ORIGINAL_ARTICLE
Cover vol. 9, no.2, June 2012--
http://ijfs.usb.ac.ir/article_2814_3efdaf4b7d7898bb81bd2a5adc4dfb94.pdf
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10.22111/ijfs.2012.2814
ORIGINAL_ARTICLE
BEHAVIOR OF SOLUTIONS TO A FUZZY NONLINEAR
DIFFERENCE EQUATION
In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{Ax_n+x_{n-1}}{B+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $A, B$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.
http://ijfs.usb.ac.ir/article_186_e63ac844771ce71765a6ddb982c26c4c.pdf
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10.22111/ijfs.2012.186
Fuzzy difference equation
Boundedness
Persistence
Equilibrium
point
Stability
Qianhong
Zhang
zqianhong68@com.cn
true
1
Guizhou Key Laboratory of Economics System Simulation, Guizhou
University of Finance and Economics, Guiyang, Guizhou 550004, P. R. China
Guizhou Key Laboratory of Economics System Simulation, Guizhou
University of Finance and Economics, Guiyang, Guizhou 550004, P. R. China
Guizhou Key Laboratory of Economics System Simulation, Guizhou
University of Finance and Economics, Guiyang, Guizhou 550004, P. R. China
LEAD_AUTHOR
Lihui
Yang
ll.hh.yang@gmail.com
true
2
Department of Mathematics, Hunan City University, Yiyang, Hunan
413000, P. R. China
Department of Mathematics, Hunan City University, Yiyang, Hunan
413000, P. R. China
Department of Mathematics, Hunan City University, Yiyang, Hunan
413000, P. R. China
AUTHOR
Daixi
Liao
liaodaixizaici@sohu.com
true
3
Basic Science Department, Hunan Institute of Technology, Hengyang,
Hunan 421002, P. R. China
Basic Science Department, Hunan Institute of Technology, Hengyang,
Hunan 421002, P. R. China
Basic Science Department, Hunan Institute of Technology, Hengyang,
Hunan 421002, P. R. China
AUTHOR
bibitem{AbAl: Mfs}
1
S. Abbasbandy and M. Alavi, {it A method for solving fuzzy linear system}, Iranian Journal of Fuzzy Systems, {bf 2} (2005), 37-43.
2
bibitem{BeFr: Aam}
3
D. Benest and C. Froeschle, {it Analysis and modelling of discrete dynamical
4
systems}, Gordon and Breach Science Publishers, The Netherland, 1998.
5
bibitem{DeKo: Abf}
6
E. Y. Deeba and A. De Korvin, {it Analysis of fuzzy difference equations of
7
a model of $CO_2$ level in the blood}, Appl. Math. Lett., {bf 12} (1999), 33-40.
8
bibitem{DeKo:Afd}
9
E. Y. Deeba, A. De Korvin and E. L. Koh, {it A fuzzy difference equation with an
10
application}, J. Difference Equation Appl., {bf 2} (1996), 365-374.
11
bibitem{DeLa: Nsc}
12
R. DeVault, G. Ladas and S. W. Schultz, {it Necessary and sufficient conditions
13
the boundedness of $x_{n+1}=A/x_n^p+B/x_{n-1}^q$}, J. Difference
14
Equations Appl., {bf 3} (1998), 259-266.
15
bibitem{DeLa: Ors}
16
R. DeVault, G. Ladas and S. W. Schultz, {it On the recursive sequence $x_{n+1}=A/x_n+1/x_{n-2}$}, Proc. Amer. Math. Soc.,
17
{bf 126} (1998), 3257-3261.
18
bibitem{KoLa:Gbn}
19
V. L. Kocic and G. Ladas, {it Golobal behavior of nonlinear difference
20
equations of higher order with applications}, Kluwer Academic Publishers, 1993.
21
bibitem{KuLa: Rde}
22
M. R. S. Kulenvic, G. Ladas and N. R. Prokup, {it A rational difference equation}, Comput. Math. Appl., {bf 41} (2001),
23
671-678.
24
bibitem{LiSu: Drd}
25
W. Li and H. Sun, {it Dynamics of a rational difference equation}, Appl. Math. Comput.,
26
{bf 163} (2005), 577-591.
27
bibitem{PaPa: Ofd1}
28
G. Papaschinopoulos and B. K. Papadopoulos, {it On the fuzzy difference equation $x_{n+1}=A+B/x_n$},
29
Soft Comput., {bf 6} (2002), 456-461.
30
bibitem{PaPa:Ofd2}
31
G. Papaschinopoulos and B. K. Papadopoulos, {it On the fuzzy difference equation
32
$x_{n+1}=A+x_n/x_{n-m}$}, Fuzzy Sets and Systems, {bf 129} (2002), 73-81.
33
bibitem{PaSc: Ost}
34
G. Papaschinopoulos and C. J. Schinas, {it On a systems of two nonlinear difference equation},
35
J. Math. Anal. Appl., {bf 219} (1998), 415-426.
36
bibitem{PaSc: Ofd}
37
G. Papaschinopoulos and C. J. Schinas, {it On the fuzzy difference equation $x_{n+1}=sum_{i=0}^{k-1}A_i/x_{n-i}^{p_i}+1/x_{n-k}^{p_k}$},
38
J. Difference Equation Appl., {bf 6(7)} (2000), 85-89.
39
bibitem{PaSt: Bab}
40
G. Papaschinopoulos and G. Stefanidou, {it Boundedness and asymptotic
41
behavior of the solutions of a fuzzy difference equation}, Fuzzy Sets and Systems, {bf 140} (2003), 523-539.
42
bibitem{PhPu: Gai}
43
C. G. Philos, I. K. Purnaras and Y. G. Sficas, {it Global attractivity in a
44
nonlinear difference equation}, Appl. Math. Comput., {bf 62} (1994), 249-258.
45
bibitem{StPa: Fde}
46
G. Stefanidou and G. Papaschinopoulos, {it A fuzzy difference equation of a rational form}, J. Nonlin. Math. Phys.,
47
Supplement, {bf 12(2)} (2005), 300-315.
48
bibitem{WuZh: Epn}
49
C. Wu and B. Zhang, {it Embedding problem of noncompact fuzzy number space
50
$E^{sim}$}, Fuzzy Sets and Systems, {bf 105} (1999), 165-169.
51
ORIGINAL_ARTICLE
GENERALIZED FUZZY VALUED $theta$-Choquet INTEGRALS
AND THEIR DOUBLE-NULL ASYMPTOTIC ADDITIVITY
The generalized fuzzy valued $\theta$-Choquet integrals will beestablished for the given $\mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-double-null asymptotic additivity of thefuzzy valued set functions formed are studied when the fuzzymeasure satisfies autocontinuity from above (below).\\
http://ijfs.usb.ac.ir/article_188_27cf7a6a718a90a8e7f25002c7228b8f.pdf
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24
10.22111/ijfs.2012.188
Fuzzy measures
Fuzzy valued $theta$-Choquet integrals
Autocontinuous
from above (below)
Double-null asymptotic additive
Pseudo-double-null asymptotic additive
Gui-jun
Wang
tjwgj@126.com
true
1
School of Mathematics Science, Tianjin Normal University, Tianjin
300387, China
School of Mathematics Science, Tianjin Normal University, Tianjin
300387, China
School of Mathematics Science, Tianjin Normal University, Tianjin
300387, China
LEAD_AUTHOR
Xiao-ping
Li
lxpmath@126.com
true
2
School of Management, Tianjin Normal University, Tianjin 300387,
China
School of Management, Tianjin Normal University, Tianjin 300387,
China
School of Management, Tianjin Normal University, Tianjin 300387,
China
AUTHOR
[1] C. Alaca, A new perspective to the mazur-ulam problem in 2-fuzzy 2-normed linear spaces,
1
Iranian Journal of Fuzzy Systems, 7(2) (2010), 109-119.
2
[2] A. Maturo, On some structures of fuzzy numbers, Iranian Journal of Fuzzy Systems, 6(4)
3
(2009), 49-59.
4
[3] E. Pasha, A. Saiedifar and B. Asady, The percentiles of fuzzy numbers and their applications,
5
Iranian Journal of Fuzzy Systems, 6(1) (2009), 27-44.
6
[4] M. Sugeno, Theory of fuzzy integrals and its applications, Ph. D. Dissertation, Tokyo Institute
7
of Technology, 1974.
8
[5] Z. Y. Wang, The autocontinuity of set function and the fuzzy integral, J. Math. Anal. Appl.,
9
99 (1984), 195-218.
10
[6] Z. Y. Wang, Asymptotic structural characteristics of fuzzy measure and their applications,
11
Fuzzy Sets and Systems, 16(2) (1985), 227-290.
12
[7] Z. Y. Wang, J. K. George and W. Wang, Monotone set functions dened by Choquet integral,
13
Fuzzy Sets and Systems, 81(2) (1996), 241-250.
14
[8] G. J. Wang and X. P. Li, On the convergence of fuzzy valued functional dened by-integrable
15
fuzzy valued functions, Fuzzy Sets and Systems, 107(2) (1999), 219-226.
