Applying Half-Circle Fuzzy Numbers to Control System: A Preliminary Study on Development of Intelligent System on Marine Environment and Engineering
This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.
[1] A. Bogomolny, On the perimeter and area of fuzzy sets, Fuzzy Sets and
Systems, 23 (1987) 257-269.
[2] D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and
Applications, Academic Press, New York 1980.
[3] H. J. Zimmermann, Fuzzy Sets, Decision Making and Expert Systems,
(1991) Boston: Kluwer Academic Publisher.
[4] H. J. Zimmermann., Fuzzy Set Theory and Its Applications, (1991)
Kluwer,Dordrecht.
[5] J. J. Buckley, E. Eslami, Fuzzy plane geometry I: Points and lines,
Fuzzy Sets and Systems, 86 (1997) 179-187.
[6] J.J. Buckley, E. Eslami, Fuzzy plane geometry II: Circles and polygons,
Fuzzy Sets and Systems, 87 (1997) 79-85.
[7] J. J. Buckley, Ranking alternatives using fuzzy number, Fuzzy Set and
System, 15 (1985) 21 -31.
[8] J. J. Buckley, Fuzzy Hierarchical Analysis, Fuzzy Sets and System, 17
(1985) 233-247.
[9] P.J.M. van Laarhoven and W. Perdrycz, A fuzzy Extension of Saaty
priority theory, Fuzzy Set and Systems, 11 (1983) 229-241.
[10] Jr. Roy Goetschel and Voxman William, Topological properties of fuzzy
numbers, Fuzzy Sets and Systems, 10 (1983) 87-99.
[11] J.M. Mendel, Fuzzy logic systems for engineering: A tutorial,
Proceedings of the IEEE, 83 March 1995.
[12] 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, 13 (2005) 281-295.
[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, 66 (2004) 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, 52 (2005)1883- 1893.
[15] C.Y. Chen, R.C. Hsu and C.W. Chen, Fuzzy logic derivation of neural
network models with time delays in subsystems, International Journal on
Artificial Intelligence Tools, 14 (2005) 967-974.
[16] T.Y. Hsieh, Morris H. L. Wang, and C.W. Chen et al., A new viewpoint
of s-curve regression model and its application to construction
management, International Journal on Artificial Intelligence Tools, 15
(2006)131-142.
[17] 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, 15 (2006) 163-171.
[18] C.W. Chen, C.L. Lin, C.H. Tsai, C.Y. Chen, and K. Yeh, A novel delaydependent
criteria for time-delay T-S fuzzy systems using fuzzy
Lyapunov method, International Journal on Artificial Intelligence Tools,
16 (2007) 545-552.
[19] V.E. Omurlu, S.N. Engin, and I. Yuksek, Application of fuzzy PID
control to cluster control of viaduct road vibration, Journal of Vibration
and Control, 14 (2008) 1201-1215.
[20] F. H. Hsiao, J. D. Hwang, C.W. Chen and Z. R. Tsai, Robust
stabilization of nonlinear multiple time-delay large-scale systems via
decentralized fuzzy control, IEEE Trans. Fuzzy Systems, 13 (2005) 152-
163.
[21] F. Amini and R. Vahdani, Fuzzy optimal control of uncertain dynamic
characteristics in tall buildings subjected to seismic excitation, Journal
of Vibration and Control, 14 (2008) 1843-1867.
[22] C.W. Chen, Stability conditions of fuzzy systems and its application to
structural and mechanical systems, Advances in Engineering Software,
37 (2006) 624-629.
[23] F.H. Bellamine and A. Elkamel, Model order reduction using neural
network principal component analysis and generalized dimensional
analysis, Engineering Computations, 25 (2008) 443-463.
[24] C.W. Chen, K. Yeh, W.L. Chiang, C H∞ control and stability analysis fo.rY s.t rCuhcetunr aaln dsy sDte.Jm. sW uus,i nMg oTdaeklainggi-,
Sugeno fuzzy model, Journal of Vibration and Control, 13 (2007) 1519-
1534.
[25] T.C. Kuo, Y.J. Huang, H.H. Yu, FRSMC Design for the steering control
and diving control of underwater vehicles, Journal of Marine Science
and Technology, 17 (2009) 50-59.
