Study On The 2-tuple Linguistic Intuitionistic Fuzzy Multi-attribute Decision Making Method

The multi-attribute decision making mainly researches the finite alternatives on discrete evaluation values,whose characteristics are that a group of experts make decisions for a set of finite feasible alternatives on a set of attributes,and then choose the best alternative by comprehensive analysis.Due to the complexity and inaccuracy of practical decision-making problems or the ambiguity of human thinking,it is difficult for decision makers to give precise estimates.So there are many uncertain multi-attribute decision making methods.As an important part of uncertain multi-attribute decision-making,fuzzy multi-attribute decision making is the extension of classical multi-attribute decision-making in theory and has been extensively applied to various areas,such as resources management,purchasing and outsourcing,supplier selection,technology selection and so on.As a generalization of fuzzy sets,intuitionistic fuzzy sets are evaluated by the "belonging to","not belonging to" and "hesitation" in three aspects,which can describe the vague essence of objective object more profoundly.For qualitative attributes,decision makers are difficult to give precise values for "belonging to" or "not belonging to",and usually use rough or imprecise language to give evaluation information.As a kind of linguistic representative methods,2-tuple linguistic intuitionistic fuzzy sets(2TLIFSs)combine the advantages of both linguistic term sets and intuitionistic fuzzy numbers(IFNs),which are characterized by the linguistic membership degree and linguistic nonmembership degree.This paper mainly investigates the 2-tuple linguistic intuitionistic fuzzy multiple attribute decision making method and the main contents are as follows:(1)Combined the linguistic power aggregation(LPA)operator with 2TLIFSs,this paper proposes the linguistic intuitionistic fuzzy power average(LIFPA)operator and applies it to the multiple attribute group decision making problem with the known weights of decision makers in the environment of linguistic intuitionistic fuzzy sets.In order to obtain the support degree of two 2-tuple linguistic intuitionistic fuzzy sets in the LIFPA operator,the Hamming distance between the 2-tuple linguistic intuitionistic fuzzy sets is defined.In addition,this paper proves that the operator is commutative,bounded and idempotent.(2)Based on the LIFPA operator and OWA operator,this paper proposes the linguistic intuitionistic fuzzy power ordered weighted average(LIFPOWA)operator and applies it to the multiple attribute group decision problem with the unknown weights of decision makers in the environment of linguistic intuitionistic fuzzy sets.In addition,this paper proves that the operator is commutative,bounded and idempotent.(3)Based on 2-tuple linguistic intuitionistic fuzzy sets,this paper provides the TOPSISmethod.In order to obtain the distance between the alternatives and the positive and negative ideal solutions,the 2-tuple linguistic intuitionistic fuzzy decision matrix is defined and the Hamming distance between two linguistic intuitionistic fuzzy decision matrices is proposed.To verify the usefulness and effectiveness of proposed TOPSIS method,this paper compares it with the linguistic TOPSIS method.(4)This paper proposes the TOPSIS method based on multi-granularity linguistic intuitionistic fuzzy sets.In order to deal with the multi-granularity linguistic evaluation information effectively,the conversion method of multi-granularity linguistic intuitionistic fuzzy sets is given.And this paper further compares it with the TOPSIS method based on uncertain linguistic variables.