Data envelopment analysis using fuzzy concept

Mathematical programming is one of the areas to which fuzzy set theory has been applied extensively. Primarily based on Bellman and Zadeh's model of decision in fuzzy environments, models have been suggested which allow flexibility in constraints and nonlinear programming. Data envelopment analysis (DEA) is a method of evaluating relative efficiencies for a group of similar units based on an efficiency concept. In DEA, the same set of factors is measured for each unit, and there are multiple and non-commensurate inputs and outputs. Efficiency is measured as the weighted sum of output over the weighted sum of input. This is the DEA ratio model. The other models are radial models, additive models, multiplicative models, hyperbolic models, nonradial models. In this paper, assuming hat the values of inputs and outputs in DEA are not known with certainty, a fuzzy mathematical programming is proposed. The objective function and the constraints are represented by using their degrees of membership in DEA. The main advantage of this solution that the decision maker is not forced into a precise formulation for mathematical reasons.