral operator

ABSTRACTThe Choquet integral (IL) operator is an effective approach for handling interdependence among decision attributes in complex decision-making problems. However, the fuzzy measures of attributes and attribute sets required by IL are difficult to achieve directly, which limits the application of IL. This paper proposes a new method for determining fuzzy measures of attributes by extending Marichal's concept of entropy for fuzzy measure. To well represent the assessment information, interval-valued 2-tuple linguistic context is utilised to represent information. Then, we propose a Choquet integral operator in an interval-valued 2-tuple linguistic environment, which can effectively handle the correlation between attributes. In addition, we apply these methods to solve multi-attribute group decision-making problems. The feasibility and validity of the proposed operator is demonstrated by comparisons with other models in illustrative example part.

Precursor Selection for Sol–Gel Synthesis of Titanium Carbide Nanopowders by a New Cubic Fuzzy Multi-Attribute Group Decision-Making Model

Abstract In this paper, we construct an extended version of the TOPSIS method by using cubic information, and provide a numerical application to verify and demonstrate the practicality of the method. A new extension of the gray relation analysis (GRA) method is introduced by using cubic information. We also propose the cubic fuzzy multi-attribute group decision-making model, and the relation between the cubic TOPSIS method and the cubic gray relation analysis (CGRA) method is introduced. Finally, the proposed method is used for selection in sol–gel synthesis of titanium carbide nanopowders. We analyzed the proposed method by using a numerical application to sol–gel synthesis of titanium carbide nanopowders.

A minimum adjustment cost feedback mechanism based consensus model for group decision making under social network with distributed linguistic trust

A theoretical feedback mechanism framework to model consensus in social network group decision making (SN-GDM) is proposed with following two main components: (1) the modelling of trust relationship with linguistic information; and (2) the minimum adjustment cost feedback mechanism. To do so, a distributed linguistic trust decision making space is defined, which includes the novel concepts of distributed linguistic trust functions, expectation degree, uncertainty degrees and ranking method. Then, a social network analysis (SNA) methodology is developed to represent and model trust relationship between a networked group, and the trust in-degree centrality indexes are calculated to assign an importance degree to the associated user. To identify the inconsistent users, three levels of consensus degree with distributed linguistic trust functions are calculated. Then, a novel feedback mechanism is activated to generate recommendation advices for the inconsistent users to increase the group consensus degree. Its novelty is that it produces the boundary feedback parameter based on the minimum adjustment cost optimisation model. Therefore, the inconsistent users are able to reach the threshold value of group consensus incurring a minimum modification of their opinions or adjustment cost, which provides the optimum balance between group consensus and individual independence. Finally, after consensus has been achieved, a ranking order relation for distributed linguistic trust functions is constructed to select the most appropriate alternative of consensus.

Sustainable supplier selection by a new decision model based on interval-valued fuzzy sets and possibilistic statistical reference point systems under uncertainty

ABSTRACTEvaluating and selecting appropriate sustainable supplier is regarded as a significant decision that plays a main role to successfully manage the sustainable supply chain. This study introduces a novel interval-valued fuzzy group decision model for evaluating sustainability performance of suppliers in the sustainable supply chain management (S-SCM). For this purpose, values of two high possibilisic mean and low possibilistic standard deviations are presented to provide new separation measures matrixes. Then, new interval-valued fuzzy indexes are proposed based on concepts of fuzzy possibilistic statistical reference point system. In addition, evaluation criteria from sustainable development dimensions are considered along with the conventional criteria for comprehensive assessment approach. Steps of the proposed interval-valued fuzzy group decision model are implemented to a case study in the supply chain for the sustainable supplier selection problem. The computational results of the presented model are compared with two recent fuzzy decision methods from the related literature. The model can assist supply chain experts or decision-makers to systematically determine preference order of sustainable supplier candidates under uncertain conditions.

