Consensus Model For Group Decision Research Articles

Robust maximum expert consensus model with adjustment path under uncertain environment

The maximum expert consensus model (MECM) is a commonly used consensus model in group decision making (GDM). In traditional MECM, the consensus constraints are not fully considered and the adjustment cost of decision maker (DM) is certain. Moreover, directing the DM’s opinion in a visual path is seldom considered in the consensus reaching process (CRP) of MECM. Inspired by these issues, this paper first proposed two MECMs with different types of consensus constraints. Then, this paper incorporated an adjustment path into MECM by using feedback coefficients that can prevent opinions from being overadjusted. Furthermore, the robust MECM (RMECM) is developed to address the uncertainty of unit adjustment cost under three uncertainty sets. Finally, the feasibility of the proposed models is verified by applying them to the allocation of special funds in the Chinese film industry, which is a large-scale group decision making (LSGDM) problem. The sensitivity analysis and comparative analysis are also conducted to show the efficiency of the proposed models.

A Stackelberg game model for large-scale group decision making based on cooperative incentives

With the rapid development of novel technological paradigms such as e-democracy, e-government, and collective intelligence, large-scale group decision making (LSGDM) has become an emerging topic. In LSGDM, a clustering algorithm is usually adopted to cluster experts into multiple subgroups with the aim of reducing the dimension of the problem. Because of the clustering process, a large group spans three hierarchies of a moderator, multiple subgroup spokesmen, and corresponding experts in each subgroup. The moderator first proposes an incentive to encourage subgroups to modify their opinions to reach an expected degree of consensus. Then, in each subgroup, the spokesman invokes sub-games with involved experts to negotiate the number of changed opinions through allocating incentives. Considering such a hierarchical decision-making structure, this study introduces a hierarchical Stackelberg game model to address the interactions between different players. A critical value is proposed to define the reward or punishment according to the degree of cooperativeness of experts and subgroups. The existence and uniqueness of the Stackelberg equilibrium is verified. We also put forward a consensus model for group decision making based on the Stackelberg equilibrium. A numerical example is provided to demonstrate the applicability of the model, and numerical studies are given to investigate the influence of some parameters.

A Consensus Model for Group Decision Making with Hesitant Fuzzy Information

This article presents a more improved consensus-based method for dealing with multi-person decision making (MPDM) that uses hesitant fuzzy preference relations (HFPRís) that arenít in the usual format. We proposed a Lukasiewicz transitivity (TL-transitivity)-based technique for establishing normalised hesitant fuzzy preference relations (NHFPRís) at the most essential level, after that, a model based on consensus is constructed. After that, a transitive closure formula is created in order to build TL -consistent hesitant fuzzy preference relations (HFPRís) and symmetrical matrices. Afterwards, a consistency analysis is performed to determine the degree of consistency of the data given by the decision makers (DMs), as a result, the consistency weights must be assigned to them. After combining consistency weights and preset(predeÖned) priority weights, the Önal priority weights vector of DMs is obtained (if there are any). The consensus process determines either data analysis and selection of a suitable alternative should be done directly or externally. The enhancement process aims to improve the DMís consensus measure, despite the implementation of an indicator for locating sluggish points, in the circumstance that an unfavorable agreement is achieved. Finally, a comparison case demonstrates the relevance and e§ectiveness of the proposed system. The conclusions indicate that the suggested strategy can provide insight into the MPDM system.

An Interactive Consensus Model in Group Decision Making with Heterogeneous Hesitant Preference Relations

This paper proposes an interactive consensus reaching model in the group decision making for heterogeneous hesitant preference relations (i.e., hesitant fuzzy preference relations, hesitant multiplicative preference relations, hesitant fuzzy linguistic preference relations). First, the consistencies of three hesitant preference relations are defined, respectively. Then, based on their definitions, three optimization models are constructed to obtain the weight vector of alternatives, based on which an interactive consensus adjustment algorithm is established based on the direct consensus framework. This framework adopts feedback mechanism to facilitate the information correction of decision makers. After several rounds of adjustment, the decision results with satisfactory consensus level are achieved. Finally, the practicability and effectiveness of the model are illustrated through a case study of mine accident emergency decision making.

