The Research On Multi-attribute Group Decision Making Methods Based On Linguistic Intutionistic Fuzzy Numbers

Most of the multiple attributes decision making problems is uncertain and fuzzy,so it is difficult to use crisp number to describe decision information.In order to express the uncertain information more comprehensively,many scholars devote themselves to propose new languages.The mean of expression went through real numbers to fuzzy numbers,linguistic variables and intuitionistic fuzzy numbers.Intuitionistic fuzzy numbers is an effective method to describe fuzzy multiple attribute decision making(FMADM)for it can describe the degree of certainty and uncertainty of the cognitive through membership function and the membership functions respectively.But the membership and the membership functions are expressed with accurate number,not always enough to solve the fuzzy and uncertain information in practice,especially for the qualitative evaluation.Language information is the most widely used form of expression for it can describe the fuzzy nature of the object more precisely.So Chen Z.C.put forward the concept of linguistic intuitionistic fuzzy number(LIFN),which uses the language based on a given set of linguistic variables to represent the membership and the membership degree.However,the newly proposed language has not been widely studied especially in terms of operator and methods.The existing research of this language focus on the condition that evaluation values are mutually independent and the weight is unknown.In addition,its combing with operators and methods need to be proposed.In order to make up for the deficiency,this paper combine the LIFN with three operators and one method.One is the generalized aggregation operator which is widely used in decision making.The other two operators are the Power operator and the Power Bonferroni operator.The Power operator make weights according to the support of other values and the Power Bonferroni operator take the relationship of values into account.Through the combining,a series of new operators are developed.After that the expanded TODIM approaches are proposed in two cases: the weight is known or not.These methods are a supplement to existing methods in solving the multiple attribute group decision making(MAGDM)problems desc-ribed by linguistic intuitionistic fuzzy numbers which has important theoretical and realistic significance.Innovation points of this article are:(1)Define distance between LIFNs.(2)Propose the linguistic intuitionistic fuzzy generalized operator,linguistic intuitionistic fuzzy Power average operator and linguistic intuitionistic fuzzy Power Bonferroni operator and discussed some properties and theorems of them.(3)Some linguistic intuitionistic fuzzy multiple attribute decision making methods were proposed based on these operators and the extended TODIM method and the feasibility and effectiveness of them are proved.