A Novel Technique for Solving Intuitionistic Fuzzy DEA Model: An Application in Indian Agriculture Sector

Abstract

Fuzzy DEA is a performance measurement tool that is used to assess the performance of DMUs in highly uncertain environment. In this article, the Intuitionistic fuzzy DEA (IFDEA) model is proposed based on the triangular intuitionistic fuzzy numbers (TIFNs). The weighted Possibility mean for TIFNs are used to compare and rank the TIFN. The weighted possibility mean approach is proposed to solve IFDEA model that the IFDEA model is converted into its equivalent crisp DEA model to assess the relative efficiencies of the DMUs. One advantage of the proposed approach is that the attitude of the decision maker is considered while measuring the efficiency of the DMUs. The weight or risk factor δ є [0,1] indicates whether the decision maker is a risk taker, neutral, or adverse. The crisp DEA model is a LP problem that is solved by using an existing LP method with different risk factors to determine the efficiency score of the DMUs. The DMUs are ranked based on the overall efficiency score of the DMUs that is arithmetic mean of the efficiency scores of the DMUs with different risk factors. Two numerical example is given here to demonstrate the validity and applicability of the proposed technique and to compare the performance of the DMUs in the proposed approach with exciting ranking approach and expected value approach. A case study on the agriculture sector has been conducted in order to evaluate the agricultural performance of Indian states using the IFDEA model. According to the results of the IFDEA model, 15 (53.57%) out of the 28 Indian states were found to be efficient.

A Proposed DEA Window Analysis for Assessing Efficiency from Asymmetry Dynamic Data

“…The model was implemented in poultry farming. Mohanta et al [35] developed an intuitionistic fuzzy DEA (IFDEA) model based on triangular intuitionistic fuzzy numbers (TIFNs). The weighted possibility means for TIFNs were then utilized to compare and rank the TIFNs.…”