A Data Envelopment Analysis Model with Triangular Intuitionistic Fuzzy Numbers

Abstract

DEA (Data Envelopment Analysis) is a technique for evaluating the relative effectiveness of decision-making units (DMU) with multiple inputs and outputs data based on non-parametric modeling using mathematical programming (including linear programming, multi-parameter programming, stochastic programming, etc.). The classical DEA methods are developed to handle the information in the form of crisp number but have no capability in dealing with fuzzy information like triangular intuitionistic fuzzy numbers (TIFNs), which is flexible in reflecting the uncertainty and hesitation associated with the decision-makers' opinion. In this paper, an extended model of DEA is proposed under the triangular intuitionistic fuzzy environment where the inputs and outputs of DMUs are TIFNs. At first, the definition and characteristics of a classical model of DEA and the comparative TIFNs are introduced. In addition, a new ranking function considering the interaction between membership and non-membership values of different intuitionistic fuzzy sets are defined. Then, the triangular intuitionistic DEA model is proposed. Finally, the new approach is illustrated with the help of a numerical example.