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Half-Circle Fuzzy Number Threshold Determination via Swarm Intelligence Method

Authors: P.-W. Tsai, J.-W. Chen, C.-W. Chen, C.-Y. Chen


In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.

Keywords: half-circle fuzzy numbers, predictions, Lyapunov method, swarm intelligence

Digital Object Identifier (DOI):

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[1] A. Bogomolny, "On the perimeter and area of fuzzy sets, Fuzzy Sets and Systems,” vol. 23, 1987, pp. 257-269.
[2] P.J.M. van Laarhoven and W. Perdrycz, "A fuzzy Extension of Saaty priority theory,” Fuzzy Set and Systems, vol. 11, 1983, pp. 229-241.
[3] D. Dubois and H. Prade, "Fuzzy Sets and Systems: Theory and Applications,” Academic Press, New York 1980.
[4] H. J. Zimmermann, Fuzzy Sets, Decision Making and Expert Systems, (1991) Boston: Kluwer Academic Publisher.
[5] H. J. Zimmermann., Fuzzy Set Theory and Its Applications, (1991) Kluwer, Dordrecht.
[6] C. Y. Chen, W. I. Lee, Y. C. Sui, and C. W. Chen, "Applying half-circle fuzzy numbers to control system: a preliminary study on development of intelligent system on marine environment and engineering,” World Academy of Science, Engineering and Technology, vol. 72, 2010, pp. 204-209.
[7] F.H. Hsiao, W.L. Chiang, C.W. Chen, S.D. Xu and S.L. Wu, "Application and robustness design of fuzzy controller for resonant and chaotic systems with external disturbance,” International Journal of Uncertainty, Fuzziness and Knowledge-Based System, vol. 13, 2005, pp. 281-295.
[8] S.-C. Chu, and P.-W. Tsai, "Computational Intelligence Based on the Behavior of Cats,” International Journal of Innovative Computing, Information and Control, vol. 3, no. 1, 2007, pp. 163-173.
[9] S.-C. Chu, P.-W. Tsai, and J.-S. Pan, "Cat Swarm Optimization,” in Proc. 9th Pacific Rim International Conference on Artificial Intelligence, LNAI 4099, 2006, pp. 854-858.
[10] J.-S. Pan, P.-W. Tsai, and B.-Y. Liao, "Fish Migration Optimization Based on the Fishy Biology,” in Proc. of 2010 4th International Conference on Genetic and Evolutionary Computing, 2010, pp. 783-786.
[11] P.-W. Tsai, J.-S. Pan, B.-Y. Liao, M.-J. Tsai, and V. Istanda, "Bat Algorithm Inspired Algorithm for Solving Numerical Optimization Problems,” Applied Mechanics and Materials, vol. 148-149, 2012, pp. 134-137.
[12] C.W. Chen, W.L. Chiang, and C.H. Tsai et al., "Fuzzy Lyapunov method for stability conditions of nonlinear systems,” International Journal on Artificial Intelligence Tools, vol. 15, 2006, pp. 163-171.
[13] C.W. Chen, W.L. Chiang, and F.H. Hsiao, "Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems,” Mathematics and Computers in Simulation, vol. 66, 2004, pp. 523-537.
[14] F.H. Hsiao, C.W. Chen, and Y.W. Liang et al., "T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays,” IEEE Trans. Circuits & Systems-I, vol. 52, 2005, pp. 1883- 1893.
[15] W. I. Lee, C. W. Chen, C. Y. Chen, and Y. C. Sui, "Application of half-circle fuzzy numbers and development of triangular fuzzy numbers to fuzzy control,” in Proc. 10th WSEAS International Conf. on Applied Computer Sciences (ACS’10), Japan, 2010, pp. 335-340.
[16] J.M. Mendel, "Fuzzy logic systems for engineering: A tutorial,” in Proc. of the IEEE, 83 March 1995.
[17] J. J. Buckley, "Fuzzy Hierarchical Analysis,” Fuzzy Sets and System, vol. 17, 1985, pp. 233-247.
[18] C.W. Chen, C.L. Lin, C.H. Tsai, C.Y. Chen, and K. Yeh, "A novel delay-dependent criteria for time-delay T-S fuzzy systems using fuzzy Lyapunov method,” International Journal on Artificial Intelligence Tools, vol. 16, 2007, pp. 545-552.
[19] J. J. Buckley, "Ranking alternatives using fuzzy number,” Fuzzy Set and System, vol. 15, 1985, pp. 21 -31.
[20] J. J. Buckley and E. Eslami, "Fuzzy plane geometry I: Points and lines,” Fuzzy Sets and Systems, vol. 86, 1997, pp. 179-187.
[21] J.J. Buckley and E. Eslami, "Fuzzy plane geometry II: Circles and polygons,” Fuzzy Sets and Systems, vol. 87, 1997, pp. 79-85.
[22] G. Beni, J. Wang, "Swarm Intelligence in Cellular Robotic Systems,” in Proc. of NATO Advanced Workshop on Robots and Biological Systems, Tuscany, Italy, 1989.
[23] S. Mishra, and C. N. Bhende, "Bacterial Foraging Technique-Based Optimized Active Power Filter for Load Compensation”, IEEE Transactions on Power Delivery, vol. 22, no. 1, 2007, pp. 457-465.
[24] Kevin M. Passino, "Biomimicry of Bacterial Foraging for Distributed Optimization and Control,” Control Systems Magazine, June 2002, pp. 52-67.
[25] W. J. Tang, Q. H. Wu, and J. R. Saunders, "Bacterial Foraging Algorithm For Dynamic Environments,” in Proc. IEEE Congress on Evolutionary Computation, IEEE, July 2006, pp. 1324-1330.
[26] J. S. Pan, F. R. McInnes and M. A. Jack, "Application of Parallel Genetic Algorithm and Property of Multiple Global Optima to VQ Codevector Index Assignment,” Electronics Letters, Vol. 32, No. 4, 1996, pp.296-297.
[27] T.-C. Chen, P.-W. Tsai, S.-C. Chu, and J.-S. Pan, "A Novel Optimization Approach: Bacterial-GA Foraging,” in Proc. 2nd International Conf. on Innovative Computing, Information and Control (ICICIC-2007), Japan