Uncertainty Group Consensus Modelling With Normal Distribution

In complex decision making,the most apparent characteristic of decision maker 's(DM's)interval-valued judgment information is the high-level relationship between intervals and random distribution variables.Assumed that the experts' preference information for every pairwise comparison of alternatives is a random variable obeying normal distribution.This paper investigated the priority models of interval-valued fuzzy preference relation(IVFPR),intuitionistic fuzzy preference relations(IFPRs),hesitant fuzzy linguistic preference relation(HFLPR)with normal distribution,and designed the alternative selecting algorithm.The research can further enrich the theory of uncertain preference group decision making.Firstly,based on the mathematical equivalence between the IFPR and the IVFPR,we constructed the equivalent membership degree IVFPR and non-membership degree IVFPR of the IFPR.Then,we assumed that the experts' preference information for every pairwise comparison of alternatives is a random variable obeying normal distribution.Subsequently,by using the ? 3? principle" and the "minus principle of normal distribution",we constructed chance constraint optimal priority models with the IFPR and the group intuitionistic fuzzy preference relation(GIFPR)based on the multiplicative consistency property.The relationship between the priority vectors of the equivalent membership degree IVFPR and non-membership degree IVFPR is established.Secondly,in order to verify the validity of the above GIFPR optimal priority model,we further constructed the chance constraint optimal priority models with the IFPR and the GIFPR based on the multiplicative consistency property by using the "3? principle" and the "uncertainty normal theory".As the same,the relationship between the priority vectors of the equivalent membership degree IVFPR and non-membership degree IVFPR is established.The main conclusions are listed as follows:? The optimal weight vectors of the(non-)membership GIFPR obtained by using these two methods are the same,while the objective values are different.? There exists an inverse relationship between the priority weights of the membership and non-membership IVFPR.? The degree of the multiplicative consistency condition can be controlled by adjusting the probability in the chance constraint.Furthermore,referring to the situation in which experts may be hesitant while providing preference information of pairwise comparison of alternatives,we further explored hesitation from the perspective of hesitant fuzzy linguistic preference relation(HFLPR)with normal distributions.Then we obtained the optimal ranking of HFLPR based on non-additive consistency property and chance constraint programming,which provides a new approach for decision making with HFLPR.Lastly,in the aim of simulating the interactive process of the DM's uncertainty judgment information more effectively,this paper further introduced the genetic algorithm and Monte Carlo approach to investigates the consensus decision making problem of the IVFPR with distribution characteristics.The Pareto optimization solution derived is closer to reality.Therefore,this study provides a reference for the framework of the interactive decision support system.