[26] C.Y. Chang, K.C. Hsu, K.H. Chiang et al., Modified fuzzy variable
structure control method to the crane system with control deadzone
problem, Journal of Vibration and Control, 14 (2008) 953-969.
[27] S. Zadrozny and J. Kacprzyk, On an interpretation of keywords weights
in information retrieval: some fuzzy logic based approaches,
International Journal of Uncertainty, Fuzziness and Knowledge-Based
System, 17 (2009) 41-58.
[28] C. H. Tsai, C.W. Chen, W. L. Chiang, and M. L. Lin, Application of
geographic information system to the allocation of disaster shelters via
fuzzy models, Engineering Computations, 25 (2008) 86-100.
[29] M.T. Mizukoshi, L.C. Barros, R.C. Bassanezi, Stability of fuzzy
dynamic systems, International Journal of Uncertainty, Fuzziness and
Knowledge-Based System, 17 (2009) 69-83.
[30] K. Yeh, C.Y. Chen, and C.W. Chen, Robustness design of time-delay
fuzzy systems using fuzzy Lyapunov method, Applied Mathematics and
Computation, 205 (2008) 568-577.
[31] M. Rezania, A.A. Javadi, and O. Giustolisi, An evolutionary-based data
mining technique for assessment of civil engineering systems,
Engineering Computations, 25 (2008) 500-517.
[32] C. Y. Chen, C. W. Shen, C.W. Chen, K. F. R. Liu, and M. J. Jeng, A
stability criterion for time-delay tension leg platform systems subjected
to external force, China Ocean Engineering, 23 (2009) 49-57.
[33] S.H.L. Mirhosseyni and P. Webb, A hybrid fuzzy knowledge-based
expert system and genetic algorithm for efficient selection and
assignment of material handling equipment, Expert Systems with
Applications, 36 (2009) 11875-11887.
[34] G. Athanasopoulos, C.R. Riba, C. Athanasopoulou, A decision support
system for coating selection based on fuzzy logic and multi-criteria
decision making, Expert Systems with Applications, 36 (2009) 11848-
10853.
[35] S.M. Chen, N.Y. Wang, J.S. Pan, Forecasting enrollments using
automatic clustering techniques and fuzzy logical relationships, Expert
Systems with Applications, 36 (2009) 11070-10076.
[36] F.G. Zhao, J. Chen, L. Guo et al., Neuro-fuzzy based condition
prediction of bearing health, Journal of Vibration and Control, 15 (2009)
1079-1091.
[37] C.W. Chen, Modeling and control for nonlinear structural systems via a
NN-based approach, Expert Systems with Applications, 36 (2009) 4765-
4772.
[38] M.B. Trabia, J.M. Renno, K.A.F. Moustafa, Generalized design of an
anti-swing fuzzy logic controller for an overhead crane with hoist,
Journal of Vibration and Control, 14 (2008) 319-346.
[39] P.C. Chen, C.W. Chen and W.L. Chiang, GA-based modified adaptive
fuzzy sliding mode controller for nonlinear systems, Expert Systems
with Applications, 36 (2009) 5872-5879.
[40] S. Yildirim, S. Erkaya, I. Eski et al., Noise and vibration analysis of car
engines using proposed neural network, Journal of Vibration and
Control, 15 (2009) 133-156.
[41] C.Y. Chen, J.W. Lin, W.I. Lee, and C.W. Chen, Fuzzy control for an
oceanic structure: a case study in time-delay TLP system, Journal of
Vibration and Control, accepted.
[42] O. Bouidghaghen, M. Boughanem, H. Prade et al., A fuzzy logic
approach to topic extraction in texts, International Journal of
Uncertainty, Fuzziness and Knowledge-Based System, 17 (2009) 81-
112.
[43] C.W. Chen, Application of fuzzy-model-based control to nonlinear
structural systems with time delay: an LMI method, Journal of Vibration
and Control, accepted.
[44] J.W. Tu, W.L. Qu, J. Chen, An experimental study on semi-active
seismic response control of a large-span building on top of ship lift
towers, Journal of Vibration and Control, 14 (2008) 1055-1074.
