Defuzzification Method for Solving Fuzzy Linear Programming Problems
الموضوعات : مجله بین المللی ریاضیات صنعتی
Rahim Saneifard
1
(Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran)
Rasoul Saneifard
2
(Department of Engineering, Texas Southern University, Houston, Texas, USA.)
الکلمات المفتاحية: Fully fuzzy linear programming, Exact fuzzy optimal solution, Ranking function, Radius of gyration,
ملخص المقالة :
Several authors have proposed different methods to find the solution of fully fuzzy linear programming (FFLP) problems. But all the existing methods are based on the assumption that all the fuzzy coefficients and the fuzzy variables are non-negative fuzzy numbers. in this paper a new method is proposed to solve an FFLP problems with arbitrary fuzzy coefficients and arbitrary fuzzy variables, that is, there is no restriction on the elements that have been used in the FFLP problems. By using the radius of gyration function (ROG) we show that fuzzy solution obtained of solving FFLP problems, is exact fuzzy optimal solution of FFLP problems. The introduce method are very easy to understand and to apply for fully fuzzy linear systems occurring in real life situation.
[1] T. Allahviranloo, S. Abbasbandy and R. Saneifard, A method for ranking of fuzzy numbers using new weighted distance, Mathematical and Computational Applications 2 (2011) 359-369.
[2] T. Allahviranloo, S. Abbasbandy, R. Saneifard, An approximation approach for ranking fuzzy numbers based on weighted interval-value, Mathematical and Computational Applications 3 (2011) 588-597.
[3] S. J. Chen, S. M. Chen, Fuzzy risk analysis based on similarity of generalized fuzzy numbers,IEEE Transactions on Fuzzy Systems 11 (2003) 45-56.
[4] C. H. Cheng, A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems 95 (1998) 307-317.
[5] L. H. Chen, H. W. Lu, An approximate approach for ranking fuzzy numbers based on left and right dominance, Computers and Mathematics with Applications 41 (2001) 1589-1602.
[6] L. H. Chen, H. W. Lu, The preference order of fuzzy numbers, Computers and Mathematics with Applications 44 (2002) 1455-1465.
[7] T. Chu, C. Tsao, Ranking fuzzy numbers with an area between the centroid point and original point, Computers and Mathematics with Applications 43 (2002) 11-117.
[8] D. Dubois, H. Prade, Ranking of fuzzy numbers in the setting of possibility theory, Information Science 30 (1983) 183-224.
[9] H. W. Lu, C. B. Wang, An index for ranking fuzzy numbers by belief feature, Information and Management Sciences 16 (2005) 57-70.
[10] S. Murakami, S. Maeda, S. Imamura, Fuzzy decision analysis on the development of a centralized regional energy control system, In Proceedings of the IFAC symposium on fuzzy information, knowledge representationand decision analysis (1983) 363-368, Tokyo, Japan.
[11] Rahim Saneifard, Rasoul Saneifard, The Median Value of Fuzzy Numbers and its Applications in Decision Making, Journal of Fuzzy Set Valued Analysis http://dx.doi. org/10.5899/2012/jfsva-00051/.
[12] R. Saneifard, T. Allahviranloo, F. Hosseinzadeh and N. Mikaeilvand, Euclidean ranking DMU’s with fuzzy data in dea, Applied Mathematical Sciences 60 (2007) 2989-2998.
[13] R. Saneifard, A method for defuzzification by weighted distance, International Journal of Industrial Mathematics 3 (2009) 209-217.
[14] R. Saneifard, Ranking L-R fuzzy numbers with weighted averaging based on levels, International Journal of Industrial Mathematics 2 (2009) 163 - 173.
[15] R. Saneifard, Defuzzification method for solving fuzzy linear systems, International Journal of Industrial Mathematics 4 (2009) 321-331.
[16] R. Saneiafrd, Some properties of neural networks in designing fuzzy systems, Neural Computing and Appllications http://dx.doi.org/10.1007/s00521-011-0777-1/.
[17] R. Saneiafrd, Designing an algorithm for evaluating decision-making units based on neural weighted function, Neural Computing and Appllications http://dx.doi.org/10.1007/s00521-012-0878-5/.
[18] Y. M. Wang, J. B. Yang, D. L. Xu, K. S. Chin, On the centroids of fuzzy numbers, Fuzzy Sets and Systems 157 (2006) 919-926.
[19] R. R. Yager, On a general class of fuzzy connectives,Fuzzy Sets and Systems 4 (1980) 235-242.
[20] D. Yong, L. Qi, A TOPSIS-based centroidindex ranking method of fuzzy numbers and its application in decision-making, Cybernetics and Systems 36 (2005) 581-595.
