Group consensus reaching based on a combination of expert weight and expert reliability

Highlights

• A group consensus method based on expert weight and reliability is proposed.

• Expert reliability in multi-round of group analysis and discussion is constructed.

• Hybrid weight is measured dynamically based on expert reliability.

• Convergence of group consensus is accelerated based on hybrid weight.

• Evaluation of safety performance is investigated using the proposed method.

Abstract

Multi-criteria group decision making (MCGDM) as a key module in a group decision support system has attracted much attention. Different experts in MCGDM may hold different decision interests. To generate the solution that is accepted by most experts, a group consensus reaching process has been widely applied in MCGDM along with multiple rounds of group analysis and discussion (GAD). How to characterize the dynamic variation of experts’ opinions in the above process is a critical issue. To solve this problem, expert reliability is defined by measuring the dynamic variation of the support degree from other experts in GAD. By considering expert reliability and expert weight simultaneously, a group consensus measure is proposed and a group feedback mechanism is constructed to accelerate the convergence of group consensus. The dynamic variation of experts’ opinions, especially their non-cooperative behaviors, can be well addressed by using the constructed feedback mechanism. The proposed group consensus reaching process including the group consensus measure and feedback mechanism is applied to solve a problem of evaluating the safety performance of an enterprise located in Changzhou, a city in Jiangsu Province, China, in order to verify its applicability and effectiveness in MCGDM.

Introduction

The rapid development of science and technology creates the context of complex decision making that people have to face [4], [26], [33]. Multi-criteria group decision making (MCGDM) that involves several experts is more useful to help people achieve the satisfied solution to a decision problem [13], [18], [19], [21]. Different experts from the different departments and organizations may have different interests and goals for the same decision problem ([16], [20]; Pérez et al. 2013). In the beginning, it is difficult for these experts to generate a solution that is accepted by most of them. However, in practice, highly satisfactory and accepted solutions may often be required for decision making problems [14], [28], [31], such as the selection of an employee who is in charge of an important position, the evaluation of a strategic partner, and the modification of a management system. For this reason, it is necessary to generate a group consensus (GC) based solution to an MCGDM problem.

In this situation, the GC reaching process has attracted much attention and has been widely applied in solving MCGDM problems. For large group emergency decision making problems, such as the problem of selecting an appropriate rescue plan in an earthquake with a 7.0 magnitude, Xu et al. [29] introduced an exit-delegation mechanism to develop a new consensus method. The method can help accelerate group convergence to rapidly generate the final rescue plan that is accepted by most experts in the large group. In order to select outstanding Ph.D. students in a university, Liao et al. [17] provided an enhanced consensus reaching process to remove some expert opinions for reaching GC rapidly. In a group decision making problem with Analytic Hierarchy Process (AHP), Dong and Cooper [3] constructed a peer-to-peer dynamic adaptive consensus reaching model to help the experts adaptively converge in the process of handling group decision making problems. In addition, many GC reaching methods have been developed to achieve group convergence within the contexts of the different experts’ preferences, such as fuzzy preference relations [25], intuitionistic fuzzy preference relations [1], hesitant linguistic assessments [6], probabilistic linguistic term sets [34], and even heterogeneous preference structures [5].

Recently, Palomares et al. [22] pointed out the necessity of considering non-cooperative behaviors in GC reaching process, which has drawn great attention from many researchers [7], [23]. Non-cooperative behaviors may hinder the convergence of GC and should thus be addressed in the process of reaching GC [24], [29]. Overall, the literature reviewed as mentioned above indicates that the existing studies mainly focus on two hot issues related to the GC reaching process, which are the convergence of GC and the processing of non-cooperative behaviors [2], [15], [32]. However, few studies consider expert reliability in the process of reaching GC.

Both expert reliability and expert weight are applied to characterize an expert in MCGDM [9], [30]. Expert weight represents the relative importance of an expert compared with other experts. Expert reliability reflects the capability that the expert can provide the correct assessments. They are two different concepts in decision making. From the mathematical perspective, the expert weights should usually be normalized and the expert reliabilities are not normalized. That is, with the change of the number of the experts, expert weight will also be changed but expert reliability may be invariable. In general, expert weight is related to the role, position or right of an expert compared with other experts and expert reliability is associated with experience, intelligence or knowledge. For example, when facing a problem of selecting a strategic partner, three experts who are a vice general manager, a supervisor of a production department and a buyer of a purchasing department are invited. In this problem, they may require a satisfied solution that is accepted by most experts. As to the problem, the vice general manager is more important than other experts, and his weight is thus relatively higher. However, his knowledge related to the quality of the partners is less than the knowledge of the buyer, thus, his reliability is lower than the buyer on the criterion about quality.

In addition, Fu et al. [9] analyzed the influence of expert reliability on the final decision results to emphasize the importance of expert reliability in MCGDM. The experience and knowledge of an expert may change along with the in-depth group communication for an MCGDM problem. This change will result in the dynamic variation of expert reliability in the process of group analysis and discussion (GAD). For this reason, the dynamic change of expert reliability needs to be considered in the GC reaching process to guarantee the generation of an accepted solution and to accelerate the convergence of GC. Following this point, two important issues should further be addressed. One issue is to combine expert reliability and expert weight in MCGDM. Another issue is to develop a GC measure and construct a feedback mechanism by considering expert reliability and expert weight simultaneously.

To deal with the mentioned problems, this paper proposes a GC reaching process based on a combination of expert weight and expert reliability for MCGDM. In multiple rounds of GAD, expert reliability is defined as the degree to which other experts support the expert. Based on this definition, the expert reliability in each round of GAD is calculated by analyzing the variation of support degrees from other experts before and after this round of GAD; thus, the expert reliabilities are changed dynamically with increasing rounds of GAD. To combine expert reliability with expert weight, a hybrid weight is proposed to help measure the level of GC in MCGDM. Then, it is necessary to check whether the calculated GC level is satisfied with the predefined GC requirement or not. If the predefined requirement is reached, assessments provided by the experts can be combined with hybrid weights. Otherwise, a feedback mechanism based on hybrid weights should be constructed to help accelerate the convergence of GC. An identification rule and a suggestion rule with the consideration of expert reliability and expert weight are developed to identify the assessments that may hinder the GC convergence and guide the experts to update their assessments, respectively. The proposed GC reaching process is applied to solve a problem of evaluating the safety performance of an enterprise located in Changzhou, a city in Jiangsu Province, China, with the aim of demonstrating its applicability and effectiveness. Meanwhile, the influence of non-cooperative behaviors on the MCGDM problem is analyzed by using the proposed GC reaching process. The analysis indicates that the proposed feedback mechanism can avoid and prevent the non-cooperative behaviors effectively.

The rest of this paper is organized below. In Section 2, the modeling of MCGDM with GC requirements is first constructed. Then, expert reliability is proposed to help define GC measure and construct feedback mechanism. Section 3 demonstrates the process of generating a solution to the MCGDM problem with GC requirement. A real MCGDM problem is handled in Section 4 by using the proposed GC reaching process and non-cooperative behaviors are further analyzed in the problem. Section 5 concludes the whole paper and points out the future study.