A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters

In the large-scale group decision making (LGDM) consensus process, it is usually assumed that the obtained clusters do not change. However, as the individual preferences change as part of the decision process, this is generally not the case. The aim of this paper, therefore, is to propose a LGDM consensus model in which the clusters are allowed to change and the decision makers provide preferences using fuzzy preference relations. The most commonly used clustering method, k-means, is introduced to identify the subgroups and a possibility distribution based hesitant fuzzy element (PDHFE) is employed to represent each cluster preference. A novel distance measure over the PDHFEs is given to compute the various consensus measures, after which a local feedback strategy with four identification rules and two direction rules is designed to guide the consensus reaching process. The proposed model is distinguished from previous studies where the changes occur on the obtained clusters that the feedback mechanism is directly based on the decision makers in the identified clusters. Further, as the clusters (virtual or nominal) change in every interactive consensus round, the consensus process evolution can be captured. Finally, an emergency decision to choose a rescue plan is illustrated to validate the proposed method and demonstrate distinctive characteristics compared with the existing approaches.

Group decision making based on linguistic distributions and hesitant assessments: Maximizing the support degree with an accuracy constraint

The hesitant fuzzy linguistic term set (HFLTS) and the linguistic distribution are becoming popular tools to model linguistic expressions with multiple linguistic terms in decision problems. Compared with HFLTSs, linguistic distributions provide more probabilistic preference information over linguistic terms, and are useful to express decision makers' preferences accurately. However, in a group decision context a linguistic distribution based group opinion will bring great difficulty for the group to take an accurate action. Meanwhile, the linguistic group opinion should obtain enough support from decision makers in the group. To tackle these issues, based on the use of linguistic distributions and HFLTSs we propose a new linguistic group decision model called the maximum support degree model (MSDM), aiming at maximizing the support degree of the group opinion as well as guarantying the accuracy of the group opinion. A mixed 0–1 linear programming approach is presented to solve the MSDM, and a feedback adjustment is employed to improve the support degree of the group opinion. Finally, the use of the MSDM in multiple attribute group decision making is demonstrated.

Linguistic Multi-Attribute Group Decision Making with Risk Preferences and Its Use in Low-Carbon Tourism Destination Selection.

Low-carbon tourism plays an important role in carbon emission reduction and environmental protection. Low-carbon tourism destination selection often involves multiple conflicting and incommensurate attributes or criteria and can be modelled as a multi-attribute decision-making problem. This paper develops a framework to solve multi-attribute group decision-making problems, where attribute evaluation values are provided as linguistic terms and the attribute weight information is incomplete. In order to obtain a group risk preference captured by a linguistic term set with triangular fuzzy semantic information, a nonlinear programming model is established on the basis of individual risk preferences. We first convert individual linguistic-term-based decision matrices to their respective triangular fuzzy decision matrices, which are then aggregated into a group triangular fuzzy decision matrix. Based on this group decision matrix and the incomplete attribute weight information, a linear program is developed to find an optimal attribute weight vector. A detailed procedure is devised for tackling linguistic multi-attribute group decision making problems. A low-carbon tourism destination selection case study is offered to illustrate how to use the developed group decision-making model in practice.

A vague set fuzzy multi-attribute group decision-making model for selecting onsite renewable energy technologies for institutional owners of constructed facilities

Institutional owners of constructed facilities are increasingly recognizing onsite renewable energy generation as an effective way of reducing their facilities' negative impact on the environment, lowering utility bills, and improving the institution's public image. Situations often arise when owners are uncertain as to which renewable energy technology (RET) to adopt for maximum benefit. Appropriate selection of a RET for institutional owners should consider multiple attributes such as cost, reliability, environmental impact, and institutional-wide factors. Additionally, individual decision makers’ opinions from across the institution should be collected and aggregated into a group consensus opinion. This paper proposes a vague set fuzzy multi-attribute group decision-making model to select the most appropriate RET for institutional owners. The proposed model integrates group rational behavior theory with vague set fuzzy theory. The group rational behavior theory is utilized to account for the varying level of expertise and opinions of decision makers. The vague set fuzzy theory is utilized because most of the collected opinions from decision makers involve fuzzy data and information. The paper discusses the RETs that are evaluated with the proposed model followed by the factors affecting the selection process. Subsequently, the proposed model is described and illustrated using a case study.