Two flexibility degrees-driven consensus model in group decision making with intuitionistic fuzzy preference relations

A group of experts are commonly invited to find an optimal solution to a complex decision making problem. When the bipolarity of decision information should be considered in group decision making (GDM), intuitionistic fuzzy values (IFVs) have the capability to model such opinions of decision makers (DMs). This paper develops a consensus model in GDM under intuitionistic fuzzy environments with flexibility. First, it is assumed that the initial opinions of DMs are expressed as intuitionistic fuzzy preference relations (IFPRs). A novel additive consistency index is constructed to measure the deviation degree of IFPRs from fuzzy preference relations (FPRs) with additive consistency, where the non-determinacy degree of IFPRs is incorporated. The thresholds of the proposed index corresponding to IFPRs with acceptable additive consistency are discussed and computed. Second, the consensus level of DMs is defined using the similarity degree between two IFVs. An optimization problem is established by maximizing the fitness function, which is constructed by linearly combining the proposed additive consistency index and consensus level. Two flexibility degrees are offered to each DM such that the initial opinions with the bipolarity can be adjusted correspondingly. Third, individual IFPRs in GDM are optimized using the particle swarm optimization (PSO) algorithm. Numerical examples are carried out to illustrate the proposed consensus model by comparing with the existing ones. The obtained results reveal that the proposed additive consistency index can reflect the inherent property of IFPRs. Different with the previous studies, two original flexibility degrees are proposed to characterize the multi-granularity of decision information in GDM.

A genetic algorithm based on dual hesitant fuzzy preference relations for consensus group decision making

Consensus is an important issue in group decision making as it aims to avoid future contestation by the decision makers. The elicitation of criteria and decision makers’ weights is an essential part of decision-making problems. This study proposes a new consensus model for group decision making based on dual hesitant fuzzy and evolutionary algorithm for the definition of unknown criteria and decision makers’ weights. The Dual Hesitant Fuzzy Preference Relations combines the advantages of intuitionistic and hesitant fuzzy representations, and it is used to deal with the imprecision in decision makers’ judgments. In order to find decision makers weights to reach a better level of consensus without the need to modify initial assessments, the proposed Genetic Algorithm (GA) is applied. An illustrative application case is presented in a large steel company considering sustainable criteria. An instance generator was proposed to create different scenarios of decision making varying the number of criteria, decision makers, and level of hesitation. Several instances were used in the computational tests for the evaluation of the GA performance. The effectiveness of the proposed GA was verified by comparing its results with the results of the implemented Particle Swarm Optimization (PSO) algorithm. The GA yielded solutions with improved consensus levels in a reasonable runtime, especially for a small or medium number of decision makers.

A consensus model for group decision making with self‐confident linguistic preference relations

Preference relation has been one of the most useful tools for experts to express their comparison information over alternatives in group decision-making (GDM) problems. Recently, a new type of preference relations called linguistic preference relations with self-confidence (LPRs-SC) has been proposed, which makes multiple self-confidence levels into consideration when experts provide their preferences. This study focuses on the consensus reaching process for GDM with LPRs-SC. To do that, some new operational laws for LPRs-SC are presented. Subsequently, an iteration-based consensus proposal for LPRs-SC is proposed. In the proposal, we aggregate the individual LPRs-SC using a self-confidence indices-based method which gives more importance to the most self-confident experts. A self-confidence score function is presented to derive the individual and collective priority vectors. Moreover, considering experts’ acceptable adjustment range of preference values, a two-step feedback adjustment mechanism is utilized to improve the consensus level, which adjusts both the preference values and the self-confidence levels. Finally, an example and some analyses are furnished to demonstrate the feasibility and effectiveness of the proposed method.

Group decision making with hesitant fuzzy linguistic preference relations based on modified extent measurement

The paper presents a consensus model for group decision making (GDM) with hesitant fuzzy linguistic preference relations (HFLPRs), which is composed of two parts: (1) clustering HFLPRs by mapping them into a higher dimension space based on a kernel function; (2) building a consensus model based on measuring the modified extents of decision makers’ HFLPRs for reducing the biased judgements existing in their less-familiar ways. The paper further makes comprehensive analyses for the proposed model on: (1) the influence of decision makers’ different sensitive attitudes towards the distances between the individual HFLPRs and the overall HFLPRs on decision-making results; (2) the differences and complexities of another model with a different consensus perspective and the proposed model. The experimental analyses provide the support for the maximum modified extent determination in different decision scenarios, and show that the proposed consensus model makes sense. Finally, the proposed model is illustrated by the application in choosing an optimal flood discharge technique for a hydropower station.