16
[9] G. J. Wang and X. P. Li, Autocontinuity and preservation of structural characteristics of
17
generalized fuzzy number-valued Choquet integrals, Advances in Mathematics, (in Chinese),
18
34(1) (2005), 91-100.
19
[10] G. J. Wang and X. P. Li, Pseudo-autocontinuity and heredity of generalized fuzzy number-
20
valued Choquet integrals, Systems Sci. Math. Sci., (in Chinese), 26(4) (2006), 126-132.
21
[11] G. J. Wang and X. P. Li, On the C-I average convergence for sequence of fuzzy valued
22
functions, Systems Sci. Math. Sci., (in Chinese), 29(2) (2009), 253-262.
23
[12] G. Q. Zhang, Fuzzy Measure, Guiyang: Guizhou Technology Press, (in Chinese), 1998.
24
ORIGINAL_ARTICLE
OPTIMIZED FUZZY CONTROL DESIGN OF AN
AUTONOMOUS UNDERWATER VEHICLE
In this study, the roll, yaw and depth fuzzy control of an Au- tonomous Underwater Vehicle (AUV) are addressed. Yaw and roll angles are regulated only using their errors and rates, but due to the complexity of depth dynamic channel, additional pitch rate quantity is used to improve the depth loop performance. The discussed AUV has four aps at the rear of the vehicle as actuators. Two rule bases and membership functions based on Mamdani type and Sugeno type fuzzy rule have been chosen in each loop. By invoking the normalized steepest descent optimization method, the optimum values for the membership function parameters are found. Though the AUV is a highly nonlinear system, the simulation of the designed fuzzy logic control system based on the equations of motion shows desirable behavior of the AUV spe- cially when the parameters of the fuzzy membership functions are optimized.
http://ijfs.usb.ac.ir/article_190_6f00eb4c56b4a2714cdf356fa8ec77a5.pdf
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10.22111/ijfs.2012.190
Fuzzy optimized control
Autonomous underwater vehicle
Normalized
steepest descent
neural network
Behrooz
Raeisy
raeisy@shirazu.ac.ir
true
1
School of Electrical and Computer Engineering, Shiraz Univer-
sity, Shiraz, Iran and Iranian Space Agency, Iranian Space Center, Mechanic Institute,
Shiraz, Iran, P.O. Box: 71555-414
School of Electrical and Computer Engineering, Shiraz Univer-
sity, Shiraz, Iran and Iranian Space Agency, Iranian Space Center, Mechanic Institute,
Shiraz, Iran, P.O. Box: 71555-414
School of Electrical and Computer Engineering, Shiraz Univer-
sity, Shiraz, Iran and Iranian Space Agency, Iranian Space Center, Mechanic Institute,
Shiraz, Iran, P.O. Box: 71555-414
LEAD_AUTHOR
Ali Akbar
Safavi
safavi@shirazu.ac.ir
true
2
School of Electrical and Computer Engineering, Shiraz Univer-
sity, Shiraz, Iran
School of Electrical and Computer Engineering, Shiraz Univer-
sity, Shiraz, Iran
School of Electrical and Computer Engineering, Shiraz Univer-
sity, Shiraz, Iran
AUTHOR
Ali Reza
Khayatian
khayatia@shirazu.ac.ir
true
3
School of Electrical and Computer Engineering, Shiraz Uni-
versity, Shiraz, Iran
School of Electrical and Computer Engineering, Shiraz Uni-
versity, Shiraz, Iran
School of Electrical and Computer Engineering, Shiraz Uni-
versity, Shiraz, Iran
AUTHOR
[1] G. Antonelli, S. Chiaverini, N. Sarkar and M. West, Adaptive control of an autonomous
1
underwater vehicle. experimental results on ODIN, IEEE Proceedings, International Sympo-
2
sium on Computational Intelligence in Robotics and Automation, 1999.
3
[2] A. Balasuriya and L. Cong, Adaptive fuzzy sliding mode controller for underwater vehicles,
4
IEEE Proceedings, The 4th international conference on control and automations (ICCA'03),
5
Canada, June 2003.
6
[3] T. BinaZadeh, A. R. Khayatian and P. KarimAghaee, Identification and control of 6 DOF underwater
7
variable mass object, 13th iranian conference on electrical engineering (ICEE2005),
8
Zanjan, Iran, 2005.
9
[4] J. Blakelock, Automatic control of aircraft and missiles, 2nd edition, Willy, February 1991.
10
[5] F. Dougherty, T. Sherman, G. Woolweaver and G. Lovell, An autonomous underwater vehicle
11
(AUV) flight control system using sliding mode control, Proceedings, OCEANS '88.
12
Baltimore, MD USA, Oct. 1988.
13
[6] T. Fossen and M. Blanke, Nonlinear output feedback control of underwater vehicle propellers
14
using feedback from estimated axial flow velocity, IEEE Journal of Oceanic Engineering, Apr
15
[7] T. Fossen, Guidance and control of ocean vehicles, John Wiley & Sons, 1994.
16
[8] J. S. Han, H. S. Kim and J. Neggers, Actions, norms, subactions and kernels of (fuzzy)
17
norms, Iranian Journal of Fuzzy Systems, 7(2) (2010), 141-147.
18
[9] A. Hasankhani, A. Nazari and M. Sahelis, Some properties of fuzzy hilbert spaces and norm
19
of operators, Iranian Journal of Fuzzy Systems, 7(3) (2010), 129-157.
20
[10] K. Ishii and T. Ura, An adaptive neural-net controller system for an underwater vehicle,
21
Control Engineering Practice, Elsevierm, 8(2) (2000), 177-184.
22
[11] J. S. R. Jang, C. T. Sun and E. Mizutani, Neuro-fuzzy and soft computing, Prentic Hall,
23
[12] N. E. Leonard and P. S. Krishnaprasad, Motion control of an autonomous underwater vehicle
24
with an adaptive feature, IEEE Proceedings of Autonomous Underwater Vehicle Technology,
25
AUV '94, Cambridge, MA, USA, Jul 1994.
26
[13] J. H. Li, P. M. Lee and S. J. Lee, Neural net based nonlinear daptive control for autonomous
27
underwater vehicles, IEEE international Conference on Robotics and Automation, May 2002.
28
[14] Y. Nakamura and S. Savant, Nonlinear tracking control of autonomous underwater vehicles,
29
IEEE Proceedings on Robotics and Automation, May 1992.
30
[15] T. Prestero, Development of a six-degree of freedom simulation model for the REMUS autonomous
31
underwater vehicle, MTS/IEEE Conference and Exhibition, OCEANS, 2001.
32
[16] B. Raeisy, M. Kharati, A. A. Safavi and A. R. Khayatian, Equation of motion derivation of
33
variable mass underwater vehicle and 6DOF simulation with helping of neural network, 17th
34
Anual International Conference on Mechanical Engineering, Tehran, Iran, May 2009.
35
[17] B. Raeisy, A. A. Safavi and A. R. Khayatian, Fuzzy logic depth control of an autonomous
36
underwater vehicle and optimization of it with normalize steepened descent method, 17th
37
Anual International Conference on Mechanical Engineering, Tehran, Iran, May 2009.
38
[18] B. Raeisy, A. A. Safavi and A. R. Khayatian, Optimized fuzzy logic yaw and roll control of
39
an autonomous underwater vehicle, 8th Iranian Conference on Fuzzy System, Tehran, Iran,
40
October 2008.
41
[19] L. Rodrigues and P.Tavares, Sliding mode control of an AUV in the diving and steering
42
planes, MTS/IEEE Conference Proceedings, MG de Sousa Prado- OCEANS'96, Sep 1996.
43
[20] N. Sey'edi and M. A. Mirjalili, Hydrodynamic stability coefficients calculation of submarine
44
and its weapons using added mass and misile DATCOM, 4th Conference of Underwater
45
Science and Technology (fcoust), Isfahan, May 2007.
46
[21] E. Shivanian and E. Khoram, Optimization of linear objective function subject to fuzzy relation
47
inequalities constraints with max-product compozition, Iranian Journal of Fuzzy Systems,
48
7(3) (2010), 51-71.
49
[22] S. R.Vukelich, S. L. Stoy and M. E. Moore, Missile DATCOM user’s manual, Dought Aircraft
50
Company Inc., 1988.
51
[23] J. Wang and G. Lee, Self-adaptive recurrent neuro-fuzzy control of an autonomous underwater
52
vehicle, IEEE Transactions on Robotics and Automation, 19(2) (2003).
