- Volume 6 Issue 5
The fuzzy linear programming(FLP) is the useful approach to many real world problems under uncertainty. This paper deals with a FLP whose objective value is fuzzy. And the right hand sides of convergent equality constraints are fuzzy numbers. We assume that the membership function of the objective value is piecewise linear and those of the right hand side are trapezoidal. Each of these trapezoidal functions can be algebraically replaced with three linear functions. Then the FLP problem is transformed into the Zimmermann's symmetric model. The fuzzy solution based on the max-min rule can be obtained by solving the crisp linear programming problem derived from the symmetric model. A numerical example has illustrated our approach. The application of our approach to the inconsistent linear system can enable generate us to get define the useful and flexible inexact solutions within acceptable tolerance. Further research is required to generalize the membership function.
fuzzy convergent linear equality;membership function;piecewise linear;trapezoidal;max-min rule
- Y. Cui, J. Qu, Y. Peng, L. Wang, B. Li, "The Study of the Solution on Multi-Objective Linear Programming Problem under Fuzzy", IEEE Asia-Pacific Conference on Wearable Computing Systems, pp. 286-290, 2010.
- F. Herrera, J. L. Verdegay, "Fuzzy sets and operations research: Perspectives", Fuzzy Sets and Systems, Vol. 90, pp. 207-218, 1997. https://doi.org/10.1016/S0165-0114(97)00088-2
- A. V. Kamyad, N. Hassanzadeh, J. Chaji, "A new vision on solving of fuzzy linear programming", IEEE, 2009.
- H. Kuwano, "On the fuzzy multi-objective linear programming problem: Goal programming approach", Fuzzy Sets and Systems, Vol. 82, pp. 57-64, 1996. https://doi.org/10.1016/0165-0114(95)00231-6
- R. E. Bellman, I. A. Zadeh, "Decision-making in a fuzzy environment", Management Science, Vol. 17, pp. 141-164, 1970. https://doi.org/10.1287/mnsc.17.4.B141
- M. Delgado, M. A. Vila, W. Voxman, "On a canonical representation of fuzzy numbers", Fuzzy Sets and Systems, Vol. 93, pp. 125-135, 1998. https://doi.org/10.1016/S0165-0114(96)00144-3
- S. M. Guu, Wu ,Y. K., "Two-phase approach for solving the fuzzy linear programming problems", Fuzzy Sets and Systems, Vol. 107, pp. 191-195, 1999. https://doi.org/10.1016/S0165-0114(97)00304-7
- W. Tang, Y. Luo, "A new method of fuzzy linear programming problems", IEEE International Conference on Business Intelligence and Financial Eng., pp. 179-181, 2009.
- D. Wang, "An inexact approach for linear programming problems with fuzzy objective and resources", Fuzzy Sets and Systems, Vol. 89, pp. 61-68, 1997. https://doi.org/10.1016/S0165-0114(96)00090-5
- C. T. Yeh, "On the minimal solutions of max-min fuzzy relational equations", Fuzzy Sets and Systems, Vol. 159, pp. 23-39, 2008. https://doi.org/10.1016/j.fss.2007.07.017
- R. N. Gasimov, K. Yenilmez, "Solving fuzzy linear programming problems with linear membership functions", Turk Journal Math., Vol. 267, pp. 375-396, 2002.
- J. Xiao, F. Lu, X. Wang, "A New Algorithm for Solving Fuzzy Linear Programming-the Basic Line Algorithm", IEEE 2nd International Conference on Computer Modeling and Simulation, pp. 125-127, 2010.
- H. J. Zimmermann, "Fuzzy programming and linear programming with several objective functions", Fuzzy Sets and Systems, Vol. 4, pp. 37-51, 1980. https://doi.org/10.1016/0165-0114(80)90062-7
- H. J. Zimmermann, "Fuzzy set theory and applications, 4rd ed.", Kluwer Academic Publisher, 2001.
- S. Fang, S. Puthenpura, "Linear optimization and extensions", Prentice-Hall International, Inc, 1993.
- H. Anton, "Elementary linear algebra, 9th ed.", John Wiley & Sons, Inc, 2005.
- Fuzzy-AHP-Based Technology Evaluation Model for venture firms vol.14, pp.7, 2016, https://doi.org/10.14400/JDC.2016.14.7.363
- Classification of Epileptic Seizure Signals Using Wavelet Transform and Hilbert Transform vol.14, pp.4, 2016, https://doi.org/10.14400/JDC.2016.14.4.277
- An Algorithm for the Singly Linearly Constrained Concave Minimization Problem with Upper Convergent Bounded Variables vol.7, pp.5, 2016, https://doi.org/10.15207/JKCS.2016.7.5.213