In this paper, a new fuzzy inference modeling method is proposed for nonlinear systems. A proposed triangular pyramid fuzzy system (TPFS) which is proved to have second-order approximation accuracy is employed in the new modeling method. Based on the interpolation mechanism of TPFS, practical systems (which can be described by a group of fuzzy inference rules) can be converted to a simplified linear model with variable coefficients. Expressions of the time-varying local equations appears significantly simple due to the linearity of the model by using the proposed fuzzy modeling method. The approximation performance superiority of the proposed modeling method is demonstrated by simulation results.
ChangC.Y., HsuC.H., WangW.J., ChangC.L. and ChenC.Y., Operation characteristic control of direct methanol fuel cell liquid feed fuel system using adaptive neuro-fuzzy inference system model, International Journal of Innovative Computing, Information and Control8(6) (2012), 4177–4187.
2.
TongS.C. and LiY.M., Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction, Information Sciences18(23) (2010), 4619–4640.
3.
TongS.C., HeX.L. and LiY.M., Direct adaptive fuzzy backstepping robust control for single input and single output uncertain nonlinear systems using small-gain approach, Information Sciences18(9) (2010), 1738–1758.
4.
ZhangJ., ShiP. and XiaY., Robust adaptive sliding mode control for fuzzy systems with mismatched uncertainties, IEEE Transactions on Fuzzy Systems18(4) (2010), 700–711.
5.
AhmedA.N., El-ShafieA., KarimO.A. and El-ShafieA., An augmented wavelet denoising technique with neuro-fuzzy inference system for water quality prediction, International Journal of Innovative Computing, Information and Control8(10) (2012), 7055–7082.
6.
GaoH.J., LiuX.M. and LamJ., Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay, IEEE Transactions on Systems Man and Cybernetic Part B: Cybernetics39(2) (2009), 306–317.
7.
GotoS., YamauchiT., KatafuchiS., FurueT., SueyoshiM., UchidaY. and HatazakiH., Coal type selection for power plants through fuzzy inference using coal and fly ash property, International Journal of Innovative Computing, Information and Control7(1) (2011), 29–38.
8.
WangG., ShiP. and MessengerP., Representation of uncertain multichannel digital signal spaces and study of pattern recognition based on metrics and difference values on fuzzy n-cell number spaces, IEEE Trans on Fuzzy Systems17(2) (2009), 421–439.
9.
SatoY., MikiT. and HondaK., A multi-core processor based real-time multi-modal emotion extraction system employing fuzzy inference, International Journal of Innovative Computing, Information and Control7(8) (2011), 4603–4620.
10.
WangG.X., ShiP. and WenC.L., Fuzzy approximation relations on fuzzy n-cell number space and their applications in classification, Information Sciences181(18) (2011), 846–3860.
11.
WuL.G., SuX.J., ShiP. and QiuJ.B., Model approximation for discrete-time state-delay systems in the T-S fuzzy framework, IEEE Transaction on Fuzzy Systems19(2) (2011), 366–378.
12.
WangL.X., Fuzzy Systems Are Universal Approximators, IEEE International Conference on Fuzzy Systems (1992), pp. 1163–1170.
13.
WangL.X. and MendelJ.M., Fuzzy basis functions, universal approximation, and orthogonal least-squares learning, IEEE T Neural Networks3(5) (1992), 807–814.
14.
YingH., Sufficient conditions on general fuzzy systems as function approximators, Automatica30(3) (1994), 521–525.
15.
YingH. and ChenG., Necessary conditions for some typical fuzzy systems as universal approximators, Automatica33(7) (1997), 1333–1338.
16.
YingH., General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators, IEEE Transactions on Fuzzy Systems6(4) (1998), 582–587.
17.
YingH., Sufficient conditions on uniform approximation of multivariate functions by general Takagi-Sugeno fuzzy systems with linear rule consequent, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans28(4) (1998), 515–520.
18.
YingH., DingY., LiS. and ShaoS., Comparison of necessary conditions for typical Takagi-Sugeno and Mamdani fuzzy systems as universal approximators, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans29(5) (1999), 508–514.
19.
LiH.X., WangJ.Y. and MiaoZ.H., Modelling on fuzzy control systems, Science in China Series A: Mathematics45(12) (2002), 1506–1517.
20.
LiH.X., WangJ.Y. and MiaoZ.H., Marginal linearization method in modeling on fuzzy control systems, Progress in Nature Science13(7) (2003), 489–496.
21.
WangD.G., SongW.Y. and ShiP., Approximation to a class of non-autonomous systems by dynamic fuzzy inference marginal linearization method, Information Sciences245 (2013), 197–217.
22.
WangD.G., ChenC.L. and SongW.Y., Error-compensated marginal linearization method for modeling a fuzzy system, IEEE Transactions on Fuzzy Systems23(1) (2015), 215–222.
23.
YuanX.H., LiH.X. and YangX., Fuzzy system and fuzzy inference modeling method based on fuzzy transformation, Acta Electronica Sinica41(4) (2013), 674–680.
24.
LiH.X., Interpolation mechanism of fuzzy control, Science in China Series E: Technological Sciences28(3) (1998), 259–267.
25.
WuJ.Y. and LeeR., The advantages of triangular and tetrahedral edge elements for electromagnetic modeling with the finiteelement method, IEEE Transactions on Antennas and Propagation45(9) (1997), 1431–1437.