A consensus model for group decision making under additive reciprocal matrices with flexibility

A consensus model is proposed for group decision making (GDM) with additive reciprocal preference relations based on the technique for order preference by similarity to an ideal solution (TOPSIS). The initial positions of decision makers are expressed as additive reciprocal matrices. A method of obtaining a collective ideal additive reciprocal matrix is proposed in terms of individual ones. A novel fitness function is constructed through a linear combination of two objective functions involving the consensus degree within the group of experts and the consistency measure of individual preference relations. A new algorithm based on particle swarm optimization (PSO) is proposed to model the dynamic and iterative consensus process of GDM with flexibility. Numerical results are reported to illustrate the proposed model through some comparisons with the existing ones. The weight variance is proposed to characterize the dispersion degree of the weights of alternatives, and analyzed by considering the effects of the flexibility degree and the constraint conditions. The observations reveal that with an increasing of the flexibility degree, the dominant alterative may be chosen, or any solution may not be reached by a group of experts.

Group Decision Making with Heterogeneous Preference Structures: An Automatic Mechanism to Support Consensus Reaching

In real-world decision problems, decision makers usually express their opinions with different preference structures. In order to deal with the heterogeneous preference information in group decision making, this paper presents an optimization-based consensus model for group decision making with heterogeneous preference structures (utility values, preference orderings, multiplicative preference relations and additive preference relations). This proposal seeks to minimize the information loss between decision makers’ heterogeneous preference information and individual preference vectors and also seeks the collective solution with a consensus. Meanwhile, in order to justify the consensus model, we discuss its internal aggregation operator between the obtained individual and group preference vectors, demonstrate that the proposed model satisfies the Pareto principle of social choice theory, and prove the uniqueness of the solution to the optimization model. Furthermore, based on the proposed optimization-based consensus model, we present an automatic mechanism to support consensus reaching in the group decision making with heterogeneous preference structures. In the consensus reaching process, the obtained individual and group preference vectors are considered as a decision aid which decision makers can use as a reference to adjust their preference opinions. Finally, detailed simulation experiments and comparison analysis are conducted to demonstrate the feasibility and effectiveness of our proposed model.

A PSO-based group decision making model with multiplicative reciprocal matrices under flexibility

Using the method of the analytic hierarchy process (AHP), multiple experts are invited to pairwise compare a finite set of alternatives and find a solution in group decision making. Under the AHP framework, the given multiplicative reciprocal preference relations are allowed to be deviated from the consistent matrices to a certain degree. In this study, it is assumed that the initial positions of the experts in a group decision making problem are characterized by multiplicative reciprocal matrices over a set of alternatives. A flexibility degree is offered to each expert so that her/his position can be modified opportunely. The information granules are constructed according to two different approaches. In order to build consensus in group decision making, a novel objective function is established to measure the consensus level within the multiple experts and to quantify the level of group consistency. Based on a modified particle swarm optimization (PSO) algorithm, the dynamic and iterative consensus process in group decision making is modeled by minimizing the objective function. Numerical results are reported to illustrate the proposed consensus model in group decision making. The novelty is revealed by comparing the existing group decision making model based on the PSO method. The proposed model could be used to deal with the large-scale group decision making problem with social network information.

A Modified Consensus Model in Group Decision Making With an Allocation of Information Granularity

In order to deal with a complex decision making problem, a group of experts are commonly invited to express their opinions and reach a final decision. For the purpose of building consensus among the members of the group, it is requisite to include iterative mechanisms of brain storming. The particle swarm optimization (PSO) method can be used to model the interactive process of forming decisions. In this paper, we propose a modified consensus model of group decision making augmented by an allocation of information granularity. Under a level of information granularity, it is found that the consistency indexes of randomly created multiplicative reciprocal matrices in the analytic hierarchy process may be bigger than unity. To alleviate this limitation, a modified objective function is proposed, and it is optimized by using the modified PSO method. The information granularity is allocated by considering the reciprocity of preference relations. Some comparative studies are carried out to illustrate the proposed consensus model through numerical examples. The observations reveal that a more consistent decision can be achieved by the proposed approach.

