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

• Autorzy: Uemura Y.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

DEA; Charnes-Cooper-Rhodes model; fuzzy log-linear model; fuzzy goal

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2006
• Tom: Vol. 35, no 2
• Strony: 487--495
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Uemura Y.

• Faculty of Education, Mie University, Tsu Mie 514, Japan

Bibliografia

• CHARNES A., COOPER W. W. and RHODES E. (1978) Measuring the Efficiency of Decision Making Units. EJOR 2, 429-444.
• SAKAWA M. (1993) Fuzzy Sets and Interactive Multiobjective Optimization. Plenum Press.
• SATO K. (1975) Theory of Production Function (in Japanese). Soubunnsha.
• TANAKA H. (1991) Fuzzy Modelling and Its Applications (in Japanese). Asakura Bookstore.
• TONE K. (1993) Data Envelopement Analysis (in Japanese). Nikagircn.
• UEMURA Y., KOBAYASHI M. and HIRO K. (1996) Application of Fuzzy Log-linear Regression Analysis to Evaluation of Efficiency for DMUs. J. of Fuzzy Mathematics 4, 1, 199-206.
• UEMURA Y. (1998a) A comparative study of fuzzy loglinear model and DEA in evaluation of DMUs. Control and Cybernetics 27, 3, 459-465.
• UEMURA Y. (1998b) Satisfactional method introducing the concept of fuzzy goal and fuzzy constraints into DEA. Control and Cybernetics 27, 3, 453-457.
• UEMURA Y. (1998c) Fusion of Evaluation of Possibility Production Function and DEA by Introducing a Fuzzy Goal. Proc. of 2nd International Conference on Knowledge-based Intelligent Electronic Systems, Adelaide, Australia, 1, 285-288.
• UEMURA Y. (2001) Fuzzy Mixed CCR Model with an Application to Banking. J. of Fuzzy Mathematics 9, 1, 517-524.
• UEMURA Y. (2003) Fuzzy satisfactional method by fuzzy multi-objective linear problem introducing two fuzzy goals from possibility production function into DEA. J. of Fuzzy Mathematics 11, 2, 333-340.
• WATADA J. and MORIMOTO M. (1992) Analysis of Japanese Industries Based on Possibilistic Production Function (in Japanese). Proc. of 2nd Workshop on Fuzzy Systems, 22-25.