A comparative study of the fuzzy linear model and the DEA in evaluation of efficiency of the DMUs

Evaluation of efficiency for every DMU (Decision Making Unit) in a company is a very important issue. Thus, the studies of evaluation of efficiency are being actively carried out on the basis of production functions. Until now, loglinear production function (Cobb-Douglas model) has been used for evaluation. This loglinear model evaluates DMUs by measuring the average. Recently, DEA (Data Envelopment Analysis) has been applied as the available method involving, for example, the CCR (Charnes-Cooper-Rhodes) and BCC (Banker-Charnes-Cooper) models. However, the IDEA models do not have the lower limit on the production set, but only the upper limit. Since, however, we consider that the real problems have the production set extending from the lower limit to the upper limit, we propose the possibility production function obtained by introducing the fuzziness into the loglinear production function. As we try to evaluate the efficiency by this possibility production function we can obtain two efficiency ratings: for the upper and lower limits. Though both DEA and fuzzy loglinear model include all the DMU data, in the DEA approach we obtain the lower limit on inputs for the given output, while in the fuzzy loglinear approach we obtain the possibility maximum output for the given inputs. By making full use of the difference between the two approaches, we try to compare the DEA and the fuzzy loglinear model in the evaluation of efficiency of the DMUs. In terms of two efficiency ratings, fuzzy loglinear model can yield more exact ranking for every DMU than DEA. Genarally, when a DMU has efficiency less that 1 by fuzzy loglinear analysis, it means that there is a possibility of obtaining larger output for the given inputs.