[45] P.C. Chen, C.W. Chen and W.L. Chiang, GA-based fuzzy sliding mode
controller for nonlinear systems, Mathematical Problems in
Engineering, Doi: 10.1155/2008/325859 (2008).
[46] F.H. Hsiao, C.W. Chen, Y.H. Wu and W.L. Chiang, Fuzzy controllers
for nonlinear interconnected TMD systems with external force, Journal
of The Chinese Institute of Engineers, 28 (2005) 175-181.
[47] Q.S. Zhong, J.F. Bao, and Y.B. Yu, et al., Impulsive control for T-S
fuzzy model-based chaotic systems, Mathematics and Computers in
Simulation, 79 (2008) 464-475.
[48] C.L. Lin, J.F. Wang, C.Y. Chen, C.W. Chen, and C.W. Yen, Improving
the generalization performance of RBF neural networks using a linear
regression technique, Expert Systems with Applications, 36 (2009)
12049-12053.
[49] G. Buyukozkan, and D. Ruan, Evaluation of software development
projects using a fuzzy multi-criteria decision approach, Mathematics
and Computers in Simulation, 77 (2008) 409-415.
[50] K. Guesmi, N. Essounbouli, and A. Hammoui, et al., Shifting nonlinear
phenomena in a DC-DC converter using a fuzzy logic controller,
Mathematics and Computers in Simulation, 76 (2008) 398-409.
[51] C.W. Chen, The stability of an oceanic structure with T-S fuzzy models,
Math. Comput. Simul. (2009), doi:10.1016/j.matcom.2009.08.001.
[52] F. Amini and R. Vahdani, Fuzzy optimal control of uncertain dynamic
characteristics in tall buildings subjected to seismic excitation, Journal
of Vibration and Control, 14 (2008) 1843-1867.
[1] A. Bogomolny, On the perimeter and area of fuzzy sets, Fuzzy Sets and
Systems, 23 (1987) 257-269.
[2] D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and
Applications, Academic Press, New York 1980.
[3] H. J. Zimmermann, Fuzzy Sets, Decision Making and Expert Systems,
(1991) Boston: Kluwer Academic Publisher.
[4] H. J. Zimmermann., Fuzzy Set Theory and Its Applications, (1991)
Kluwer,Dordrecht.
[5] J. J. Buckley, E. Eslami, Fuzzy plane geometry I: Points and lines,
Fuzzy Sets and Systems, 86 (1997) 179-187.
[6] J.J. Buckley, E. Eslami, Fuzzy plane geometry II: Circles and polygons,
Fuzzy Sets and Systems, 87 (1997) 79-85.
[7] J. J. Buckley, Ranking alternatives using fuzzy number, Fuzzy Set and
System, 15 (1985) 21 -31.
[8] J. J. Buckley, Fuzzy Hierarchical Analysis, Fuzzy Sets and System, 17
(1985) 233-247.
[9] P.J.M. van Laarhoven and W. Perdrycz, A fuzzy Extension of Saaty
priority theory, Fuzzy Set and Systems, 11 (1983) 229-241.
[10] Jr. Roy Goetschel and Voxman William, Topological properties of fuzzy
numbers, Fuzzy Sets and Systems, 10 (1983) 87-99.
[11] J.M. Mendel, Fuzzy logic systems for engineering: A tutorial,
Proceedings of the IEEE, 83 March 1995.
[12] 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, 13 (2005) 281-295.
[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, 66 (2004) 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, 52 (2005)1883- 1893.
[15] C.Y. Chen, R.C. Hsu and C.W. Chen, Fuzzy logic derivation of neural
network models with time delays in subsystems, International Journal on
Artificial Intelligence Tools, 14 (2005) 967-974.
[16] T.Y. Hsieh, Morris H. L. Wang, and C.W. Chen et al., A new viewpoint
of s-curve regression model and its application to construction
management, International Journal on Artificial Intelligence Tools, 15
(2006)131-142.
[17] 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, 15 (2006) 163-171.
