Half-Circle Fuzzy Number Threshold Determination via Swarm Intelligence Method
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.
[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
[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
@article{"International Journal of Information, Control and Computer Sciences:67803", author = "P.-W. Tsai and J.-W. Chen and C.-W. Chen and C.-Y. Chen", title = "Half-Circle Fuzzy Number Threshold Determination via Swarm Intelligence Method", abstract = "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, swarm
intelligence, Lyapunov method.", volume = "8", number = "5", pages = "906-4", }