53
ORIGINAL_ARTICLE
NON-FRAGILE GUARANTEED COST CONTROL OF
T-S FUZZY TIME-VARYING DELAY SYSTEMS WITH
LOCAL BILINEAR MODELS
This paper focuses on the non-fragile guaranteed cost control problem for a class of T-S fuzzy time-varying delay systems with local bilinear models. The objective is to design a non-fragile guaranteed cost state feedback controller via the parallel distributed compensation (PDC) approach such that the closed-loop system is delay-dependent asymptotically stable and the closed-loop performance is no more than a certain upper bound in the presence of the additive controller gain perturbations. A sufficient condition for the existence of such non-fragile guaranteed cost controllers is derived via the linear matrix inequality (LMI) approach and the design problem of the fuzzy controller is formulated in term of LMIs. The simulation examples show that the proposed approach is effective.
http://ijfs.usb.ac.ir/article_195_cc8ebb13014dde2ae177412f1e3d190d.pdf
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10.22111/ijfs.2012.195
Fuzzy control
Non-fragile control
Guaranteed cost control
Delaydependent
Linear Matrix Inequality (LMI)
T-S fuzzy bilinear model
Junmin
Li
jmli@mail.xidian.edu.cn
true
1
Department of Mathematics, Xidian University, 710071, Xi'an, P.R. China
Department of Mathematics, Xidian University, 710071, Xi'an, P.R. China
Department of Mathematics, Xidian University, 710071, Xi'an, P.R. China
LEAD_AUTHOR
Guo
Zhang
gzhang163163@163.com
true
2
Department of Electrical Engineering and Automation, Luoyang Insti-
tute of Science and Technology, Luoyang, 471023, P.R. China
Department of Electrical Engineering and Automation, Luoyang Insti-
tute of Science and Technology, Luoyang, 471023, P.R. China
Department of Electrical Engineering and Automation, Luoyang Insti-
tute of Science and Technology, Luoyang, 471023, P.R. China
AUTHOR
[1] B. Chen and X. P. Liu, Delay-dependent robust H-innite control for T-S fuzzy systems with
1
time delay, IEEE Trans. Fuzzy Systems, 13 (2005), 238-249.
2
[2] B. Chen, C. Lin, X. P. Liu and S. C. Tong, Guaranteed cost control of T{S fuzzy systems
3
with input delay, Int. J. Robust Nonlinear Control, 18 (2008), 1230-1256.
4
[3] B. Chen, X. P. Liu, S. C. Tong and C. Lin, Observer-based stabilization of T{S fuzzy systems
5
with input delay, IEEE Trans. Fuzzy Systems, 16 (2008), 652-663.
6
[4] B. Chen, X. Liu, S. Tong and C. Lin, guaranteed cost control of T-S fuzzy systems with state
7
and input delay, Fuzzy Sets and Systems, 158 (2007), 2251-2267.
8
[5] M. Chen, G. Feng, H. Ma and G. Chen, Delay-dependent H-innite lter design for discrete-
9
time fuzzy systems with time-varying delays, IEEE Trans. Fuzzy Systems, 17 (2009), 604-616.
10
[6] W. H. Chen, Z. H. Guan and X. M. Lu, Delay-dependent output feedback guaranteed cost
11
control for uncertain time-delay systems, Automatica, 44 (2004), 1263-1268.
12
[7] J. Dong, Y. Wang and G. Yang, Control synthesis of continuous-time T-S fuzzy systems
13
with local nonlinear models, IEEE Trans. Systems, Man, Cybernetics-Part B, 39 (2009),
14
1245-1258.
15
[8] B. Z. Du, J. Lam and Z. Shu, Stabilization for state/input delay systems via static and
16
integral output feedback, Automatica, 46 (2010), 2000-2007.
17
[9] D. L. Elliott, Bilinear systems in Encyclopedia of Electrical Engineering, New York: Wiley,
18
[10] H. J. Gao, J. Lam and Z. D. Wang, Discrete bilinear stochastic systems with time-varying
19
delay: stability analysis and control synthesis, Chaos, Solitons and Fractals, 34 (2007), 394-
20
[11] H. J. Gao, X. Liu and J. Lam, Stability analysis and stabilization for discrete-time fuzzy
21
systems with time-varying delay, IEEE Trans. Systems, Man, Cybernetics-Part B, 39 (2009),
22
[12] D. W. C. Ho and Y. Niu, Robust fuzzy design for nonlinear uncertain stochastic systems via
23
sliding-mode control, IEEE Trans Fuzzy Systems, 15 (2007), 350-358.
24
[13] H. L. Huang and F. G. Shi, Robust H1 control for TCS time-varying delay systems with
25
norm bounded uncertainty based on LMI approach, Iranian Journal of Fuzzy Systems, 6
26
(2009), 1-14.
27
[14] L. H. Keel and S. P. Bhattacharryya, Robust, fragile, or optimal, IEEE Trans. Automatic
28
Control, 42 (1997), 1098-1105.
29
[15] J. H. Kim, Delay-dependent robust and non-fragile guaranteed cost control for uncertain
30
singular systems with time-varying state and input delays, International Journal of Control,
31
Automation and Systems, 7 (2009), 357-364.
32
[16] F. Leibfritz, An LMI-based algorithm for designing suboptimal static H2/H-innite output-
33
feedback controllers, SIAM J Control Optimization, 57 (2001), 1711-1735.
34
[17] J. M. Li, G. Zhang and C. Du, Robust H-innity control for a class of multiple input fuzzy
35
bilinear systems with uncertainties, Control Theory and Applications, 26 (2009), 1298-1302.
36
[18] L. Li and X. D. Liu, New approach on robust stability for uncertain T{S fuzzy systems with
37
state and input delays, Chaos, Solitons and Fractals, 40 (2009), 2329-2339.
38
[19] T. H. S. Li and S. H. Tsai, T-S fuzzy bilinear model and fuzzy controller design for a class
39
of nonlinear systems, IEEE Trans. Fuzzy Systems, 15 (2007), 494-505.
40
[20] T. H. S. Li, S. H. Tsai and et al, Robust H-innite fuzzy control for a class of uncertain
41
discrete fuzzy bilinear systems, IEEE Trans. Systems, Man, Cybernetics-Part B, 38 (2008),
42
[21] R. R. Mohler, Bilinear control processes, New York: Academic, 1973.
43
[22] C. T. Pang and Y. Y. Lur, On the stability of Takagi-Sugeno fuzzy systems with time-varying
44
uncertainties, IEEE Trans. Fuzzy Systems, 16 (2008), 162-170.
45
[23] R. E. Precup, S. Preitl, J. K. Tar, M. L. Tomescu, M. Takacs, P. Korondi and P. Baranyi,
46
Fuzzy control systems performance enhancement by iterative learning control, IEEE Trans.
47
Industrial Electronics, 55 (2008), 3461-3475.
48
[24] K. Tanaka and H. O. Wang, Fuzzy control systems design and analysis: a linear matrix
49
inequality approach, John Wiley and Sons, 2001.
50
[25] S. H. Tsai and T. H. S. Li, Robust fuzzy control of a class of fuzzy bilinear systems with
51
time-delay, Chaos, Solitons and Fractals, 39 (2007), 2028-2040.
52
[26] R. J. Wang, W. W. Lin and W. J. Wang, Stabilizability of linear quadratic state feedback
53
for uncertain fuzzy time-delay systems, IEEE Trans. Systems, Man, Cybernetics-Part B, 34
54
(2004), 1288-1292.
55
[27] H. N. Wu and H. X. Li, New approach to delay-dependent stability analysis and stabilization
56
for continuous-time fuzzy systems with time-varying delay, IEEE Trans. Fuzzy Systems, 15
57
(2007), 482-493.
58
[28] D. D. Yang and K. Y. Cai, Reliable guaranteed cost sampling control for nonlinear time-delay
59
systems, Mathematics and Computers in Simulation, 80 (2010), 2005-2018.
60
[29] G. H. Yang and J. L. Wang, Non-fragile H-innite control for linear systems with multiplica-
61
tive controller gain variations, Automatica, 37 (2001), 727-737.
62
[30] G. H. Yang, J. L. Wang and C. Lin, H-innite control for linear systems with additive
63
controller gain variations, Int. J Control, 73 (2000), 1500-1506.
64
[31] J. S. Yee, G. H. Yang and J. L. Wang, Non-fragile guaranteed cost control for discrete-time
65
uncertain linear systems, Int. J Systems Science, 32 (2001), 845-853.
66
[32] K. W. Yu and C. H. Lien, Robust H-innite control for uncertain T{S fuzzy systems with
67
state and input delays, Chaos, Solitons and Fractals, 37 (2008), 150-156.
68
[33] D. Yue and J. Lam, Non-fragile guaranteed cost control for uncertain descriptor systems with
69
time-varying state and input delays, Optimal Control Applications and Methods, 26 (2005),
70
[34] B. Y. Zhang, S. S. Zhou and T. Li, A new approach to robust and non-fragile H-innitecontrol
71
for uncertain fuzzy systems, Information Sciences, 177 (2007), 5118-5133.
72
[35] J. Zhang, Y. Xia and R. Tao, New results on H-innite ltering for fuzzy time-delay systems,
73
IEEE Trans. Fuzzy Systems, 17 (2009), 128-137.
74
[36] J. H. Zhang, P. Shi and J. Q. Qiu, Non-fragile guaranteed cost control for uncertain stochastic
75
nonlinear time-delay systems, Journal of the Franklin Institute, 3462009676-690.