[18] C.W. Chen, C.L. Lin, C.H. Tsai, C.Y. Chen, and K. Yeh, A novel delaydependent
criteria for time-delay T-S fuzzy systems using fuzzy
Lyapunov method, International Journal on Artificial Intelligence Tools,
16 (2007) 545-552.
[19] V.E. Omurlu, S.N. Engin, and I. Yuksek, Application of fuzzy PID
control to cluster control of viaduct road vibration, Journal of Vibration
and Control, 14 (2008) 1201-1215.
[20] F. H. Hsiao, J. D. Hwang, C.W. Chen and Z. R. Tsai, Robust
stabilization of nonlinear multiple time-delay large-scale systems via
decentralized fuzzy control, IEEE Trans. Fuzzy Systems, 13 (2005) 152-
163.
[21] F. Amini and R. Vahdani, Fuzzy optimal control of uncertain dynamic
characteristics in tall buildings subjected to seismic excitation, Journal
of Vibration and Control, 14 (2008) 1843-1867.
[22] C.W. Chen, Stability conditions of fuzzy systems and its application to
structural and mechanical systems, Advances in Engineering Software,
37 (2006) 624-629.
[23] F.H. Bellamine and A. Elkamel, Model order reduction using neural
network principal component analysis and generalized dimensional
analysis, Engineering Computations, 25 (2008) 443-463.
[24] C.W. Chen, K. Yeh, W.L. Chiang, C H∞ control and stability analysis fo.rY s.t rCuhcetunr aaln dsy sDte.Jm. sW uus,i nMg oTdaeklainggi-,
Sugeno fuzzy model, Journal of Vibration and Control, 13 (2007) 1519-
1534.
[25] T.C. Kuo, Y.J. Huang, H.H. Yu, FRSMC Design for the steering control
and diving control of underwater vehicles, Journal of Marine Science
and Technology, 17 (2009) 50-59.
[26] C.Y. Chang, K.C. Hsu, K.H. Chiang et al., Modified fuzzy variable
structure control method to the crane system with control deadzone
problem, Journal of Vibration and Control, 14 (2008) 953-969.
[27] S. Zadrozny and J. Kacprzyk, On an interpretation of keywords weights
in information retrieval: some fuzzy logic based approaches,
International Journal of Uncertainty, Fuzziness and Knowledge-Based
System, 17 (2009) 41-58.
[28] C. H. Tsai, C.W. Chen, W. L. Chiang, and M. L. Lin, Application of
geographic information system to the allocation of disaster shelters via
fuzzy models, Engineering Computations, 25 (2008) 86-100.
[29] M.T. Mizukoshi, L.C. Barros, R.C. Bassanezi, Stability of fuzzy
dynamic systems, International Journal of Uncertainty, Fuzziness and
Knowledge-Based System, 17 (2009) 69-83.
[30] K. Yeh, C.Y. Chen, and C.W. Chen, Robustness design of time-delay
fuzzy systems using fuzzy Lyapunov method, Applied Mathematics and
Computation, 205 (2008) 568-577.
[31] M. Rezania, A.A. Javadi, and O. Giustolisi, An evolutionary-based data
mining technique for assessment of civil engineering systems,
Engineering Computations, 25 (2008) 500-517.
[32] C. Y. Chen, C. W. Shen, C.W. Chen, K. F. R. Liu, and M. J. Jeng, A
stability criterion for time-delay tension leg platform systems subjected
to external force, China Ocean Engineering, 23 (2009) 49-57.
[33] S.H.L. Mirhosseyni and P. Webb, A hybrid fuzzy knowledge-based
expert system and genetic algorithm for efficient selection and
assignment of material handling equipment, Expert Systems with
Applications, 36 (2009) 11875-11887.
[34] G. Athanasopoulos, C.R. Riba, C. Athanasopoulou, A decision support
system for coating selection based on fuzzy logic and multi-criteria
decision making, Expert Systems with Applications, 36 (2009) 11848-
10853.
[35] S.M. Chen, N.Y. Wang, J.S. Pan, Forecasting enrollments using
automatic clustering techniques and fuzzy logical relationships, Expert
Systems with Applications, 36 (2009) 11070-10076.
