Study On Group Decision Making Method Based On Linguistic Intuitionistic Fuzzy Sets

Decision making is one of the most common social activities in real life.It happens anytime and anywhere and has been widely used in various fields such as engineering technology and economic management.When dealing with decision making problems,in order to avoid the inaccuracy of decision making results caused by the limitation of individual decision makers' own knowledge background,a group of decision makers are usually convened to make decisions together,which is called group decision making for short.Group decision making generally refers to the decision making process in which a group of decision makers select the best object or alternative after comparing a group of objects or alternative based on the existing decision-making information.Group decision making improves the accuracy and reliability of decision results.Because of the complexity and fuzziness of the concrete decision making problems in real life and the uncertainty of human subjective judgment,it is often difficult for decision makers to use exact values for evaluation.Therefore,people extend the classical decision making method and propose uncertain decision making method.As the extension of fuzzy sets,intuitionistic fuzzy sets depict things from the three aspects of "belonging","not belonging" and "hesitating",which accords with human subjectively describing objective things from the aspects of "affirmation","negation" and "hesitating".In fact,the decision-making information can not be expressed completely in the exact numerical value of quantitative form or even only in the fuzzy language value of qualitative form.Therefore,fuzzy language values are more appropriate than specific values.The linguistic intuitionistic fuzzy set,which is put forward by intuitionistic fuzzy set and fuzzy linguistic approach,intuitively expresses membership degree and non-membership degree in terms of language terms.It has the advantages of language terms set and intuitionistic fuzzy set and is more suitable for practical decision problems.This paper mainly focuses on the group decision making problem of linguistic intuitionistic fuzzy information.The main work is summarized as follows:(1)Study on aggregation operators of linguistic intuitionistic fuzzy information.By existing linguistic intuitionistic fuzzy aggregation operator and generalized intuitionistic fuzzy aggregation operator,generalized linguistic intuitionistic fuzzy aggregation operator is put forward,including generalized linguistic intuitionistic fuzzy weighted average operator,generalized linguistic intuitionistic fuzzy ordered weighted averaging operator and generalized linguistic intuitionistic fuzzy hybrid average operator.It is proved they are permutation invariant,monotonic,idempotency and bounded.At the same time,the paper discusses the representation of the weight information by the linguistic intuitionistic fuzzy number,proposes linguistic intuitionistic fuzzy linguistic aggregation operator,including linguistic intuitionistic fuzzy linguistic weighted average operator and linguistic intuitionistic fuzzy linguistic ordered weighted averaging operator,and proves that they are permutation invariant and monotonic.(2)A study on the ranking method of linguistic intuitionistic fuzzy numbers.According to Atanassov's partial order,a new definition of the probability degree of intuitionistic fuzzy sets is given,some reasonable properties are discussed,and a sorting method based on the probability degree is proposed.Combination with the definition of the probability degree of the uncertain language variable,and the definition of the probability degree of the linguistic intuitionistic fuzzy set and the ranking method based on the probability degree are proposed.The method is applied to a practical example and the existing sorting method for comparative analysis,and the validity of the method is verified.(3)Group decision making method for linguistic intuitionistic fuzzy preference relation.According to the existing definition of additive consistency of linguistic intuitionistic fuzzy preference relations,a construction method is proposed to convert the standard intuitionistic fuzzy weight vector given at random into the additive consistent linguistic intuitionistic fuzzy preference relations.What's more,for any linguistic intuitionistic fuzzy preference relation,a goal programming model is design to obtain its intuitionistic fuzzy weight vector.Because decision makers usually cannot give the additive consistent linguistic intuitionistic fuzzy preference relations,the consistency index based on Hamming distance and the acceptable additive consistency of linguistic intuitionistic fuzzy preference relation are defined.As for the inconsistent linguistic intuitionistic fuzzy preference relation,the maximum distance local iteration method is proposed to improve the consistency index to reach the acceptable additive consistency,and the reasonable preference information in the original linguistic intuitionistic fuzzy preference relation is preserved as much as possible.At the same time,a new consensus reaching process is proposed,and the maximum distance local iteration method is adopted to improve the consensus degree and make it reach the acceptable group consensus,so as to help decision makers find the best decision result.Then,a group decision making method considering consistency and consensus in the context of linguistic intuitionistic fuzzy preference relation is proposed and its rationality and validity are verified by case analysis.