Study On Multiple Attribute Decision Making Under Linguistic Environment By Bipolar2-Tuple Fuzzy Linguistic Representation Model

In the process of linguistic multiple attribute decision making, there have been extension principle, symbolic method, linguistic variables direct operation method and2-tuple fuzzy linguistic representation model to aggregate linguistic information. Although,2-tuple model has been widely applied to many fields, the theory of this model is not very mature. There still have been many blemishes in2-tuple model. To overcome the lack of2-tuple model, it is extended to bipolar linguistic term set, and a bipolar2-tuple fuzzy linguistic representation model is proposed. Because of the numerical attribute weights, multiple attribute decision making is not strictly a linguistic multi-attribute decision making problem. Moreover, some dispute is produced in aggregating linguistic information and real numbers. In order to improve2-tuple model in the linguistic multiple attribute decision making, the linguistic attribute weights and linguistic attribute values are studied, and a bipolar2-tuple weighted arithmetic averaging(2-LWAA)operator is defined. Based on the relationship between the judgment matrix elements and the weight, the logical relation of the elements in multiplicative fuzzy consistent complementary judgment matrix with the priorities is deduced. The main results are listed as follows:(1) The unipolar linguistic term set is extended to bipolar linguistic term set. Based on the relation between semantics of bipolar linguistic term set and bipolar linguistic term set, bipolar2-tuple linguistic representation model is established.(2) The triangular fuzzy numbers on [0,1] is extended to the ones on [-1,1]. The bipolar2-tuple model is expressed by the triangular fuzzy numbers on [-1,1]. The transformation between bipolar2-tuple model and values on [-1,1] is studied according to the relation between2-tuple model and values on [0,1].(3) The linguistic attribute weights and linguistic attribute values are introduced in linguistic multiple attribute decision making. The weighted arithmetic averaging(WAA)operator and the ordered weighted averaging(OWA) operator are developed to the linguistic environment. The bipolar2-tuple weighted arithmetic averaging(2-LWAA) operator is defined. A new method of multiple attribute decision making about bipolar2-tuple is studied.(4) On the basis of the relationship between the judgment matrix elements and the weights, a logical relation of the elements in multiplicative fuzzy consistent complementary judgment matrix with the priorities is deduced. The logical relation is used to get the priorities, and the order of alternatives is obtained.