Modified Fuzzy Data Envelopment

Analysis Models

Dike, I. J.

Department of Statistics and Operations Research

Modibbo Adama University of Technology, Yola

Adamawa State, Nigeria

Abstract

This paper examines the use of data envelopment analysis (DEA) in the conduct of efficiency measurement involving fuzzy (interval) input-output values. Data envelopment analysis is a linear programming method for comparing the relative productivity (or efficiency) of multiple service units. Standard DEA models assume crisp data for both the input and output values. In practice however, input and output values may be uncertain, vague, imprecise or incomplete. New pairs of fuzzy DEA (FDEA) models are presented which differ from existing fuzzy DEA models handling uncertain data. In this approach, upper bound interval data are used exclusively to obtain the upper frontier values while lower bound interval data are used exclusively to obtain the lower frontier values. The outcome, when compared with the outcome of existing approach, based on the same set of data, shows a swap in the upper and lower frontier values with exactly the same number of efficient decision-making units (DMUs). This new approach therefore clears the ambiguity occasioned by the mixture of upper and lower bound values in the determination of the upper and lower frontier efficiency scores respectively. The modified FDEA models make application and interpretation of results easy. The most efficient units, for each of the models, have efficiency score of 1 with equivalent ranking score of 1. These efficient units also serve as reference sets to the inefficient units. The inefficient units have efficiency scores less than 1 for all the models. The most inefficient unit is S13 for all the models and it has the least efficiency score in each case and a ranking score of 25.

Keywords: Fuzzy, Data envelopment analysis, Modified, Models.