Group Consensus Modeling With Multiple Heterogeneous Preference Relations

With the era of big data,consensus reaching for group decision-making(GDM)needs effective process rules and solutions.Generally,expression from multiple decision makers(DMs)differ sharply in GDM,and in order to fully consider the opinion preference and vital interest of each DM,it is necessary to explore a set of rules to achieve the unification of heterogeneous opinions.On the other hand,it is vital for consensus to introduce a moderator,who can make use of his/her influence to balance all DMs' opinions preferences.Among them,the unification of various opinions preferences,avoiding information loss/alienation,and the problem of minimum consensus cost are all the focuses of this paper.Laying emphasis upon heterogeneous preferences opinions,this paper not only explores the traditional forms of uncertain preference,such as interval fuzzy preference relation(IFPR),hesitant fuzzy preference relation(HFPR),two-tuple linguistic fuzzy preference relations(LFPRs)and so on,but also introduces random distributions and utility functions into GDM for increasing the generality of its formal application.Additionally,we prove the pairwise equivalent transformation form between heterogeneous fuzzy preference relations,and realize the unification of heterogeneous information.Furthermore,the paper constructs the minimum cost consensus models based on random opinions,the ordering model for multiple preference relations and the optimization ordering model for intuitionistic fuzzy preference relations.Depending on above models,practical GDM cases,such as China's urban demolition negotiation,global supplier selection,are able to achieve group consensus or obtain optimal ranking.Consequently,probabilistic planning based on genetic algorithm is designed for those modes with random distributions,which has the advantages of good convergence,high precision,saving computing time and so on.Comparison analyses with existing approaches are summarized to demonstrate the feasibility and advantage of proposed algorithm.The innovations of this paper are as follows: Random distributions and complex utility functions are introduced into fuzzy preference relations,which can simulate uncertain characteristics of DMs' opinion more effectively and are more favorable for acquiring the true judgment information from the DM's uncertain judgment;Assimilating heterogeneous fuzzy preference relations into a unified expression based on multiple heterogeneous their equivalent transformation method,that guarantees the integrity and accuracy of the original information;Proposed models show the mathematical form of GDM problems with the aim of cost,ranking,and consistency,and provide reference for solving practical GDM problems;The probabilistic programming method based on genetic algorithm is designed,which provides an effective solution for GDM model with random distributions.