Study On Linguistic Information Aggregation Operators

In the past years, the theory and applications of multiple attribute group decision making have become hot research topics of applied mathematics, management science and decision science, etc. Especially, the researches of multiple attribute group decision making about linguistic information are concerned, this kind of problem not only has important theoretical significance, but also has wide application prospect.One of the key to solve this kind of decision making problems is to choose appropriate linguistic information aggregation operators.Some linguistic aggregation operators, for example,2-tuple linguistic aggregation op-erators, uncertain linguistic aggregation operators, etc., have been proposed and applied to multiple attribute decision making in the literatures.However, problems of multiple attribute group decision making under linguistic infor-mation environment are quite complicated, there are still some problems to be solved. For instance, whether the results of decision making by using different aggregation operators about same decision making problems are consistent; if we can find aggregation operator on complex multiple attribute decision making problems with parameter for the same decision making problems, when parameters of aggregation operators change, we can analysis the result of decision making and the selection of the parameter etc.Based on above considerations, in this thesis, properties of the existing linguistic ag-gregation operators are further studied, and some new linguistic aggregation operators are proposed. At the same time, some ideal properties of these new operators are discussed. Furthermore, the new approaches to multiple attribute group decision making with the proposed new linguistic aggregation operators are introduced. Through solving practical multiple attribute decision making problems, the practicality of new approaches are showed.The main research topics and results of this thesis are as follows:Based on the 2-tuple linguistic environment and the power average operator, a type of new appregation operators, called the 2-tuple linguistic generalized power hybrid aver-age operators are proposed, and their ideal properties, such as boundedness, monotonicity, idempotency and commutativity are verified. Compared with the existing 2-tuple linguistic aggregation operators, the new operators have some advantages. Finally, based on t-norms and t-conorms, the 2-tuple linguistic weighted average operators based on t-norms and t-conorms are introduced. So a new organic connection between fuzzy logic and fuzzy decision is established.Based on uncertain linguistic environment and Hero average operators, the uncertain linguistic Hero geometrical average operators are proposed, and their properties and several special subclasses are discussed.Finally, the new approaches to multiple attribute group decision making based on the new linguistic aggregation operators are introduced. And these new approaches are applied to real problems. The differences of results about different approaches based on linguistic multiple attribute group decision making are also discussed. So some meaningful conclusions and recommendations are given.