Modeling Fuzzy DEA with Type-2 Fuzzy Variable Coefficients
Data envelopment analysis (DEA) is an effective method for measuring the relative efficiency of a set of homogeneous decision-making units (DMUs). However, the data in traditional DEA model are limited to crisp inputs and outputs, which cannot be precisely obtained in many production processes or social activities. This paper attempts to extend the traditional DEA model and establishes a DEA model with type-2 (T2) fuzzy inputs and outputs. To establish this model, we first propose a reduction method for T2 fuzzy variables based on the expected value of fuzzy variable. After that, we establish a DEA model with the obtained fuzzy variables. In some special cases such as the inputs and outputs are independent T2 triangular fuzzy variables, we provide a method to turn the original DEA model to its equivalent one. At last, we provide a numerical example to illustrate the efficiency of the proposed DEA model.
KeywordsData envelopment analysis Relative efficiency Decision-making units Type-2 fuzzy variable Reduction method
Unable to display preview. Download preview PDF.
- 10.Mitchell, H.: Ranking Type-2 Fuzzy Numbers. IEEE Tansactions on Fuzzy Systems 14, 327–348 (2006)Google Scholar
- 11.Zeng, J., Liu, Z.Q.: Type-2 Fuzzy Sets for Pattern Recognition: the State-of-the-Art. Journal of Uncertain Systems 1, 163–177 (2007)Google Scholar
- 12.Liu, Z.Q., Liu, Y.K.: Fuzzy Possibility Space and Type-2 Fuzzy Variable. In: Proc. of IEEE Symp. Found. Comput. Intell., Piscataway, NJ, pp. 616–621 (2007)Google Scholar
- 18.Wang, S., Liu, Y., Dai, X.D.: On the Continuity and Absolute Continuity of Credibility Functions. Journal of Uncertain Systems 1, 185–200 (2007)Google Scholar
- 19.Liu, Y.K., Wang, S.: Theory of Fuzzy Random Optimization. China Agricultural University Press, Beijing (2006)Google Scholar