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Fuzzy satisfactory evaluation method for covering the ability comparison in the context of DEA efficiency

Uemura Y.

Control and Cybernetics

2006

Vol. 35, no 2

487-495

Evaluation of efficiency of each of the DMUs (Decision Making Units) in a company is a very important task. Thus, the studies of evaluation of efficiency are being actively carried out, based on production function. Until quite recently, the loglinear production function (the Cobb-Douglas function) has been used for evaluation purposes. The loglinear model evaluates the DMUs by measuring the average efficiency. Of late, the DEA (Data Envelopment Analysis) focussed the interest as the available method, in the form of either the CCR (Charnes-Cooper-Rhodes) or the BCC (Banker-Charnes-Cooper) model. However, the DEA approach does not provide for the lower limit of the production set, but only for the upper one. Hence, considering the fact that in the real-life problems the production set ranges between the lower and the upper limit, it is proposed that the possibility production function be constructed by introducing fuzziness into the loglinear production function. When we try to evaluate efficiency with the help of this possibility function, we can obtain from it two efficiency ratings, corresponding to the upper and lower limits. The DEA and the fuzzy loglinear models perform evaluation in the sense of inclusion of all the DMU data and provide a dual possibility image of efficiency in the sense that the DEA assesses the lower limit of inputs for the given output, while the fuzzy loglinear model assesses the maximum output for the given inputs. Hence, by making full use of this duality, we try to fuse the DEA and the fuzzy loglinear model in the evaluation of DMU efficiency by introducing a fuzzy goal. We propose to construct the fuzzy goal by evaluating the ratings for individual outputs with the help of fuzzy loglinear analysis, and introduce this fuzzy goal into the DEA. This approach can yield both efficiency and ability as obtained from the comparison of the CCR-based efficiencies.

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

Uemura Y.

Control and Cybernetics

1998

Vol. 27, no 3

471-477

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.