A novel group decision-making model based on triangular neutrosophic numbers

In group decision-making (GDM) model, experts often evaluate their opinion by using triangular fuzzy numbers. The preference relations with triangular fuzzy numbers are in consistent in nature, so we turned to neutrosophic in this paper. It is very important to take into account consistency of expert opinion and consensus degree in GDM. In order to distinguish the typical consistency, the concept of additive approximation consistency is proposed for triangular neutrosophic additive reciprocal matrices. The properties of triangular neutrosophic additive reciprocal matrices with additive approximation consistency are studied in detail. Second, by using $$(n-1)$$ restricted preference values, a triangular neutrosophic additive reciprocal preference relation with additive approximation consistency is constructed. The differences among expert’s opinions are measured using consensus degree. For generating a collective triangular neutrosophic additive reciprocal matrix with additive approximation consistency, the neutrosophic triangular weighted aggregation operator is used. Finally, a novel algorithm for the group decision-making problem with triangular neutrosophic additive reciprocal preference relations is presented. A numerical example is carried out to illustrate the proposed definitions and algorithm.

A consensus model for group decision making under trapezoidal fuzzy numbers environment

Natural linguistic terms can preferably express the opinions of decision makers in complicated decision environment. Group decision making with multiplicative trapezoidal fuzzy preference relations transforming from natural linguistic terms attracts the attention of researchers for its important research significant. The developed approach is based on consensus improving process by using a new similarity measure and a trapezoidal fuzzy power ordered weighted geometric averaging (TFPOWGA) operator. In order to introduce this approach, firstly, trapezoidal fuzzy power geometric averaging operator and TFPOWGA operator are presented to aggregate trapezoidal fuzzy numbers (TFNs). Secondly, a new similarity measure for TFNs is introduced by combining centroids and areas of TFNs. We further propose a new consensus improving algorithm that consists of consensus measure and a dynamic feedback mechanism containing a multi-objective optimization model and some indirect rules. And then a selection stage is described to rank the alternatives. At last, an example is implemented to demonstrate effectiveness of the approach.

A decision support model for group decision making with intuitionistic fuzzy linguistic preferences relations

As a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was introduced to efficiently cope with situations in which the membership degree and non-membership degree are represented as linguistic terms. For group decision making (GDM) problems with IFLPRs, two significant and challenging issues are individual consistency and group consensus before deriving the reliable priority weights of alternatives. In this paper, a novel decision support model is investigated to simultaneously deal with the individual consistency and group consensus for GDM with IFLPRs. First, the concepts of multiplicative consistency and weak transitivity for IFLPRs are introduced and followed by a discussion of their desirable properties. Then, a transformation approach is developed to convert the normalized intuitionistic fuzzy priority weights into multiplicative consistent IFLPR. Based on the distance of IFLPRs, the consistency index, individual consensus degree and group consensus degree for IFLPRs are further defined. In addition, two convergent automatic iterative algorithms are proposed in the investigated decision support model. The first algorithm is utilized to convert an unacceptable multiplicative consistent IFLPR to an acceptable one. The second algorithm can assist the group decision makers to achieve a predefined consensus level. The main characteristic of the investigated decision support model is that it guarantees each IFLPR is still acceptable multiplicative consistent when the predefined consensus level is achieved. Finally, several numerical examples are provided, and comparative analyses with existing approaches are performed to demonstrate the effectiveness and practicality of the investigated model.

A group consensus decision support model for hesitant 2-tuple fuzzy linguistic preference relations with additive consistency

Hesitant fuzzy linguistic term sets suit the modelling of qualitative setting so that experts provide several possible linguistic values than a single term for an indicator, alternative, variable, etc. This paper proposes a consistency and consensus based decision support model for group decision m aking with hesitant 2-tuple fuzzy linguistic preference relations (H2TFLPRs). A revised definition of hesitant fuzzy linguistic preference relation (HFLPR) is presented. In order to measure the consensus degrees, two indexes, an individual to group consensus index (ICI) and a group consensus index (GCI) are introduced, respectively. A consistency control process is developed to transform an unacceptable consistency H2TFLPR to an acceptable one. Then, an iterative group consensus reaching process is designed to conduct the decision makers (DMs) to achieve the predefined consensus level. In the consistency and consensus improving process, both the feedback mechanism and no-feedback mechanism are devised to conduct the DMs how to modify their original judgments, and both mechanisms can retain the DMs’ original information as much as possible. Finally, a numerical example is illustrated to demonstrate the effectiveness of the proposed method.