The influence of mutual interaction behaviors on the opinions and consensus process has gradually emerged due to the information sharing in social networks. Currently, the cost of making individual decisions and the similarity between experts’ decision behaviors are relatively less addressed in the social network decision process. Therefore, in this study, a consensus approach with the trust relationships and adjustment cost is proposed to fill in such a gap. The method is divided into three stages: 1) trust propagation; 2) weight allocation; and 3) consensus reaching. In the trust propagation phase, uninorm is extended to the uncertain theory and employed in the transmission and integration problems of trust relationships. In the weight allocation stage, the comprehensive weight is assigned based on network structure and strength of relationship. In the consensus-reaching process, two levels of consensus are considered: 1) consensus among individuals and 2) consensus between individuals and the collective group, and chance-constrained programming models are constructed to obtain collective decision opinions. Moreover, a comparative analysis is performed to clarify the effectiveness and advancement of the proposed consensus method.

Clustering analysis is a key technique in reducing the dimensionality of high volume irregular data containing large-scale group decision-making (LSGDM) information. Uncertainty theory is suitable for subjective estimation or situation, such as lack of historical data, and it can be employed to effectively express the uncertainty of trust and preference information in LSGDM problems. This paper studies the dimensionality reduction and subgroup optimization in LSGDM by utilizing linear uncertain variables in social networks. A clustering method is proposed to decompose the large group into several subgroups of higher consilience degrees and higher preference similarities, and lower the dimension of information for LSGDM. In the clustering process, two measurement attributes, trust relationship and preference relationship of decision-makers, are combined, and information consistent degree is utilized as the clustering indicator. This approach does not need to preset the threshold and the number of subgroups, and can be employed to obtain subgroups with similar preferences and stable trust relationship. Through the clustering reliability evaluation of subgroups, the rationality of large-scale group clustering results is verified. Subgroup consensus contribution is used to identify superior subgroups and quantify the role of subgroups in improving the consensus level. An example of emergency decision-making and comparative analysis is provided to explain the feasibility and advantages of the proposed method.

A promising feature for group decision making (GDM) lies in the study of the interaction between individuals. In conventional GDM research, experts are independent. This is reflected in the setting of preferences and weights. Nevertheless, each expert's role is played through communication, collaboration, and cooperation with other individuals. The interaction from others may affect the power of an expert as well as his/her opinion. Furthermore, it is noted that a link path with the highest degree of trust is the most efficient information transmission channel. Inspired by these findings, an optimal trust-induced consensus process is designed with the usage of intuitionistic fuzzy preference relation. The comprehensive weight of each expert is decomposed into two portions, namely: 1) the individual weights and 2) interactive weights. Three optimization models are constructed to achieve weight parameters under different decision situations, where the weight parameters are represented through a 2-order additive fuzzy measure and the Shapley value. To reflect the interaction, the Choquet integral is employed for aggregating opinions, and a novel distance measure is adopted for accomplishing a consensus index. An illustrative example and comparison are put in practice to show the effectiveness and improvements of the proposed method.

Two aspects of problems including selection of aggregation operator for extreme fuzzy evaluation value and risk attitude of decision makers cannot be well solved in Pythagorean fuzzy (PF) multiattribute group decision making (MAGDM). This paper extends the evidential reasoning aggregation method in the intuitionistic fuzzy environment, expands the dictionary ranking method by constructing interval-valued numbers through the proposed credibility functions of PF values and the concept of closeness degree, widens the continuous generalized ordered weighted average ( C - GOWA ) operator to establish a risk attitude ranking measure, and puts forward a PF MAGDM approach based on risk attitude and evidence reasoning methodology (ERM). First, the proposed method utilizes the ERM to aggregate each decision maker's decision matrix and the weights of the attributes to get his/her aggregated decision matrix. Then, it incorporates the obtained aggregated decision matrices of the experts, the weights of the experts and the ERM to accomplish the aggregated PF value of each alternative. Finally, the ranking measure value of risk attitude on each alternative's PF value is calculated, and the sensitivity analysis on the ranking measure function is carried out. The proposed method has overcome the drawbacks of the existing methods for fuzzy MAGDM in PF environments.