The Bonferroni mean (BM) was originally introduced by Bonferroni and then more recently generalized by Yager. The desirable characteristic of the BM is its capability to capture the interrelationship between input arguments. Nevertheless, it seems that the existing literature only considers the BM for aggregating crisp numbers instead of any other types of arguments. In this paper, we investigate the BM under intuitionistic fuzzy environments. We develop an intuitionistic fuzzy BM (IFBM) and discuss its variety of special cases. Then, we apply the weighted IFBM to multicriteria decision making. Some numerical examples are given to illustrate our results.

Intuitionistic Fuzzy Bonferroni Means

In social network group decision making (SNGDM), the consensus reaching process (CRP) is used to help decision makers with social relationships reach consensus. Many CRP studies have been conducted in SNGDM until now. This paper provides a review of CRPs in SNGDM, and as a result it classifies them into two paradigms: (i) the CRP paradigm based on trust relationships, and (ii) the CRP paradigm based on opinion evolution. Furthermore, identified research challenges are put forward to advance this area of research.

Consensus Reaching in Social Network Group Decision Making: Research Paradigms and Challenges

A theoretical visual interaction framework to model consensus in social network group decision making (SN-GDM) is put forward with following three main components: (1) construction of trust relationship; (2) trust based recommendation mechanism; and (3) visual adoption mechanism. To do that, dual trust propagation is investigated to connect incomplete trust relationship by trusted third partners, in a way that it can fit our intuition in these cases: trust values decrease while distrust values increase. Trust relationship is proposed to be used in determining the trust degree of experts and in aggregating individual opinions into a collective one. Three levels of consensus degree are defined and used to identify the inconsistent experts. A trust based recommendation mechanism is developed to generate advices according to individual trust relationship, making recommendations more likeable to be implemented by the inconsistent experts to achieve higher levels of consensus. Therefore, it has an advantage with respect to existing interaction models because it does not force the inconsistent experts to accept advices irrespective of their trust on them. Finally, a visual adoption mechanism, which provides visual information representations on experts individual consensus positions before and after adopting the recommendation advices, is presented and analysed theoretically. Experts can select their appropriate feedback parameters to achieve a balance between group consensus and individual independence. Consequently, the proposed visual interaction model adds real and needed flexibility in guiding the consensus reaching process in SN-GDM.

A visual interaction consensus model for social network group decision making with trust propagation

Emergency situations often demand high-quality decision-making results because a wrong decision may cause incalculable losses Therefore, in such cases, the views of all decision makers should be fully considered, especially minority opinions, and the interests of all parties should be well balanced Additionally, an emergency decision often has to be made within a short period of time, which may require the rational treatment of non-cooperative behaviors Classical consensus models mainly focus on group decision-making problems where a small number of decision makers participate However, an emergency decision often involves many stakeholders, and thus requires the participation of larger number of decision makers In this paper, an improved consensus model is proposed for large-group emergency decision making, and an approach to managing minority opinions and non-cooperative behaviors is described By simulating the consensus reaching process, a method is presented to determine two important parameters: the minimum group consensus threshold and the maximum number of iterations Finally, an illustrative example proves that the proposed consensus model is feasible and effective, and a detailed discussion highlights the advantages of this model for managing large-group emergency decision-making problems A consensus model for large-group emergency decision making is developedThe model is designed to manage minority opinions and non-cooperative behaviorsA method is presented for getting the two required parametersWe put forward the concept of comprehensive adjustment coefficientA discussion is conducted to show the advantage of the proposed consensus model

Consensus model for multi-criteria large-group emergency decision making considering non-cooperative behaviors and minority opinions

The use of hesitant information in pairwise comparisons enriches the flexibility of qualitative decision making and allows for hesitant fuzzy linguistic preference relation (HFLPR). This paper develops separate consistency and consensus processes to deal with HFLPR individual rationality and group rationality. First, a possibility distribution approach and a 2-tuple linguistic model are introduced as support tools. Then, a new consistency measure is defined and a convergent algorithm described to aid the consistency improvement process in a given HFLPR. The algorithm adopts a local revision strategy and can be easily interpreted. Further, a direct consensus reaching process is presented to solve the HFLPR consensus problems. A prominent characteristic of this consensus reaching process is that the feedback system is based directly on the consensus degrees, thereby reducing the proximity measure calculations. Finally, the proposed consistency and consensus processes are applied to an investment project selection problem. The results and an in-depth comparative analysis verify the potential use and effectiveness of the proposed methods.

Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations

Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual

Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations

This paper proposes a least squares method and a goal programming method to get the priority of the intuitionistic fuzzy preference relation (IFPR). The relation between the IFPR and the interval fuzzy number preference relation (IFNPR) is established by splitting the IFPR into the membership degree interval judgment matrix and the non-membership degree interval judgment matrix. Considering the fact that the priority method must be based on the consistent condition, we propose the additive consistent conditions of the IFPR according to that of the IFNPR. However, in real-life decision situations, such consistent conditions are hard to be satisfied. For deriving the priority vector of the IFPR, the least squares model and the goal programming model are put forward. It is also shown that the same methods apply to the circumstance of group decision making. The numerical examples are provided to show that the methods proposed are valid, and the case study of selecting industries with higher meteorological sensitivity by using the intuitionistic fuzzy hierarchic structure model is given to show that the methods proposed are practical.

The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity

In complex group decision making (GDM), reaching a consensus needs both the adequate communication and exchange between the individual decision makers (DMs) and the input of a moderator, who may take various effective actions, such as providing financial compensation (collectively referred to as "consensus cost"), to convince the DMs to gradually modify their opinions and to reach a final consensus. This study constructs new consensus models that aim to maximize the GDM utility under the premise of limited consensus cost and nonlinear utility/preference constraints for both the individual DMs and the moderator. The objective function (the utility level of the entire GDM) derived from the proposed models can be seen as a measurement of the group consensus degree. Moreover, using the pollutant reduction negotiations between the government and manufacturing enterprises as a case background, we construct a group reduction consensus model based on nonlinear preference constraints and limited consensus cost and economically interpret the model parameters. Results show that different preference combinations of the DM and moderator will affect the optimal consensus values. Additionally, the moderator's preference structure influences the final GDM results to some extent. The modeling mechanism used in this paper will be reference for solving real-life consensus GDM problems.

Consensus modeling with nonlinear utility and cost constraints

This paper mainly focuses on the consensus problem with utility preferences denoted by simple trapezoidal membership function. In group decision-making (GDM), for acquiring the best consensus opinion, not only the total cost required by achieving the consensus, but also the utility of all the decision-makers (DMs) should be considered. Ben-Arieh et al. propose a consensus model from the view of the minimized cost. Based on their models, a kind of optimization consensus model has been put forward under the constraints of limited budget and different kinds of utility, whose objective function aims to obtain the maximum utility level of the whole GDM process. From an economic point of view, results show that different utility preferences of all the individual DMs have impacts on the final optimal consensus opinion. Besides, the moderator has a dominant role in the development trends throughout the whole decision-making process to some extent. Numerical examples are given to deeply explain the proposed models.

Lianshui Li

Papers

Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual

Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations

The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity

Consensus modeling with nonlinear utility and cost constraints

On consensus models with utility preferences and limited budget