Group consensus reaching process based on information measures with probabilistic linguistic preference relations

For practical group decision-making (GDM) problems, DMs play varying degrees of importance. Thus, determining the weight of decision makers (DMs) is one of the key issues in GDM. Additionally, it is known that information measures methods have been a growing focus in recent years. Therefore, under the probabilistic linguistic fuzzy information environment, a group consensus reaching approach with the help of information measures is designed. First, two axiomatic notions regarding to entropy and similarity measures for probabilistic linguistic term sets (PLTSs) are introduced. Then, in line accordance with logarithmic function, two novel methods of entropy and similarity measures with PLTSs are established, which is followed by the determination of the weight vector of DMs by using probabilistic linguistic fuzzy entropy. Subsequently, based on probabilistic linguistic fuzzy entropy and similarity measures, we develop a group consensus reaching process (CRP), which is convergent and able to enhance the group consensus level. Moreover, the proposed group CRP can calculate the weight vector with the initial probabilistic linguistic evaluation information of DMs. Finally, for displaying the applicability and merits of the developed group CRP, the numerical example, sensitivity analysis and comparative analysis are provided. It's worth noting that our proposed measure fully utilizes the elements of the original probabilistic linguistic preference relationships (PLPRs), which can reduce the systematic error of the entire decision model, thereby making the results more reflective of the original decision information from DMs. The novelties of this paper are as follows: (1) The proposed novel way can estimate the degree of importance of DMs by the mean fuzzy entropy of PLPRs; (2) We construct two formulas about fuzzy entropy and similarity measures for PLTSs and proof these formulas, which are both reasonable and effective.