76
[37] S. S. Zhou, J. Lam and W. X. Zheng, Control design for fuzzy systems based on relaxed
77
non-quadratic stability and H-innite performance conditions, IEEE Trans. Fuzzy Systems,
78
15 (2007), 188-198.
79
[38] S. S. Zhou and T. Li, Robust stabilization for delayed discrete-time fuzzy systems via basis-
80
dependent Lyapunov-Krasovskii function, Fuzzy Sets and Systems, 151 (2005), 139-153.
81
ORIGINAL_ARTICLE
Statistical Convergence and Strong $p-$Ces`{a}ro\ Summability of Order $beta$
in Sequences\ of Fuzzy Numbers
In this study we introduce the concepts of statistical convergence of order$beta$ and strong $p-$Ces`{a}ro summability of order $beta$ for sequencesof fuzzy numbers. Also, we give some relations between the statisticalconvergence of order $beta$ and strong $p-$Ces`{a}ro summability of order$beta$ and construct some interesting examples.
http://ijfs.usb.ac.ir/article_207_08995fac86ec1ef481d2824f5ac8adbd.pdf
2012-06-10T11:23:20
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63
73
10.22111/ijfs.2012.207
Fuzzy number
Statistical convergence
Cesro summability
H.
Altinok
hifsialtinok@yahoo.com
true
1
Department of Mathematics, Firat University, 23119, Elazig, Turkey
Department of Mathematics, Firat University, 23119, Elazig, Turkey
Department of Mathematics, Firat University, 23119, Elazig, Turkey
AUTHOR
Y.
Altin
yaltin23@yahoo.com
true
2
Department of Mathematics, Firat University, 23119, Elazig, Turkey
Department of Mathematics, Firat University, 23119, Elazig, Turkey
Department of Mathematics, Firat University, 23119, Elazig, Turkey
LEAD_AUTHOR
M.
Isik
misik63@yahoo.com
true
3
Department of Statistics, Firat University, 23119, Elazig, Turkey
Department of Statistics, Firat University, 23119, Elazig, Turkey
Department of Statistics, Firat University, 23119, Elazig, Turkey
AUTHOR
bibitem{altin2}
1
Y. Altin, M. Et and M. Bac{s}ari r, textit{On some
2
generalized difference sequences of fuzzy numbers}, Kuwait J. Sci. Eng.,
3
{bf 34(1A)} (2007), 1-14.
4
bibitem{altinok}H. Altinok, R. c{C}olak and M. Et, $lambda
5
-$textit{Difference sequence spaces of fuzzy numbers}, Fuzzy Sets and
6
Systems, textbf{160(21)} (2009), 3128-3139.
7
bibitem{Aytar}S. Aytar and S. Pehlivan, textit{Statistically convergence
8
of sequences of fuzzy numbers and sequences of }$alpha-$textit{cuts},
9
International J. General Systems, (2007), 1-7.
10
bibitem{burgin}M. Burgin, textit{Theory of fuzzy limits}, Fuzzy Sets and
11
Systems, textbf{115} (2000), 433-443.
12
bibitem{Connor}J. S. Connor, textit{The statistical and strong }%
13
$p-$textit{Ces`{a}ro convergence of sequences}, Analysis, textbf{8(1-2)} (1988), 47-63.
14
bibitem{colakb}R. c{C}olak, textit{Statistical convergence of order
15
}$alpha,$ Modern Methods in Analysis and its Applications, Anamaya Publ.
16
New Delhi, India, (2010), 121-129.
17
bibitem{Diamond}P. Diamond and P. Kloeden, textit{Metric spaces of fuzzy
18
sets}, Fuzzy Sets and Systems, textbf{35(2)} (1990), 241-249.
19
bibitem{Fang}J. X. Fang and H. Hung, textit{On the level convergence of
20
a sequence of fuzzy numbers}, Fuzzy Sets and Systems, textbf{147} (2004), 417-435.
21
bibitem{Fast}H. Fast, textit{Sur la convergence statistique}, Colloquium
22
Math., textbf{2} (1951), 241-244.
23
bibitem{Fridy}J. A. Fridy, textit{On statistical convergence}, Analysis,
24
textbf{5(4)} (1985), 301-313.
25
bibitem{gadjiev}A. D. Gadjiev and C. Orhan, textit{Some approximation
26
theorems via statistical convergence}, Rocky Mountain J. Math., textbf{32(1)} (2002), 129-138.
27
bibitem{hancl}J. Hanv{c}l, L. Miv{s}'{i}k and J. T'{o}th,
28
textit{Cluster points of sequences of fuzzy real numbers}, Soft Computing,
29
textbf{14(4)} (2010), 399-404.
30
bibitem{kumar}V. Kumar and K. Kumar, textit{On the ideal convergence of
31
sequences of fuzzy numbers}, Information Sciences, textbf{178(24)} (2008), 4670-4678.
32
bibitem{kwon}J. S. Kwon, textit{On statistical and }$p-$%
33
textit{Ces`{a}ro convergence of fuzzy numbers}, Korean J. Comput. &Appl.
34
Math., textbf{7(1)} (2000), 195-203.
35
bibitem{Matloka}M. Matloka, textit{Sequences of fuzzy numbers}, BUSEFAL,
36
textbf{28} (1986), 28-37.
37
bibitem{mur}M. Mursaleen and M. Bac{s}ari r, textit{On some new
38
sequence spaces of fuzzy numbers}, Indian J. Pure Appl. Math., textbf{34(9)} (2003), 1351-1357.
39
bibitem{Nuray}F. Nuray and E. Savac{s}, textit{Statistical convergence
40
of sequences of fuzzy real numbers}, Math. Slovaca, textbf{45(3)} (1995), 269-273.
41
bibitem{Schoenberg}I. J. Schoenberg, textit{The integrability of certain
42
functions and related summability methods}, Amer. Math. Monthly, textbf{66} (1959), 361-375.
43
bibitem{talo}"{O}. Talo and F. Bac{s}ar, textit{On the space }%
44
$bv_{p}(F)$textit{ of sequences of }$p-$textit{bounded variation of fuzzy
45
numbers}, Acta Math. Sin. Engl. Ser., textbf{24(7)} (2008), 1205-1212.
46
bibitem{Tri}B. C. Tripathy and A. J. Dutta, textit{On fuzzy
47
real-valued double sequence space }$_{2}ell_{F}^{p}$textit{, Math. Comput.
48
Modelling}, {bf 46(9-10)} (2007), 1294-1299.
49
ORIGINAL_ARTICLE
A MODIFICATION ON RIDGE ESTIMATION FOR FUZZY
NONPARAMETRIC REGRESSION
This paper deals with ridge estimation of fuzzy nonparametric regression models using triangular fuzzy numbers. This estimation method is obtained by implementing ridge regression learning algorithm in the La- grangian dual space. The distance measure for fuzzy numbers that suggested by Diamond is used and the local linear smoothing technique with the cross- validation procedure for selecting the optimal value of the smoothing param- eter is fuzzi ed to t the presented model. Some simulation experiments are then presented which indicate the performance of the proposed method.
http://ijfs.usb.ac.ir/article_208_2e0cee241fca30013729165d21197b5d.pdf
2012-06-10T11:23:20
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75
88
10.22111/ijfs.2012.208
Fuzzy regression
Ridge estimation
Fuzzy nonparametric regression
Local linear smoothing
Rahman
Farnoosh
rfarnoosh@iust.ac.ir
true
1
School of Mathematics, Iran University of Science and Tech-
nology, Narmak, Tehran-16846, Iran
School of Mathematics, Iran University of Science and Tech-
nology, Narmak, Tehran-16846, Iran
School of Mathematics, Iran University of Science and Tech-
nology, Narmak, Tehran-16846, Iran
LEAD_AUTHOR
Javad
Ghasemian
jghasemian@iust.ac.ir, jghasemian@gmail.com
true
2
School of Mathematics, Iran University of Science and Technol-
ogy, Narmak, Tehran-16846, Iran
School of Mathematics, Iran University of Science and Technol-
ogy, Narmak, Tehran-16846, Iran
School of Mathematics, Iran University of Science and Technol-
ogy, Narmak, Tehran-16846, Iran
AUTHOR
Omid
Solaymani Fard
osfard@du.ac.ir, omidsfard@gmail.com
true
3
School of Mathematics and Computer Science, Damghan Uni-
versity, Damghan, Iran
School of Mathematics and Computer Science, Damghan Uni-
versity, Damghan, Iran
School of Mathematics and Computer Science, Damghan Uni-
versity, Damghan, Iran
AUTHOR
[1] C. B. Cheng and E. S. Lee, Fuzzy regression with radial basis function networks, Fuzzy Sets
1
and Systems, 119 (2001), 291-301.
2
[2] P. Diamond, Fuzzy least squares, Information Sciences, 46 (1988), 141-157.
3
[3] N. R. Draper and H. Smith, Applied Regression Analysis, Wiley, New York, 1980.
4
[4] H. Drucker, C. Burges, L. Kaufman, A. Smola and V. N. Vapnik, Support vector regression
5
machines, in: M. C. Mozer, M. I. Jordan, T. Petsche, Eds., Advances in Neural Information
6
Processing Systems, MIT Press, Cambridge, MA, 9 (1996), 155-162.
