Exact Solutions of Fuzzy Linear System Equations
Subject Areas : Fuzzy Optimization and Modeling JournalMohammad Adabitabar Firozja 1 , Bahram Agheli 2 *
1 - Department of mathematics, Qaemshahr Branch, Islamic Azad University,Qaemshahr, Iran
2 - Department of Mathematics, Qaemsahhr Branch, Islamic Azad University, Qaemshahr Branch
Keywords: Fuzzy linear system, fuzzy number, fuzzy arithmetic, alpha-cut,
Abstract :
Systems of simulations linear equations play major role in various areas such as mathematics, statistics, and social sciences. Since in many applications, at least some of the system’s parameters and measurements are represented by fuzzy rather than crisp numbers, therefore, it is important to develop mathematical models and numerical procedures that would appropriately treat general fuzzy linear systems and solve them. In this paper, a new method based on fuzzy operations approach for solving Fuzzy Linear System (FLS) is introduced. The related theorems are proved in details. Finally, the proposed method is illustrated by solving two numerical examples.
1. Abbasbandy, S., & Viranloo, T. A. (2004). Numerical Solution of Fuzzy Differential Equation by Runge-Kutta Method. Nonlinear Studies, 11(1).
2. Abbasbandy, S., Viranloo, T. A., Lopez-Pouso, O., & Nieto, J. J. (2004). Numerical methods forfuzzy differential inclusions. Computers & Mathematics with Applications, 48(10-11), 1633-1641.
3. Allahviranloo, T. (2004). Numerical methods for fuzzy system of linear equations. Applied Mathematics and Computation, 155(2), 493-502.
4. Allahviranloo, T. (2005). Successive over relaxation iterative method for fuzzy system of linear equations. Applied Mathematics and Computation, 162(1), 189-196.
5. Caldas, M., & Jafari, S. (2005). θ-Compact fuzzy topological spaces. Chaos, Solitons & Fractals, 25(1), 229-232.
6. Chang, S. S., & Zadeh, L. A. (1972). On fuzzy mapping and control. IEEE Transactions on Systems, Man, and Cybernetics, (1), 30-34.
7. Dubois, D. J. (1980). Fuzzy sets and systems: theory and applications (Vol. 144). Academic press.
8. Dubois, D., & Prade, H. (1993). Fuzzy numbers: an overview. Readings in Fuzzy Sets for Intelligent Systems, 112-148.
9. El Naschie, M. S. (2004). A review of E infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals, 19(1), 209-236.
10. El Naschie, M. S. (2005). From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold. Chaos, Solitons & Fractals, 25(5), 969-977.
11. El Naschie, M. S. (2006). Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics. Chaos, Solitons & Fractals, 27(2), 297-330.
12. El Naschie, M. S. (2006). Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics. Chaos, Solitons & Fractals, 27(2), 297-330.
13. El Naschie, M. S. (2006). Superstrings, entropy and the elementary particles content of the standard model. Chaos, Solitons & Fractals, 29(1), 48-54.
14. Feng, G., & Chen, G. (2005). Adaptive control of discrete-time chaotic systems: a fuzzy control approach. Chaos, Solitons & Fractals, 23(2), 459-467.
15. Goetschel Jr, R., & Voxman, W. (1981). A pseudometric for fuzzy sets and certain related results. Journal of Mathematical Analysis and Applications, 81(2), 507-523.
16. Goetschel Jr, R., & Voxman, W. (1983). Topological properties of fuzzy numbers. Fuzzy Sets and Systems, 10(1-3), 87-99.
17. Jiang, W., Guo-Dong, Q., & Bin, D. (2005). H∞ variable universe adaptive fuzzy control for chaotic system. Chaos, Solitons & Fractals, 24(4), 1075-1086.
18. Ma, M., Friedman, M., & Kandel, A. (1999). A new fuzzy arithmetic. Fuzzy sets and systems, 108(1), 83-90.
19. Negoiţă, C. V., & Ralescu, D. A. (1975). Applications of fuzzy sets to systems analysis (p. 187). Basel, Switzerland:: Birkhäuser.
20. Wang, X., Zhong, Z., & Ha, M. (2001). Iteration algorithms for solving a system of fuzzy linear equations. Fuzzy Sets and Systems, 119(1), 121-128.