Abstract

The defuzzification process converts fuzzy numbers to crisp ones and is an important stage in the implementation of fuzzy systems. In many actual applications, we encounter cases, in which the observed or derived values of the variables are approximate, yet the variables themselves must satisfy a set of relationships dictated by physical principle. When the observed values do not satisfy the relationships, each value is adjusted until they satisfy the relationships among observed data indicating their mathematical dependence on one another. Hence, this study proposes a new method based on the Data Envelopment Analysis (DEA) model to defuzzify groups of fuzzy numbers. It also aims to assume that each observed value is an approximate number (or a fuzzy number) and the true value (crisp value) is found in the production possibility set of the DEA model. The proposed method partitions the fuzzy numbers and the relationships among these observed data are observed as constraints. The paper presents the model, the computational process and applications in a real problem.

Keywords:

Data envelopment analysis, defuzzification, groups of fuzzy numbers, observed data,

References

1. Asady, B. and A. Zendehnam, 2007. Ranking fuzzy numbers by distance minimization. Appl. Math. Model., 31(11): 2589-2598.
   CrossRef    
2. Esogbue, A.O., Q. Song and W.E. Hearnes II, 2000. Defuzzification filters and applications to power system stabilization problems. J. Math. Anal. Appl., 251(1): 406-432.
   CrossRef    
3. Kikuchi, S., 2000. A method to defuzzify the fuzzy number: Transportation problem application. Fuzzy Set. Syst., 116(1): 3-9.
   CrossRef    
4. Lai, Y.J. and C.L. Hwang, 1992. Fuzzy Mathematical Programming: Methods and Applications. Springer-Verlag, Berlin, Heidelberg.
   CrossRef    
5. Lee, C., 1990. Fuzzy logic in control systems: Fuzzy logic controller. II. IEEE T. Syst. Man Cyb., 20(2): 419-435.
   CrossRef    
6. Leekwijck, W.V. and E.E. Kerre, 1999. Defuzzification: Criteria and classification. Fuzzy Set. Syst., 108(2): 159-178.
   CrossRef    
7. Ma, M., A. Kandel and M. Friedman, 2000. A new approach for defuzzification. Fuzzy Set. Syst., 111(3): 351-356.
   CrossRef    
8. Mahdiani, H.R., A. Banaiyan, M. Haji Seyed Javadi, S.M. Fakhraie and C. Lucas, 2013. Defuzzification block: New algorithms, and efficient hardware and software implementation issues. Eng. Appl. Artif. Intel., 26(1): 162-172.
   CrossRef    
9. Naaz, S., A. Alam and R. Biswas, 2011. Effect of different defuzzification methods in a fuzzy based load balancing application. Int. J. Comput. Sci. Issues, 8(5): 261-267.
   Direct Link
10. Nurcahyo, G., 2014. Selection of defuzzification method to obtain crisp values for representing uncertain data in a modified sweep algorithm. J. Ilmiah Elektron, 5(2): 13-28.
    
11. Saneifard, R. and R. Ezatti, 2010. Defuzzification through a bi-symmetrical weighted function. Aust. J. Basic Appl. Sci., 4(10): 4976-4984.
    
12. Sladoje, N., J. Lindblad and I. Nyström, 2011. Defuzzification of spatial fuzzy sets by feature distance minimization. Image Vision Comput., 29(2-3): 127-141.
    CrossRef    
13. Sugeno, M., 1985. An introductory survey of fuzzy control. Inform. Sciences, 36(1-2): 59-83.
    CrossRef    
14. Yeh, C.H. and Y.H. Chang, 2009. Modeling subjective evaluation for fuzzy group multicriteria decision making. Eur. J. Oper. Res., 194(2): 464-473.
    CrossRef    
15. Zadeh, L.A., 1965. Fuzzy sets. Inform. Control, 8(3): 338-353.
    CrossRef    
16. Zerafat, A.L.M., A. Emrouznejad, A. Mustafa and A. Rashidi Komijan, 2009. Selecting the most preferable alternatives in a group decision making problem using DEA. Expert Syst. Appl., 36(5): 9599-9602.
    CrossRef    

Competing interests

The authors have no competing interests.

Open Access Policy

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Copyright

The authors have no competing interests.