7
[5] O. S. Fard and A. V. Kamyad, Modied k-step method for solving fuzzy initial value problems,
8
Iranian Journal of Fuzzy Systems, 8(1) (2011), 49-63.
9
[6] J. Fan and I. Gijbels, Local Polynomial Modeling and Its Applications, Chapman & Hall,
10
London, 1996.
11
[7] W. Hardle, Applied Nonparametric Regression, Cambridge University Press, New York, 1990.
12
[8] J. D. Hart, Nonparametric Smoothing and Lack-of-t Tests, Springer-Verlag, New York, 1997.
13
[9] T. J. Hastie and R. J. Tibshirani, Generalized Additive Models, Chapman & Hall, London,
14
[10] D. H. Hong and C. Hwang, Support vector fuzzy regression machines, Fuzzy Sets and Systems,
15
138 (2003), 271-281.
16
[11] D. H. Hong, C. Hwang and C. Ahn, Ridge estimation for regression models with crisp inputs
17
and Gaussian fuzzy output, Fuzzy Sets and Systems, 142 (2004), 307-319.
18
[12] A. E. Hoerl and R. W. Kennard, Ridge regression: biased estimates for nonorthogonal prob-
19
lems, Technometrics, 12 (1970), 55-67.
20
[13] H. Ishibuchi and H. Tanaka, Fuzzy regression analysis using neural networks, Fuzzy Sets and
21
Systems, 50 (1992), 257-265.
22
[14] H. Ishibuchi and H. Tanaka, Fuzzy neural networks with interval weights and its application
23
to fuzzy regression analysis, Fuzzy Sets and Systems, 57 (1993), 27-39.
24
[15] B. Kim and R. R. Bishu, Evaluation of fuzzy linear regression models by comparing mem-
25
bership functions, Fuzzy Sets and Systems, 100 (1998), 343-352.
26
[16] R. X. Liu, J. Kuang, Q. Gong and X. L. Hou, Principal component regression analysis with
27
SPSS, Computer Methods and Programs in Biomedicine, 71 (2003), 141-147.
28
[17] S. Pourahmad, S. M. T. Ayatollahi and S. M. Taheri, Fuzzy logistic regression: a new possi-
29
bilistic model and its application in clinical vague status, Iranian Journal of Fuzzy Systems,
30
8 (2011), 1-17.
31
[18] H. Shakouri G and R. Nadimi, A novel fuzzy linear regression model based on a non-equality
32
possibility index and optimum uncertainty, Applied Soft Computing, 9 (2009), 590-598.
33
[19] C. Saunders, A. Gammerman and V. Vork, Ridge regression learning algorithm in dual vari-
34
able, Proceedings of the 15th International Conference on Machine Learning, (1998), 515-521.
35
[20] N. Wang, W. X. Zhang and C. L. Mei, Fuzzy nonparametric regression based on local linear
36
smoothing technique, Information Sciences, 177 (2007), 3882-3900.
37
[21] M. S. Yang and C. H. Ko, On a class of fuzzy c-numbers clustering procedures for fuzzy data,
38
Fuzzy Sets and Systems, 84 (1996), 49-60.
39
ORIGINAL_ARTICLE
Delay-dependent robust stabilization and $H_{infty}$
control for uncertain stochastic T-S fuzzy systems with multiple
time delays
In this paper, the problems of robust stabilization and$H_{infty}$ control for uncertain stochastic systems withmultiple time delays represented by the Takagi-Sugeno (T-S) fuzzymodel have been studied. By constructing a new Lyapunov-Krasovskiifunctional (LKF) and using the bounding techniques, sufficientconditions for the delay-dependent robust stabilization and $H_{infty}$ control scheme are presented in terms of linear matrixinequalities (LMIs). By solving these LMIs, a desired fuzzycontroller can be obtained which can be easily calculated byMatlab LMI control toolbox. Finally, a numerical simulation isgiven to illustrate the effectiveness of the proposed method.
http://ijfs.usb.ac.ir/article_210_c71a2f62a18060ea4d8bb698859af37c.pdf
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89
111
10.22111/ijfs.2012.210
Takagi-Sugeno (T-S) fuzzy systems
Robust $H_{infty}$ control
Stochastic system
Linear matrix inequalities (LMIs)
Multiple time
delays
Lyapunov-Krasovskii functional (LKF)
T.
Senthilkumar
tskumar2410@gmail.com
true
1
Department of Mathematics, Gandhigram Rural Institute-Deemed
University, Gandhigram - 624 302, Tamilnadu, India
Department of Mathematics, Gandhigram Rural Institute-Deemed
University, Gandhigram - 624 302, Tamilnadu, India
Department of Mathematics, Gandhigram Rural Institute-Deemed
University, Gandhigram - 624 302, Tamilnadu, India
AUTHOR
P.
Balasubramaniam
balugru@gmail.com
true
2
Department of Mathematics, Gandhigram Rural Institute-
Deemed University, Gandhigram - 624 302, Tamilnadu, India
Department of Mathematics, Gandhigram Rural Institute-
Deemed University, Gandhigram - 624 302, Tamilnadu, India
Department of Mathematics, Gandhigram Rural Institute-
Deemed University, Gandhigram - 624 302, Tamilnadu, India
LEAD_AUTHOR
bibitem{BR} M. Basin and A. Rodkina, {it On delay-dependent stability for a class of
1
nonlinear stochastic systems with multiple state delays}, Nonlinear
2
Anal., {bf 68} (2008), 2147-2157.
3
bibitem{BL} E. K. Boukas and Z. K. Liu, {it Deterministic and stochastic time-delay
4
systems}, Birkhäuser, Boston, 2002.
5
bibitem{BGFB} S. Boyd, L. E. Ghauoi, E. Feron and V. Balakrishnan, {it Linear matrix inequalities in
6
system and control theory}, SIAM, Philadelphia, PA, 1994.
7
bibitem{CF} Y. Y. Cao and P. M. Frank, {it Stability analysis and synthesis of nonlinear
8
time-delay systems via linear Takagi-Sugeno fuzzy models},
9
Fuzzy Sets and Systems, {bf 124} (2001), 213-229.
10
bibitem{CRF} S. G. Cao, N. W. Rees and G. Feng, {it Stability analysis and design
11
for a class of continuous-time fuzzy control systems},
12
Int. J. Control, {bf 64} (1996), 1069-1087.
13
bibitem{CGL} W. H. Chen, Z. H. Guan and X. Lu, {it Delay-dependent exponential stability
14
of uncertain stochastic systems with multiple delays: an LMI approach},
15
Syst. Control. Lett., {bf 54} (2005), 547-555.
16
bibitem{CL} B. Chen and X. Liu, {it Delay-dependent robust $H_{infty}$ control for T-S
17
fuzzy systems with time delay}, IEEE Trans. Fuzzy Syst., {bf 13} (2005), 544-556.
18
bibitem{CLLL} B. Chen, X. Liu, C. Lin and K. Liu, {it Robust $H_{infty}$ control of
19
Takagi-Sugeno fuzzy systems with state and input time delays},
20
Fuzzy Sets and Systems, {bf 160} (2009), 403-422.
21
bibitem{F} G. Feng, {it A survey on analysis and design of model-based fuzzy control systems},
22
IEEE Trans. Fuzzy Syst., {bf 14} (2006), 676-697.
23
bibitem{GLW} H. Gao, J. Lam and C. Wang, {it Robust energy-to-peak filter design for
24
stochastic time-delay systems}, Syst. Control. Lett., {bf 55} (2006), 101-111.
25
bibitem{GC} X. P. Guan and C. L. Chen, {it Delay-dependent guaranteed cost control for
26
T-S fuzzy systems with time delays}, IEEE Trans. Fuzzy Syst.,
27
{bf 12} (2004), 236-249.
28
bibitem{HP} L. V. Hien and V. N. Phat, {it Robust stabilization of linear polytopic control
29
systems with mixed delays}, Acta Math. Vietnamica, {bf 35} (2010), 427-438.
30
bibitem{HPSIAM} D. Hinrichsen and A. J. Pritchard, {it Stochastic $H_{infty}$}, SIAM J. Control
31
Optim., {bf 36} (1998), 1504-1538.
32
bibitem{H} F. H. Hsiao, {it Robust $H_{infty}$ fuzzy control of nonlinear systems with
33
multiple time delays}, Int. J. Syst. Sci., {bf 38} (2007), 351-360.
34
bibitem{HY} L. Hu and A. Yang, {it Fuzzy model-based control of nonlinear stochastic
35
systems with time-delay}, Nonlinear Anal. TMA., {bf 71} (2009), 2855-2865.
36
bibitem{HH} H. Huang and D. W. C. Ho, {it Delay-dependent robust control of uncertain
37
stochastic fuzzy systems with time-varying delay}, IET Control Theory
38
Appl., {bf 1} (2007), 1075-1085.
