Study Of Group Decision Making Methods Based On Hesitant Preference Relations

Group decision making(GDM)is an important part of decision theory.GDM is to aggregate multiple decision makers’ preference information into a consensus or comprise preference of the group by means of some rules.GDM benefits focusing the wisdom of experts in different fields,making full use of the different professional knowledge,experience and background of its members to improve the comprehensiveness and scientificity of decision making.With the development of society,people face increasingly complex decision-making environment.Hence,decision makers often hesitate to evaluate complex problems because each decision maker has limited knowledge and experience and time pressure.Under the circumstances,hesitant fuzzy set is an effective tool for decision-makers to express their hesitant information.Preference relation is the essential tool expressing preference information provided by the decision maker in the decision making problem.The use of hesitant preference relations to express the preference information is more close to the cognitive psychology of human being,and avoids the loss of information.Therefore,this paper mainly studies the GDM methods based on the hesitant preference relations.In order to ensure the scientificity and credibility of the GDM results,the GDM based on the preference relations usually needs to consider two aspects: the consistency of individual preference relation and the realization of group consensus.On the one hand,individual consistency is used to ensure that the preference information given by the decision maker is logical and is not arbitrary,which ensures the accuracy of the decision-making premise;on the other hand,the GDM result with a satisfactory group consensus can be accepted by most decision makers.GDM methods based on the hesitant preference relations still exist the following problems: the individual hesitant preference relations usually do not have the perfect consistency or satisfactory consistency,the existing consistency definitions and improved consistency methods for hesitant preference relations have some defects and controversies;The GDM methods based on incomplete hesitate preference relations are relatively less;There are also defects in the existing GDM methods based on heterogeneous hesitant preference relations,such as their range of use is limited and they cannot deal with the heterogeneous hesitant GDM problem that contains the hesitant fuzzy linguistic preference relations.Therefore,this paper establishes GDM methods based on individual consistency and group consensus for hesitant preference relations.The contents and the related results are specifically given as follows:(1).The GDM methods based on hesitant fuzzy preference relations are investigated.The expected consistency of hesitant fuzzy preference relation is defined,and then the priority weights of alternatives is obtained by the optimization model,based on which,an interactive group consensus reaching model is established.This method avoids the addition of new elements and preservs the original information of the experts to the maximum extent.Moreover,this paper obtains the GDM method with incomplete hesitant fuzzy preference relations based on the optimization model and the group consensus reaching algorithm.(2).A GDM method with hesitant fuzzy linguistic preference realtions is studied.Based on the additive consistency of hesitant fuzzy linguistic preference realtion,this paper proposes a convergence automatic iteration group consensus algorithm.The research enrichs the group decision theory of hesitant fuzzy linguistic preference realtions and expands its application field.(3).The GDM methods based on incomplete hesitant fuzzy linguistic preference realtions are proposed.A filling method is established to obtain complete hesitant fuzzy linguistic preference realtions based on the additive consistency,and the complete hesitant fuzzy linguistic preference realtions are improved to be additive consistent.Finally,the satisfied group consensus is obtained by means of automatic iterative algorithm;In addition,a simple nonfilling method is put forward to extract complete consistent fuzzy linguistic preference relation as the most reasonable information from the given incomplete hesitate fuzzy linguistic preference relation by optimization method based on the additive and multiplicative consistency,respectively.Finally,a group consensus reaching algorithm is implemented,respectively.This study provides a new way to solve the GDM problems with incomplete hesitant fuzzy linguistic preference relations.(4).A GDM method based on heterogeneity hesitant preference relations(hesitant fuzzy preference relation,hesitant fuzzy linguistic preference realtion,hesitant multiplicative preference realtion)is established.First of all,corresponding mathematical programmings are established for priority weights based on the consistencies of different hesitate preference relations;Then,group priority weights is obtained by IOWA operator;Finally,an interactive consensus model is established.In addition,a goal programming of the minimum total consistent deviation is proposed to obtain directly the weight and order of each option.The established method need not transform hesitant preference relation and avoids the loss of information so that it makes the decision result more credible.To summarize,the proposed GDM mehods based on hesitant preference relations can manage complex problems under uncertain environment.These methods are not only applied in choice of emergency decision plan,supplier selection,optimal investment etc.,but also provide the decision support for the economy,military science,medical science and other fields.