Reduction Methods For Type-2 Fuzzy Variables And Their Applications In Dea

Type-2 fuzzy variable is a map from a fuzzy possibility space to the real number space, and it is an appropriate tool to describe type-2 fuzziness. This thesis firstly proposes two class of novel reduction methods for a type-2 fuzzy variable, which one refered to as mean reduction methods and critical value reduction methods, respectively, and discusses their basic properties. Secondly, this thesis applies the reduction methods to data envelopment analysis (DEA) models with type-2 fuzzy inputs and outputs, and develops two new class of fuzzy DEA models. According to the properties of generalized credibility, when the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we can turn the proposed fuzzy DEA models into their equivalent parametric programming problems, in which the param-eters can be used to characterize the degree of uncertainty about type-2 fuzziness. For any given parameters, each of the parametric programming models becomes a nonlinear or linear programming one that can be solved by standard optimization solvers. For each class of the modelss, we provide one numerical example to illustrate its modeling idea and efficiency.The main contribution of this thesis contains the following four aspects:(â…°) two class of novel reduction methods for a type-2 fuzzy variable are proposed, and some properties of the reduction methods are discussed; (â…±) with the proposed reduction methods, two new class of fuzzy DEA models are esstablished; (â…²) the equivalent parametric programming problems of the established models are discussed under the assumption that the inputs and outputs are mutually independent type-2 trianglar fuzzy variables, and (â…³) two numerical examples are provided to illustrate the modeling ideas and the effectiveness of the proposed DEA models.