[36] F.G. Zhao, J. Chen, L. Guo et al., Neuro-fuzzy based condition
prediction of bearing health, Journal of Vibration and Control, 15 (2009)
1079-1091.
[37] C.W. Chen, Modeling and control for nonlinear structural systems via a
NN-based approach, Expert Systems with Applications, 36 (2009) 4765-
4772.
[38] M.B. Trabia, J.M. Renno, K.A.F. Moustafa, Generalized design of an
anti-swing fuzzy logic controller for an overhead crane with hoist,
Journal of Vibration and Control, 14 (2008) 319-346.
[39] P.C. Chen, C.W. Chen and W.L. Chiang, GA-based modified adaptive
fuzzy sliding mode controller for nonlinear systems, Expert Systems
with Applications, 36 (2009) 5872-5879.
[40] S. Yildirim, S. Erkaya, I. Eski et al., Noise and vibration analysis of car
engines using proposed neural network, Journal of Vibration and
Control, 15 (2009) 133-156.
[41] C.Y. Chen, J.W. Lin, W.I. Lee, and C.W. Chen, Fuzzy control for an
oceanic structure: a case study in time-delay TLP system, Journal of
Vibration and Control, accepted.
[42] O. Bouidghaghen, M. Boughanem, H. Prade et al., A fuzzy logic
approach to topic extraction in texts, International Journal of
Uncertainty, Fuzziness and Knowledge-Based System, 17 (2009) 81-
112.
[43] C.W. Chen, Application of fuzzy-model-based control to nonlinear
structural systems with time delay: an LMI method, Journal of Vibration
and Control, accepted.
[44] J.W. Tu, W.L. Qu, J. Chen, An experimental study on semi-active
seismic response control of a large-span building on top of ship lift
towers, Journal of Vibration and Control, 14 (2008) 1055-1074.
[45] P.C. Chen, C.W. Chen and W.L. Chiang, GA-based fuzzy sliding mode
controller for nonlinear systems, Mathematical Problems in
Engineering, Doi: 10.1155/2008/325859 (2008).
[46] F.H. Hsiao, C.W. Chen, Y.H. Wu and W.L. Chiang, Fuzzy controllers
for nonlinear interconnected TMD systems with external force, Journal
of The Chinese Institute of Engineers, 28 (2005) 175-181.
[47] Q.S. Zhong, J.F. Bao, and Y.B. Yu, et al., Impulsive control for T-S
fuzzy model-based chaotic systems, Mathematics and Computers in
Simulation, 79 (2008) 464-475.
[48] C.L. Lin, J.F. Wang, C.Y. Chen, C.W. Chen, and C.W. Yen, Improving
the generalization performance of RBF neural networks using a linear
regression technique, Expert Systems with Applications, 36 (2009)
12049-12053.
[49] G. Buyukozkan, and D. Ruan, Evaluation of software development
projects using a fuzzy multi-criteria decision approach, Mathematics
and Computers in Simulation, 77 (2008) 409-415.
[50] K. Guesmi, N. Essounbouli, and A. Hammoui, et al., Shifting nonlinear
phenomena in a DC-DC converter using a fuzzy logic controller,
Mathematics and Computers in Simulation, 76 (2008) 398-409.
[51] C.W. Chen, The stability of an oceanic structure with T-S fuzzy models,
Math. Comput. Simul. (2009), doi:10.1016/j.matcom.2009.08.001.
[52] F. Amini and R. Vahdani, Fuzzy optimal control of uncertain dynamic
characteristics in tall buildings subjected to seismic excitation, Journal
of Vibration and Control, 14 (2008) 1843-1867.
@article{"International Journal of Information, Control and Computer Sciences:60399", author = "Chen-Yuan Chen and Wan-I Lee and Yi-Chaio Sui and Cheng-Wu Chen", title = "Applying Half-Circle Fuzzy Numbers to Control System: A Preliminary Study on Development of Intelligent System on Marine Environment and Engineering", abstract = "This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.
", keywords = "triangular fuzzy number, half-circle fuzzy numbers, predictions, polar coordinates, Lyapunov method", volume = "4", number = "12", pages = "1956-5", }
