Data Envelopment Analysis with Fuzzy Input-Output Data

In this paper, we develop a DEA (Data Envelopment Analysis) with fuzzy input-output data. There are several approaches to extend the DEA to the case of fuzzy input-output data. We chose the most natural approaches among them. In one of these approaches, a linear programming problem solved in the conventional DEA is regarded as a mapping from an input-output data set to the efficiency score set. Applying the extension principle to the mapping, we obtain a fuzzy set of efficiency scores from given fuzzy input-output data. We also propose an efficiency analysis based on possibility theory. The relations between the fuzzy set of efficiency scores and the possibilistic efficiency analysis are investigated.

[1]  P. Andersen,et al.  A procedure for ranking efficient units in data envelopment analysis , 1993 .

[2]  N. Petersen,et al.  Chance constrained efficiency evaluation , 1995 .

[3]  Masahiro Inuiguchi.  Stochastic Programming Problems versus Fuzzy Mathematical Programming Problems , 1992 .

[4]  Jens Leth Hougaard,et al.  Theory and Methodology Fuzzy scores of technical e ciency , 1999 .

[5]  Lawrence M. Seiford,et al.  Stability regions for maintaining efficiency in data envelopment analysis , 1998, Eur. J. Oper. Res..

[6]  D. Dubois,et al.  FUZZY NUMBERS: AN OVERVIEW , 1993 .

[7]  W. Hogan.  Point-to-Set Maps in Mathematical Programming , 1973 .

[8]  A. Charnes,et al.  Data Envelopment Analysis Theory, Methodology and Applications , 1995 .

[9]  Abraham Charnes,et al.  Sensitivity analysis of the additive model in data envelopment analysis , 1990 .

[10]  Lawrence M. Seiford,et al.  CHARACTERISTICS ON STOCHASTIC DEA EFFICIENCY : RELIABILITY AND PROBABILITY BEING EFFICIENT , 1999 .

[11]  Zhimin Huang,et al.  Dominance stochastic models in data envelopment analysis , 1996 .

[12]  Russell G. Thompson,et al.  Sensitivity Analysis of Efficiency Measures with Applications to Kansas Farming and Illinois Coal Mining , 1994 .

[13]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[14]  Hideo Tanaka,et al.  Fuzzy DEA with Fuzzy Data , 1997 .

[15]  Hiroshi Morita.  Fuzzy Categorical Inputs in Data Envelopment Analysis , 1995 .