The optimization-based aggregation and consensus with minimum-cost in group decision making under incomplete linguistic distribution context

In real decision making, due to the limitation of knowledge, problem complexity and time pressure, it is natural that decision makers express their opinions with incomplete linguistic information. This paper developed a novel consensus model for group decision making (GDM) with incomplete linguistic distribution assessments (ILDAs). Firstly, we defined the concept of ILDAs and the consensus measure for GDM with ILDAs. Then, we presented a consensus-oriented aggregation model, which can obtain a collective opinion with maximum consensus, and further developed a minimum-cost consensus model with variable unit consensus cost. Following this, based on the proposed aggregation and consensus models, we proposed a novel consensus reaching process for GDM with ILDAs. Finally, a numerical example is conducted to demonstrate the validity of the proposed consensus reaching process.

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.

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 consensus model for group decision making under interval type-2 fuzzy environment

We propose a new consensus model for group decision making (GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets (IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situations. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute comparable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.

A new consensus model for group decision making using fuzzy linguistic preference relations with heterogeneous experts

Group decision making (GDM) problems consist of finding the most acceptable solution based on a group of experts’ preferences. Sometimes, the experts experience difficulty expressing their preferences using crisp values or making comparisons between each pair of alternatives. Meanwhile, because of their different backgrounds or knowledge concerning a specific problem, the opinions of different experts may carry different weights along the decision process. Thus, a new consensus model is proposed to solve these problems. First, experts are required to express their opinions using fuzzy linguistic preference relations, and then, a new method is proposed for classifying the experts into three different importance levels according to these opinions. Then, consistency measures and proximity measures are used to guide the decision-making process. A new feedback mechanism that generates advice for experts according to their different levels is proposed. The importance degrees of experts are taken into consideration throughout the process, which is one of the main novelties of this model. Finally, a numerical example is conducted to illustrate the utilization and compared results are also presented to check the feasibility of the proposed model.

A Consensus Model for Group Decision Making with Hesitant Fuzzy Information

Hesitant fuzzy sets, permitting the membership of an element to be a set of several possible values, can be used as an efficient mathematical tool for modeling people's hesitancy in daily life. The aim of this paper is to present a consensus support model for group decision making with hesitant fuzzy information. This model is composed of two processes: a consensus process and a selection process. The consensus process is carried out to reach a high level of consensus among experts' opinions before applying a selection process. We first aggregate the hesitant fuzzy decision matrix into a group decision matrix by using the additive aggregation (AA) operator. Then the consensus measure is used to design a feedback mechanism that generates advice to the experts on how they should change their preferences to obtain a solution with a high consensus degree. In the selection process, based on the consentaneous group decision matrix, the additive weighted aggregation (AWA) operator is utilized to derive the overall attribute values of alternatives, by which the most desirable alternative can be found out. Finally, a practical example is proposed to illustrate the application of the proposed model.

A New Consensus Model for Group Decision Making Problems With Non-Homogeneous Experts

In the literature, we find that the consensus models proposed for group decision making problems are guided by consensus degrees and/or similarity measures and/or consistency measures . When we work in heterogeneous group decision making frameworks, we have importance degrees associated with the experts by expressing their different knowledge levels on the problem. Usually, the importance degrees are applied in the weighted aggregation operators developed to solve the decision situations. In this paper, we study another application possibility, i.e., to use heterogeneity existing among experts to guide the consensus model. Thus, the main goal of this paper is to present a new consensus model for heterogeneous group decision making problems guided also by the heterogeneity criterion. It is also based on consensus degrees and similarity measures, but it presents a new feedback mechanism that adjusts the amount of advice required by each expert depending on his/her own relevance or importance level.

A new consensus model for group decision making using fuzzy ontology

Involving many people in decision making does not guarantee success. In practice, there are always individuals who try to exert pressure in order to persuade others who could easily be influenced. In these situations, classical group decision making models fail. Thus, there is still the necessity of developing tools to help users reach collective decisions as if they participated in a real face to face meeting. In such a way, a proper negotiation process can lead to successful solutions. Therefore, we propose a new consensus model to deal with the psychology of negotiation by using the power of a fuzzy ontology as weapon of influence in order to improve group decision scenarios making them more precise and realistic. In addition, the use of a fuzzy ontology gives us the possibility to take into account large sets of alternatives.