Modeling fuzzy data envelopment analysis by parametric programming method

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiency of decision making units (DMUs) consuming the same types of inputs and producing the same types of outputs. This paper studies the DEA models with type-2 data variations. In order to deal with the existed type-2 fuzziness, we propose the mean reduction methods for type-2 fuzzy variables. Based on the mean reductions of the type-2 fuzzy inputs and outputs, we formulate a new class of fuzzy generalized expectation DEA models. When the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we discuss the equivalent parametric forms for the constraints and the generalized expectation objective, where the parameters characterize the degree of uncertainty of the type-2 fuzzy coefficients so that the information cannot be lost via our reduction method. For any given parameters, the proposed model becomes nonlinear programming, which can be solved by standard optimization solvers. To illustrate the modeling idea and the efficiency of the proposed DEA model, we provide one numerical example.

Research highlights
► A new mean reduction method for type-2 fuzzy variable is proposed.
► The properties of the generalized credibility for reduced fuzzy variables are discussed.
► A new class of fuzzy generalized expectation DEA models is developed.
► The equivalent parametric programming problem of proposed DEA model is established.
► The modeling idea and the efficiency of proposed DEA model are demonstrated via numerical experiments.