39
bibitem{HSIJFS} H. L. Huang and F. G. Shi, {it Robust control for T-S time-varying delay
40
systems with norm bounded uncertainty based on LMI approach},
41
Iranian Journal of Fuzzy Systems, textbf{6} (2009), 1-14.
42
bibitem{KM} V. B. Kolmanovskii and A. D. Myshkis, {it Applied theory of functional
43
differential equations}, Dordrecht, The Netherlands: Kluwer, 1992.
44
bibitem{LWL} C. Lin, Q. G. Wang and T. H. Lee, {it Improvement on observer-based
45
$H_{infty}$ control for T-S fuzzy systems}, Automatica, {bf 41} (2005), 1651-1656.
46
bibitem{M} X. Mao, {it Stochastic differential equations and their applications},
47
Horwood, Chichester, 1997.
48
bibitem{MPKL} Y. S. Moon, P. Park, W. H. Kwon and Y. S. Lee, {it Delay-dependent robust
49
stabilization of uncertain state-delayed systems},
50
Int. J. Control, {bf 74} (2001), 1447-1455.
51
bibitem{P} V. N. Phat, {it Memoryless $H_{infty}$ controller design for switched
52
non-linear systems with mixed time-varying delays}, Int. J. Control, {bf 82} (2009), 1889-1898.
53
bibitem{SN} P. Shi and S. K. Nguang, {it $H_{infty}$ output feedback control of fuzzy system models
54
under sampled measurements}, Comput. Math. Appl., {bf 46} (2003), 705-717.
55
bibitem{TIW} K. Tanaka, T. Ikeda and H. O. Wang, {it Fuzzy regulators and fuzzy
56
observers: relaxed stability conditions and LMI-based designs},
57
IEEE Trans. Fuzzy Syst., {bf 6} (1998), 250-265.
58
bibitem{TS} T. Takagi and M. Sugeno, {it Fuzzy identification systems and it's application to modeling
59
and control}, IEEE Trans. Syst. Man Cybern., {bf 15} (1985), 116-132.
60
bibitem{WHL} Z. Wang, D. W. C. Ho and X. Liu, {it A note on the robust stability of
61
uncertain stochastic fuzzy systems with time-delays},
62
IEEE Trans. Syst. Man, Cybern. A, {bf 34} (2004), 570-576.
63
bibitem{WTG} H. O. Wang, K. Tanaka and M. F. Griffn, {it An approach to fuzzy control
64
of nonlinear systems: stability and design issues},
65
IEEE Trans. Fuzzy Syst., {bf 4} (1996), 14-23.
66
bibitem{WXS} Y. Wang, L. Xie and C. E. de Souza, {it Robust control of a class of
67
uncertain nonlinear system}, Syst. Control. Lett., {bf 19} (1992), 139-149.
68
bibitem{XC} S. Xu and T. Chen, {it Robust $H_{infty}$ control for uncertain stochastic
69
systems with state delay}, IEEE Trans. Automat.
70
Contr., {bf 47} (2002), 2089-2094.
71
bibitem{XL} S. Xu and J. Lam, {it Robust $H_{infty}$ control for uncertain discrete
72
time-delay fuzzy systems via output feedback controllers},
73
IEEE Trans. Fuzzy Syst., {bf 13} (2005), 82-93.
74
bibitem{YGS} R. Yang, H. Gao and P. Shi, {it Delay-dependent robust $H_{infty}$ control
75
for uncertain stochastic time-delay systems},
76
Int. J. Robust Nonlinear Control, textbf{20} (2010), 1852-1865.
77
bibitem{YH} Z. Yi and P. A. Heng, {it Stability of fuzzy control systems with bounded
78
uncertain delays}, IEEE Trans. Fuzzy Syst., {bf 10} (2002), 92-97.
79
bibitem{Y} J. Yoneyama, {it New robust stability conditions and design of robust
80
stabilizing controllers for Takagi-Sugeno fuzzy time-delay systems},
81
IEEE Trans. Fuzzy Syst., {bf 15} (2007), 828-839.
82
bibitem{ZGLD} Y. Zhao, H. Gao, J. Lam and B. Du, {it Stability and stabilization of
83
delayed T-S fuzzy systems: a delay partitioning approach},
84
IEEE Trans. Fuzzy Syst., {bf 17} (2009), 750-762.
85
bibitem{ZGW} H. Zhang, Q. Gong and Y. Wang, {it Delay-dependent robust $H_{infty}$
86
control for uncertain fuzzy hyperbolic systems with multiple delays},
87
Progr. Natur. Sci., {bf 18} (2008), 97-104.
88
bibitem{ZLL} H. Zhang, S. Lun and D. Liu, {it Fuzzy $H_{infty}$ filter design for a
89
class of nonlinear discrete-time systems with multiple time delays},
90
IEEE Trans. Fuzzy Syst., {bf 15} (2007), 453-469.
91
bibitem{ZWL} H. Zhang, Y. Wang and D. Liu, {it Delay-dependent guaranteed cost control
92
for uncertain stochastic fuzzy systems with multiple time delays},
93
IEEE Trans. Syst., Man, Cybern. B, Cybern., {bf 38} (2008), 126-140.
94
bibitem{ZXZZ} B. Zhang, S. Xu, G. Zong and Y. Zou, {it Delay-dependent stabilization
95
for stochastic fuzzy systems with time delays}, Fuzzy Sets and Systems, {bf 158} (2007), 2238-2250.
96
bibitem{ZFLX} S. Zhou, G. Feng, J. Lam and S. Xu, {it Robust $H_{infty}$ control for
97
discrete-time fuzzy systems via basis-dependent Lyapunov functions},
98
Information Sciences, {bf 174} (2005), 197-217.
99
bibitem{ZL} S. Zhou and T. Li, {it Robust stabilization for delayed discrete-time fuzzy
100
systems via basis-dependent Lyapunov-Krasovskii function},
101
Fuzzy Sets and Systems, {bf 151}(2005), 139-153.
102
ORIGINAL_ARTICLE
ON GENERALIZED FUZZY MULTISETS AND THEIR USE IN
COMPUTATION
An orthogonal approach to the fuzzification of both multisets and hybridsets is presented. In particular, we introduce $L$-multi-fuzzy and$L$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. In addition, we study the properties ofthese structures. Also, the usefulness of these structures is examined inthe framework of mechanical multiset processing. More specifically, weintroduce a variant of fuzzy P~systems and, since simplefuzzy membrane systems have been introduced elsewhere, we simply extendpreviously stated results and ideas.
http://ijfs.usb.ac.ir/article_213_88c01df01c2fd5e86ccf933534b6ff70.pdf
2012-06-10T11:23:20
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113
125
10.22111/ijfs.2012.213
L-fuzzy sets
Fuzzy Multisets
Computability
P Systems
Apostolos
Syropoulos
asyropoulos@yahoo.com
true
1
Greek Molecular Computing Group, 366, 28th October St.,
GR-67100 Xanthi, Greece
Greek Molecular Computing Group, 366, 28th October St.,
GR-67100 Xanthi, Greece
Greek Molecular Computing Group, 366, 28th October St.,
GR-67100 Xanthi, Greece
LEAD_AUTHOR
[1] M. Akay, M. Cohen and D. Hudson, Fuzzy sets in life sciences, Fuzzy Sets and Systems, 90
1
(1997), 219-224.
2
[2] S. Anelli, E. Damiani, O. D'Antona and D. E. Loeb, Getting results with negative thinking,
3
LACES 05A-95-17, eprint arXiv:math.CO/9502214.
4
[3] D. A. Baum, Individuality and the existence of species through time, Systematic Biology,
5
47(4) (1989), 641-653.
6
[4] G. Berry and G. Boudol, The chemical abstract machine, Theoretical Comput. Sci., 96
7
(1992), 217-248.
8
[5] W. Blizard, The development of multiset theory, Modern Logic, 1 (1991), 319-352.
9
[6] R. De Nicola and S. A. Smolka, Concurrency: theory and practice, ACM Computing Surveys
10
28A, 4es (1996), 52.
11
[7] J. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Application, 18 (1967), 145-
12
[8] D. E. Knuth, The art of computer programming, Seminumerical Algorithms, Addisson-
13
Wesley, 2 (1981).
14
[9] D. Loeb, Sets with a negative number of elements, Advances in Mathematics, 91 (1992),
15
[10] S. Miyamoto, Fuzzy multisets and their generalizations, In Multiset Processing, C. Calude,
16
G. Paun, G. Rozenberg and A. Salomaa, eds., in Lecture Notes in Computer Science. Springer-
17
Verlag, Berlin, 2235 (2001), 225-235.
18
[11] S. Miyamoto, Data structure and operations for fuzzy multisets, In Transactions on Rough
19
Sets II: Rough Sets and Fuzzy Sets, J. F. Peters, A. Skowron, D. Dubois, J. Grzymala-Busse
20
and M. Inuiguchi, eds., in Lecture Notes in Computer Science. Springer-Verlag, Berlin, 3135
21
(2004), 189-200.
22
[12] G. Paun, Membrane computing: an introduction, Springer-Verlag, Berlin, 2002.
