Abstract
In this paper, we construct a model of All-coefficient-fuzzy Linear Programming Based on Fuzzy Structured Element, in which all the objective function and constraint coefficients are triangular (or trapezoidal) fuzzy numbers. A new ranking criterion of fuzzy numbers is defined which is based on the method of structured element. According to this ranking criterion, fuzzy linear programming is transformed into classical linear programming, and then the rationality of the theory is proved. Compared with the other methods, the solution is superior to the other solutions and this method has fewer number of constraints. The calculation progress is simple, effectiveness and extensive application of this method. Finally, we give a numerical example to show the efficiency of this algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Rommelfanger, H.: Fuzzy linear programming and applications. Europan Journal of Operational Research 92, 512–527 (1996)
Maleki, H.R., Tata, M., Mashinchi, M.: Linear programming with fuzzy variables. Fuzzy Sets and Systems 109, 21–33 (2001)
Rommelfanger, H., Hanuscheck, R., Wolf, J.: Linear programming with fuzzy objectives. Fuzzy Sets and Systems 29, 31–48 (1989)
Wang, R.C., Liang, T.F.: Application of fuzzy multi-objective linear programming of aggregate production planning. Computers and Industrial Engineering 46, 17–41 (2004)
Delgado, M., Verdegay, J.L., Vila: A general model for fuzzy linear programming. Fuzzy Sets and Systems 29, 21–29 (1989)
Dubois, D., Prade, H.: Ranking of fuzzy numbers in the setting of possibility theory. Information Sciences 30, 183–224 (1983)
Tanaka, H., Asai, K.: A formulation of fuzzy linear programming based on comparison of fuzzy number. Control and Cybernet. 13, 185–194 (1984)
Zhang, Z.K.: Application of automatization technology in fuzzy mathematics. Tsinghua University Press, Beijing (1997)
Li, R.J.: Theory and application of fuzzy multiple criteria decision making. Scientific Press, Beijing (2002)
Zeng, Q.N.: All coefficient fuzzy linear programming with equations. Fuzzy System and Mathematics (2000)
Song, Y.X., Jing, L.P., Chen, J.Y.: Fuzzy Optimal Interval Value for a Fuzzy Linear Programming Model. Fuzzy System and Mathematics (2002)
Guo, S.Z.: Homeomorphic property between fuzzy number space and family of standard bounded monotone function. Progress in Natural Science (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhao, Hk., Guo, Sz. (2009). Solution to A-C-F-L-P Based on Fuzzy Structured Element. In: Cao, B., Li, TF., Zhang, CY. (eds) Fuzzy Information and Engineering Volume 2. Advances in Intelligent and Soft Computing, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03664-4_169
Download citation
DOI: https://doi.org/10.1007/978-3-642-03664-4_169
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03663-7
Online ISBN: 978-3-642-03664-4
eBook Packages: EngineeringEngineering (R0)