An Intuitionistic Fuzzy DEA Cross-Efficiency Methodology with an Application to Production Group Decision-Making Problems

In decision-making situations, the opinions expressed by decision-makers (DMs) are often vague. Using linguistic variables expressed in intuitionistic fuzzy numbers is a more realistic approach to describing DMs’ judgments. The paper aims to develop a Group Decision Making (GDM) methodology based on the data envelopment analysis (DEA) method with intuitionistic fuzzy information. This method is utilized once a set of Decision-Making Units (DMUs) need to be ranked based on their efficiencies over a set of input and output measures considering DMs’ weights in an intuitionistic fuzzy environment. In the proposed method, concerning the input and output measures, each DM utilizes membership and non-membership degrees to determine the degrees of satisfiability and non-satisfiability of each DMU, respectively. Besides, a new technique is presented to determine the DMs’ weights. Different values of a DMU's efficiency obtained by individual DMs are converted into an aggregated efficiency based on the DMs’ weights. Finally, the extended DEA method is used to rank the DMUs based on their efficiencies. A case study on a production company is done for illustration and verification of the proposed approach.