Group Decision Making Method And Application Based On Hesitant Fuzzy Linguistic Preference Relation

In the decision-making process,due to the limitations of subjective and objective conditions,the traditional precise value preference relationship cannot deal with the uncertainty and fuzziness in decision-making well.Moreover,in the research of some qualitative problems,the precise value can not accurately express the decision information.In contrast,natural linguistic terms can better express decision-makers’ preferences and information,and using natural linguistic variables to express decision-makers’ information is more in line with people’s expression ways.Therefore,using the term set of hesitant fuzzy linguistic can better describe the information and preferences provided by decision makers.In addition,with the development of social and economic environment and the growth of knowledge and information,more and more decision-making problems cannot be solved by a single decision maker,so it is necessary to gather multiple decision makers for group decision-making.From this point of view,it is meaningful and valuable to study hesitant fuzzy linguistic preference group decision making,which makes the decision result scientific and feasible.Consistency optimization of individual preferences and group consensus reaching are the two main problems in group decision making.There are still some limitations in the existing research on hesitant fuzzy linguistic preference group decision making: the definition of consistency and the method of optimizing consistency proposed in relevant literature are controversial;The correlation group decision model fails to consider both individual consistency and consensus improvement.Therefore,based on the existing researches and the preference relation theory of hesitant fuzzy linguistic,this paper carries out a series of researches on some problems in group decision making under hesitant fuzzy linguistic environment.Firstly,this paper studies the additive consistent definition,discrimination and optimization process of individual hesitant fuzzy linguistic preference relationship.Secondly,the determination of weight vector is studied on the basis of the consistency of additivity of individual hesitant fuzzy linguistic preference relation.Then,the consensus improvement process of group hesitant fuzzy linguistic preference relationship is studied.Finally,based on the additive agreement and group consensus optimization models of individual hesitant fuzzy linguistic preference,the group decision model is discussed.This paper applies the above research process to an example and expounds the theory and method proposed in this paper.Specific research contents and related achievements are as follows:(1)In order to solve the problem of consistency of preference relation in hesitant fuzzy linguistic,a new definition of additive consistency is proposed,which is not limited to the consideration of endpoint or local preference value,but takes into account the semantic value of each hesitant fuzzy linguistic term set.Then,based on this definition,a programming model is established to determine whether the hesitant fuzzy linguistic preference relationship is consistent.In addition,an optimization model is established for the inconsistent hesitant fuzzy linguistic preference relationship to adjust the inconsistent hesitant fuzzy linguistic preference relationship to the consistent hesitant fuzzy linguistic preference relationship.This model does not need to normalization the original hesitant fuzzy linguistic preference relationship and preserves as much original information as possible.And the preference value in the optimized hesitant fuzzy linguistic preference relation still belongs to the hesitant fuzzy linguistic term set.This study enriches the consistency correlation theory of hesitant fuzzy linguistic preference relation and provides an effective tool for discriminating and optimizing the additive consistency of hesitant fuzzy linguistic preference relation.(2)Aiming at the weight vector problem of hesitant fuzzy linguistic preference relation,the hesitant fuzzy linguistic set is introduced into the study of weight vector,and the definition of hesitant fuzzy linguistic weight vector is proposed.Under the background of hesitant fuzzy decision making,the hesitant fuzzy linguistic weight vector may be more consistent with decision preference of decision makers.In addition,according to the new additive consistent definition,a programming model is constructed to calculate the weight vector of hesitant fuzzy linguistic.This research enriches and expands the theory of weight vector.(3)Firstly,a new distance formula is proposed to measure the distance between hesitant fuzzy linguistic sets.Then,based on this formula,a new consensus improvement model of hesitant fuzzy linguistic preference relation is constructed,which makes the opinions of multiple experts meet the consensus threshold.The model not only preserves as much original information as possible,but also the collective opinions obtained have minimum entropy,which reduces the uncertainty and complexity of group decision making.In addition,the consensus optimization model takes into account the unique optimal solution problem.This study provides a new method and approach to solve the problem of consensus improvement.(4)In this paper,a new group decision making model is constructed by combining the consensus optimization model with the consensus improvement model.The model considers both individual agreement and consensus improvement,which not only ensures that the individual preference relationship meets the additive agreement,but also makes the group consensus level meet the consensus threshold.This study enriches the relational group decision theory of hesitant fuzzy linguistic preference.The proposed group decision making method based on hesitancy fuzzy language preference relation can solve uncertain and complex group decision making problems and provide effective and scientific support for decision making problems in different situations.