23
[13] J. R. Searle, Mind: a brief introduction, Oxford University Press, Oxford, UK, 2004.
24
[14] L. A. Stein, Challenging the computational metaphor: implications for how we think, Cyber-
25
netics & Systems, 30(6) (1999), 473-507.
26
[15] A. Syropoulos, Mathematics of multisets, In Multiset Processing, C. Calude, G. Paun,
27
G. Rozenberg and A. Salomaa, eds., in Lecture Notes in Computer Science. Springer-Verlag,
28
Berlin, 2235 (2001), 347-358.
29
[16] A. Syropoulos, Fuzzifying P systems, The Computer Journal, 49(5) (2006), 619-628.
30
[17] A. Syropoulos, Fuzzy chemical abstract machines, CoRR abs/0903.3513, 2009.
31
[18] A. Syropoulos, On nonsymmetric multi-fuzzy sets, Critical Review IV, (2010), 35{41.
32
[19] A. Tzouvaras, The linear logic of multisets, Logic Journal of the IGPL, 6(6) (1998), 901-916.
33
[20] A. Tzouvaras, The logic of multisets continued: the case of disjunction, Studia Logica, 75
34
(2003), 287-304.
35
[21] S. Vickers, Topology via logic, Cambridge Tracts in Theoretical Computer Science, Cambridge
36
University Press, Cambridge, U. K., 6 (1990).
37
[22] K. Weihrauch, Computable analysis: an introduction, Springer-Verlag, Berlin/Heidelberg,
38
[23] R. R. Yager, On the theory of bags, Int. J. General Systems, 13 (1986), 23-37.
39
[24] X. Zheng and K. Weihrauch, The arithmetical hierarchy of real numbers, Mathematical Logic
40
Quarterly, 47(1) (2001), 51-65.
41
ORIGINAL_ARTICLE
GLOBAL ROBUST STABILITY CRITERIA FOR T-S FUZZY
SYSTEMS WITH DISTRIBUTED DELAYS AND TIME
DELAY IN THE LEAKAGE TERM
The paper is concerned with robust stability criteria for Takagi- Sugeno (T-S) fuzzy systems with distributed delays and time delay in the leakage term. By exploiting a model transformation, the system is converted to one of the neutral delay system. Global robust stability result is proposed by a new Lyapunov-Krasovskii functional which takes into account the range of delay and by making use of some inequality techniques. Based on the interval time-varying delays, new stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, three numerical examples and their simulations are given to show the effectiveness and advantages of our results.
http://ijfs.usb.ac.ir/article_215_3ee14b4127b1a40c41c3f413180b869d.pdf
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127
146
10.22111/ijfs.2012.215
Delay-dependent stability
Linear matrix inequality
Lyapunov–Krasovskii
functional
T-S fuzzy systems
P.
Balasubramaniam
balugru@gmail.com
true
1
Department of Mathematics, Gandhigram Rural Institute-Deemed
University, Gandhigram - 624 302, Tamilnadu, India
Department of Mathematics, Gandhigram Rural Institute-Deemed
University, Gandhigram - 624 302, Tamilnadu, India
Department of Mathematics, Gandhigram Rural Institute-Deemed
University, Gandhigram - 624 302, Tamilnadu, India
LEAD_AUTHOR
S.
Lakshmanan
lakshm@gmail.com
true
2
Department of Mathematics, Gandhigram Rural Institute-Deemed
University, Gandhigram - 624 302, Tamilnadu, India
Department of Mathematics, Gandhigram Rural Institute-Deemed
University, Gandhigram - 624 302, Tamilnadu, India
Department of Mathematics, Gandhigram Rural Institute-Deemed
University, Gandhigram - 624 302, Tamilnadu, India
AUTHOR
R.
Rakkiyappan
rakkigru@gmail.com
true
3
Department of Mathematics, Bharathiar University, Coimbatore -
641 046, Tamilnadu, India
Department of Mathematics, Bharathiar University, Coimbatore -
641 046, Tamilnadu, India
Department of Mathematics, Bharathiar University, Coimbatore -
641 046, Tamilnadu, India
AUTHOR
bibitem{BGB} S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, textit{Linear
1
matrix inequalities in systems and control theory}, Philadelphia:
2
SIAM, 1994.
3
bibitem{4} M. Chadli and A. E. Hajjaji, textit{A observer-based robust fuzzy
4
control of nonlinear systems with parametric uncertainties},
5
Fuzzy Sets and Systems, textbf{157} (2006), 1279-1281
6
bibitem{CLT} B. Chen, X. P. Liu and S. C. Tong, textit{New delay-dependent stabilization conditions of T-S systems with constant delay}, Fuzzy Sets and Systems, textbf{158} (2007), 2209-2224.
7
bibitem{3} H. Gassara, A. E. Hajjaji and M. Chaabane, textit{Robust control of
8
T-S fuzzy systems with time-varying delay using new approach},
9
Int. J. Robust Nonlinear Control, textbf{20} (2010), 1566–1578
10
bibitem{iranian3} R. Ghanbari, N. Mahdavi-Amiri and R. Yousefpour, textit{Exact and approximate solutions of fuzzy lr linear systems: new algorithms using a least squares model and the abs approach}, Iranian Journal of Fuzzy
11
Systems, textbf{7} (2010), 1-18.
12
bibitem{BK} K. Gopalsamy, textit{Stability and oscillations in delay differential
13
equations of population dynamics}, Kluwer Academic Publishers,
14
Dordrecht, 1992.
15
bibitem{leak1} K. Gopalsamy, textit{Leakage delays in BAM},
16
J Math. Anal. Appl., textbf{325} (2007), 1117-1132.
17
bibitem{XPC} X. P. Guan and C. L. Chen, textit{Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays}, IEEE Trans. Fuzzy Syst., textbf{12} (2004) 236-249.
18
bibitem{Unc2} Q. L. Han, textit{Robust stability for a class of linear systems with
19
time-varying delay and nonlinear perturbations}, Comput.
20
Math. Appl., textbf{47} (2004), 1201-1209.
21
bibitem{F33} F. H. Hsiao, textit{Robust $H_{infty}$ fuzzy control of nonlinear
22
systems with multiple time delays}, In. J.
23
Syst. Sci., textbf{38} (2007), 351-360.
24
bibitem{In2} X. Jiang and Q. L. Han, textit{Delay-dependent robust stability for
25
uncertain linear systems with interval time-varying delay},
26
Automatica, textbf{42} (2006), 1059-1065.
27
bibitem{Unc1} O. M. Kwon, J. H. Park and S. M. Lee, textit{On stability criteria for
28
uncertain delay-differential systems of neutral type with
29
time-varying delays}, Appl. Math. Comput.,
30
textbf{197} (2008), 864-873.
31
bibitem{leak3} X. Li, X. Fu, P. Balasubramaniam and R. Rakkiyappan, textit{Existence,
32
uniqueness and stability analysis of recurrent neural networks
33
with time delay in the leakage term under impulsive
34
perturbations}, Nonlinear Anal. Real World Appl.,
35
textbf{11} (2010), 4092-4108.
36
bibitem{leak2} C. Li and T. Huang, textit{On the stability of
37
nonlinear systems with leakage delay}, J. Franklin Inst., textbf{346} (2009), 366-377.
38
bibitem{Comp1} C. G. Li, H. J. Wang and X. F. Liao, textit{Delay-dependent robust stability of
39
uncertain fuzzy systems with time-varying delays}, IEE
40
Proce. Control Theory Appl., textbf{151} (2004), 417-421.
41
bibitem{Comp2} C. H. Lien, textit{Further results on delay-dependent robust stability of
42
uncertain fuzzy systems with time-varying delay}, Chaos Solitons
43
Fractals, textbf{28} (2006), 422-427.
44
bibitem{Comp3}C. H. Lien, K. W. Yu, W. D. Chen, Z. L. Wan and Y. J. Chung, textit{Stability criteria for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay}, IET Control Theory Appl., textbf{1} (2007), 746-769.
45
bibitem{F31} F. Liu, M. Wu, Y. He and R. Yokoyama, textit{New delay-dependent
46
stability criteria for T-S fuzzy systems with time-varying delay},
47
Fuzzy Sets and Systems, textbf{161} (2010), 2033-2042.
48
bibitem{iranian1}M. Meidani, G. Habibagahi and S. Katebi, textit{An aggregated fuzzy reliability index for slope stability analysis}, Iranian Journal of Fuzzy Systems, textbf{1} (2004), 17-31.
49
bibitem{In1} C. Peng and Y. C. Tian, textit{Delay-dependent robust stability criteria
50
for uncertain systems with interval time-varying delay}, J.
51
Comput. Appl. Math., textbf{214} (2008), 480-494.
52
bibitem{F3} C. Peng, D. Yue, T. C. Yang and E. G. Tian, textit{On delay-dependent
53
approach for robust stability and stabilization of T-S fuzzy
54
systems with constant delay and uncertainties}, IEEE Trans. Fuzzy Syst., textbf{17} (2009), 1143-1156.
