Abstract

Data envelopment analysis (DEA) is a managerial tool used to measure the relative efficiency of decision making units (DMU). Classic DEA models estimates a production frontier using efficient DMUs. This frontier bounds all feasible production plans named production possibility set. Traditional DEA models require crisp input and output data. However, in real-world problems inputs and outputs are often imprecise like fuzzy numbers. When the inputs and outputs of the DMUs are fuzzy numbers the exact location of production frontier cannot be determined precisely, therefore production possibility set is an imprecise set. This paper considers production possibility set as a fuzzy set that all production plans are considered as its member with different degrees of membership and a membership function is derived under a geometrical approach in a two dimensional space for the case when the DMUs have only one fuzzy input or output and finally this membership function is generalized to the models with multiple fuzzy input and output.

Key words: Data envelopment analysis, production possibility set, fuzzy set, T-norm.