Particle Swarm Optimization for Solving a Class of Type-1 and Type-2 Fuzzy Nonlinear Equations

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Abstract

This paper proposes a modified particle swarm optimization (PSO) algorithm that can be used to solve a variety of fuzzy nonlinear equations, i.e. fuzzy polynomials and exponential equations. Fuzzy nonlinear equations are reduced to a number of interval nonlinear equations using alpha cuts. These equations are then sequentially solved using the proposed methodology. Finally, the membership functions of the fuzzy solutions are constructed using the interval results at each alpha cut. Unlike existing methods, the proposed algorithm does not impose any restriction on the fuzzy variables in the problem. It is designed to work for equations containing both positive and negative fuzzy sets and even for the cases when the support of the fuzzy sets extends across 0, which is a particularly problematic case.

[1] S. Abbasbandy, B. Asady, Newton’s method for solving fuzzy nonlinear equations, Applied Mathematics and Computation, Volume 159, Issue 2, Pages 349-356, ISSN 0096-3003.

[2] M. Tavassoli Kajani, B. Asady, A. Hadi Vencheh, An iterative method for solving dual fuzzy nonlinear equations, Applied Mathematics and Computation, Volume 167, Issue 1, Pages 316-323, ISSN 0096-3003.

[3] S. Abbasbandy, A. Jafarian, Steepest descent method for solving fuzzy nonlinear equations, Applied Mathematics and Computation, Volume 174, Issue 1, Pages 669-675.

[4] S. Abbasbandy, M. Otadi, Numerical solution of fuzzy polynomials by fuzzy neural network, Applied Mathematics and Computation, Volume 181, Issue 2, Pages 1084-1089, ISSN 0096-3003.

[5] S. Abbasbandy, M. Otadi, M. Mosleh, Numerical solution of a system of fuzzy polynomials by fuzzy neural network, Information Sciences, Volume 178, Issue 8, Pages 1948-1960, ISSN 0020-0255.

[6] R. Boukezzoula and S. Marteau, Exact solving of the fuzzy equation: A.X2 + B.X = C, The 14th IEEE International Conference on Fuzzy Systems, FUZZ ’05., Reno, NV, 2005, pp. 1110-1115.

[7] G. Zhou and Y. Gan, Hybrid conjugate gradient method for solving fuzzy nonlinear equations, Logistics Systems and Intelligent Management, 2010 International Conference on, Harbin, 2010, pp. 462-464.

[8] Zimmerman, H. J. (1996). Fuzzy Set theory and its Application (second edition), Allied Publishers, Indian Reprint.

[9] J. Kennedy and R. Eberhart, Particle swarm optimization, Proc. IEEE Int. Conf. Neural Networks, vol. IV, pp. 1942-1948, 1995.

[10] R.E. Moore, Interval analysis, Prentice-Hall, Englewood Cliffs, NJ, 1966.

[11] S. Sadiqbatcha, and S. Jafarzadeh, An Analytical Approach to Solving Type-1 and Type-2 Fully Fuzzy Linear Systems of Equations, IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, 2016.

[12] B. Wu, W. Zhu, N. Yan, X. Feng, Q. Xing and Q. Zhuang, An Improved Method for Deriving Daily Evapotranspiration Estimates From Satellite Estimates on Cloud-Free Days, in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 9, no. 4, pp. 1323-1330, 2016.

[13] K. Djaman, A. B. Balde, A. Sow, B. Muller, S. Irmak, M. K. N’Diaye, B. Manneh, Y. D. Moukoumbi, K. Futakuchi, K. Saito, Evaluation of sixteen reference evapotranspiration methods under sahelian conditions in the Senegal River Valley, Journal of Hydrology: Regional Studies, vol 3, pp. 139-159, ISSN 2214-5818.

[14] Allen, R.G., L.S. Pereira, D. Raes, and M. Smith. 1998. Crop evapotranspiration. Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper No. 56. United Nations Food and Agricultural Organization, Rome.

Journal of Artificial Intelligence and Soft Computing Research

The Journal of Polish Neural Network Society, the University of Social Sciences in Lodz & Czestochowa University of Technology

Journal Information

CiteScore 2017: 5.00

SCImago Journal Rank (SJR) 2017: 0.492
Source Normalized Impact per Paper (SNIP) 2017: 2.813

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