55
bibitem{Unc3} W. Qian, S. Cong, Y. Sun and S. Fei, textit{Novel robust stability criteria for
56
uncertain systems with time-varying delay}, Appl. Math.
57
Comput., textbf{215} (2009), 866-872.
58
bibitem{F4} F. O. Souza, L. A. Mozelli and R. M. Palhares,
59
textit{On stability and stabilization of T-S fuzzy time-delayed
60
systems}, IEEE Trans. Fuzzy Syst., textbf{17} (2009), 1450-1455.
61
bibitem{In4} J. Sun, G. P. Liu, J. Chen and D. Rees, textit{Improved
62
delay-range-dependent stability criteria for linear systems with
63
time-varying delays}, Automatica, textbf{46} (2010), 466-470 .
64
bibitem{triple3} J. Sun and G. P. Liu, textit{A new delay-dependent stability criterion
65
for time-delay systems}, Asian J. Control, textbf{11} (2009), 427-431.
66
bibitem{triple1} J. Sun, G. P. Liu, J. Chen and D. Rees, textit{Improved stability criteria
67
for neural networks with time-varying delay}, Phys. Lett. A, textbf{373} (2009), 342-348.
68
bibitem{iranian2} A. A. Suratgar and S. K. Y. Nikravesh, textit{Potential energy based stability analysis of fuzzy linguistic systems}, Iranian Journal of Fuzzy Systems, textbf{2} (2005), 65-74.
69
bibitem{1} T. Takagi and M. Sugeno, textit{Fuzzy identification of systems and its
70
application tomodeling and control}, IEEE Trans. Syst. Man, textbf{15} (1985), 116-132 .
71
bibitem{2} K. Tanaka and M. Sano, textit{A robust stabilization problem of fuzzy
72
control systems and its application to backing up control of a
73
truck-trailer}, IEEE Trans. Fuzzy Syst.,
74
textbf{2} (1994), 119-134
75
bibitem{F1} E. Tian and C. Peng, textit{Delay-dependent stability analysis and
76
synthesis of uncertain T-S fuzzy systems with time-varying delay},
77
Fuzzy Sets and Systems, textbf{157} (2006), 544-559.
78
bibitem{Unc4} M. Wu, Y. He, J. H. She and G. P. Liu, textit{Delay-dependent criteria for
79
robust stability of time-varying delay systems}, Automatica,
80
textbf{40} (2004), 1435-1439.
81
bibitem{F2} J. Yoneyama, textit{New delay-dependent approach to robust stability
82
and stabilization for Takagi-Sugeno fuzzy time-delay systems},
83
Fuzzy Sets and Systems, textbf{158} (2007), 2225-2237.
84
bibitem{F32} J. Yoneyama, textit{Robust stability and stabilizing
85
controller design of fuzzy systems with discrete and distributed
86
delays}, Information Sciences, textbf{178} (2008), 1935-1947.
87
bibitem{Unc11} D. Yue, E. Tian, Y. Zhang and C. Peng, textit{Delay-distribution-dependent
88
robust stability of uncertain systems with time-varying delay},
89
Int. J. Robust Nonlinear Control, textbf{19} (2009), 377-393.
90
bibitem{In3} W. Zhang, X. S. Cai and Z. Z. Han, textit{Robust stability criteria for
91
systems with interval time-varying delay and nonlinear
92
perturbations}, J. Comput. Appl. Math., textbf{234} (2010), 174-180.
93
ORIGINAL_ARTICLE
$L-$ordered Fuzzifying Convergence Spaces
Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called thecategory of principal $L-$ordered fuzzifying convergence spaces andthat of topological $L-$ordered fuzzifying convergence spaces, andit is shown that they are isomorphic to the category of$L-$fuzzifying neighborhood spaces and that of $L-$fuzzifyingtopological spaces respectively.
http://ijfs.usb.ac.ir/article_218_4456b5694af5a1cad3cb181a7369d315.pdf
2012-06-10T11:23:20
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147
161
10.22111/ijfs.2012.218
$L-$fuzzifying topology
$L-$ordered fuzzifying convergence structure
$L-$filter
Cartesian-closed category
Reflective subcategory
Wenchao
Wu
wuwenchao107@163.com
true
1
Department of Mathematics, Ocean University of China, 266100 Qing-
dao, P. R. China
Department of Mathematics, Ocean University of China, 266100 Qing-
dao, P. R. China
Department of Mathematics, Ocean University of China, 266100 Qing-
dao, P. R. China
LEAD_AUTHOR
Jinming
Fang
jinming-fang@163.com
true
2
Department of Mathematics, Ocean University of China, 266100 Qing-
dao, P. R. China
Department of Mathematics, Ocean University of China, 266100 Qing-
dao, P. R. China
Department of Mathematics, Ocean University of China, 266100 Qing-
dao, P. R. China
AUTHOR
bibitem{1} H. Boustique, R. N. Mohapatra and G. Richardson, {it Lattice-valued fuzzy interior operators}, Fuzzy Sets and Systems, {bf 160} (2009), 2947-2955.
1
bibitem{2} H. Boustique and G. Richardson, {it A note on regularity}, Fuzzy Sets and Systems, {bf 162} (2011), 64-66.
2
bibitem{3} J. Fang, {it Stratified $L-$ordered convergence structures}, Fuzzy Sets and Systems, {bf 161} (2010), 2130-2149.
3
bibitem{4} P. V. Flores, R. N. Mohapatra and G. Richardson, {it Lattice-valued spaces: fuzzy convergence}, Fuzzy Sets and Systems, {bf 157} (2006), 2706-2714.
4
bibitem{5} P. V. Flores and G. Richardson, {it Lattice-valued convergence: diagonal axioms}, Fuzzy Sets and Systems, {bf 159} (2008), 2520-2528.
5
bibitem{6} U. H"{o}hle, {it Characterization of $L-$topologies by $L-$valued neighborhoods}, Chapter 5, In:
6
Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The
7
Handbooks of Fuzzy Sets Series, (U. H"{o}hle, S. E. Rodabaugh,
8
eds.), Kluwer Academic Publishers, Boston, Dordrecht,
9
London, {bf3} (1999), 389-432.
10
bibitem{7} U. H"{o}hle and A. P. v{S}ostak, {it Axiomatic foundations of fixed-basis fuzzy topology},
11
In: Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory,
12
The Handbooks of Fuzzy Sets Series, (U. H"{o}hle, S. E. Rodabaugh,
13
eds.), Kluwer Academic Publishers, Boston, Dordrecht,
14
London, {bf3} (1999), 123-173.
15
bibitem{8} G. J"{a}ger, {it A category of $L-$fuzzy convergence spaces}, Quaestiones Mathematicae, {bf 24} (2001), 501-517.
16
bibitem{9} G. J"{a}ger, {it Subcategories of lattice-valued convergence spaces}, Fuzzy Sets and Systems, {bf 156} (2005), 1-24.
17
bibitem{10} G. J"{a}ger, {it Pretopological and topological lattice-valued convergence spaces}, Fuzzy Sets and Systems, {bf 158} (2007), 424-435.
18
bibitem{11} G. J"{a}ger, {it Fischer's diagonal condition for lattice-valued convergence spaces}, Quaestiones Mathematicae, {bf 31} (2008), 11-25.
19
bibitem{12} R. Lowen, {it Convergence in fuzzy topological spaces}, Gen. Top. Appl., {bf 10} (1979), 147-160.
20
bibitem{13} K. C. Min, {it Fuzzy limit spaces}, Fuzzy Sets and Systems, {bf 32} (1989), 343-357.
21
bibitem{14} L. Xu, {it Characterizations of fuzzifying topologies by some limit structures}, Fuzzy Sets and Systems, {bf 123} (2001), 169-176.
22
bibitem{15} W. Yao, {it On many-valued stratified $L-$fuzzy convergence spaces}, Fuzzy Sets and Systems, {bf 159} (2008), 2503-2519.
23
bibitem{16} W. Yao, {it On $L-$fuzzifying convergence spaces}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(1)} (2009), 63-80.
24
bibitem{17} M. S. Ying, {it A new approach to fuzzy topology (I)}, Fuzzy Sets and Systems, {bf 39} (1991), 303-321.
25
bibitem{18} D. Zhang, {it On the reflectivity and coreflectivity of $L-$fuzzifying topological spaces in $L-$topological
26
spaces}, Acta Mathematica Sinica (English Series), {bf
27
18}textbf{(1)} (2002), 55-68.
28
bibitem{19} D. Zhang, {it $L-$fuzzifying topologies as $L-$topologies}, Fuzzy Sets and Systems, {bf 125} (2002), 135-144.
29
bibitem{20} D. Zhang and L. Xu, {it Categories isomorphic to bf FNS}, Fuzzy Sets and Systems, {bf 104} (1999), 373-380.
30
ORIGINAL_ARTICLE
Persian-translation vol. 9, no.2, June 2012
http://ijfs.usb.ac.ir/article_2815_c720f955814b2a6e18c7d9511c5ca803.pdf
2012-06-01T11:23:20
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165
174
10.22111/ijfs.2012.2815