ORIGINAL_ARTICLE
Cover vol. 11, no. 1, February 2014
http://ijfs.usb.ac.ir/article_2691_0de979703efb6c6126122e5c4eafa558.pdf
2014-03-01T11:23:20
2017-12-11T11:23:20
0
10.22111/ijfs.2014.2691
ORIGINAL_ARTICLE
ADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF NONLINEAR SYSTEMS WITH UNKNOWN DISTRIBUTED TIME-VARYING DELAYS AND UNKNOWN CONTROL DIRECTIONS
In this paper, an adaptive fuzzy control scheme is proposed for a class of perturbed strict-feedback nonlinear systems with unknown discrete and distributed time-varying delays, and the proposed design method does not require a priori knowledge of the signs of the control gains.Based on the backstepping technique, the adaptive fuzzy controller is constructed. The main contributions of the paper are that (i) by constructing appropriate Lyapunov functionals and using the Nussbaum functions, the adaptive tracking control problem is solved for the strict-feedback unknown nonlinear systems with the unknown discrete and distributed time-varying delays and the unknown control directions (ii) the number of adaptive parameters is independent of the number of rules of fuzzy logic systems and system state variables, which reduces the computation burden greatly. It is proven that the proposed controller guaranteesthat all the signals in the closed-loop system are bounded and the system output converges to a small neighborhood of the desired reference signal. Finally, an example is used to show the effectiveness of theproposed approach.
http://ijfs.usb.ac.ir/article_1393_5998db6dda90762fa01867861621467b.pdf
2014-02-24T11:23:20
2017-12-11T11:23:20
1
25
10.22111/ijfs.2014.1393
Fuzzy adaptive control
nonlinear systems
Discrete and distributed time-varying delays
Backstepping
Lyapunov-Krasovskii functionals
Hongyun
Yue
yuehongyun0417@163.com
true
1
Department of Applied Mathematics, Xidian University, Xi'an 710071,
P.R.China
Department of Applied Mathematics, Xidian University, Xi'an 710071,
P.R.China
Department of Applied Mathematics, Xidian University, Xi'an 710071,
P.R.China
AUTHOR
Junmin
Li
jmli@mail.xidian.edu.cn
true
2
Department of Applied Mathematics, Xidian University, Xi'an 710071,
P.R.China
Department of Applied Mathematics, Xidian University, Xi'an 710071,
P.R.China
Department of Applied Mathematics, Xidian University, Xi'an 710071,
P.R.China
LEAD_AUTHOR
bibitem{BoMsCh:Dfacmntdsuanucd}
1
A. Boulkroune, M. Msaad and H. Chekireb, {it Design of a fuzzy adaptive controller
2
for MIMO nonlinear time-delay systems with unknown actuator nonlinearities and
3
unknown control direction}, Information Sciences, {bf 180}textbf{(24)} (2010), 5041-5059.
4
bibitem{BoMsFa:Afcmnstvdssin}
5
A. Boulkroune, M. Msaad and M. Farza, {it Adaptive fuzzy controller for
6
multivariable nonlinear state time-varying delay systems subject to input
7
nonlinearities}, Fuzzy Sets and Systems, {bf 164} textbf{(1)} (2011), 45-65.
8
bibitem{BoMsFa:Odobfacnsucgn} A. Boulkroune, M. Msaad and M. Farza, {it On the design of observer-based fuzzy
9
adaptive controller for nonlinear systems with unknown control gain sign}, Fuzzy Sets
10
and Systems, {bf 201}textbf{(16)} (2012), 71-85.
11
bibitem{ChLiLiShLi:Dafcnstvd}
12
B. Chen, X. P. Liu, K. F. Liu, P. Shi and C. Lin,
13
{it Direct adaptive fuzzy control for nonlinear systems with time-varying delays},
14
Information Sciences, {bf 180}textbf{(5)} (2010), 776-792.
15
bibitem{ChToLi:Faddmnsba}
16
B. Chen, S. C. Tong and X. P. Liu, {it Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping
17
approach}, Fuzzy Sets and Systems, {bf 158}textbf{(10)} (2007), 1097-1125.
18
bibitem{ChJi:Atptvnpsumnn}
19
W. S. Chen and L. C. Jiao, {it Adaptive tracking for periodically time-varying and nonlinearly parameterized systems using multilayer neural networks}, IEEE Trans. Neural Networks, {bf 21}textbf{(2)} (2010), 345-351.
20
bibitem{ChJiLiLiLi:Anbofcsnsfstvd}
21
W. S. Chen, L. C. Jiao, J. Li and R. H. Li, {it Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays}, IEEE Trans. Systems, Man and Cybernetics-Part B: Cybernetics, {bf 40}textbf{(3)} (2010), 939-950.
22
bibitem{ChJiLiLi:Abfcnpspd} W. S. Chen, L. C. Jiao, R. H. Li and J. Li, {it Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances}, IEEE Trans. Fuzzy Systems, {bf 18}textbf{(4)} (2010), 674-685.
23
bibitem{ChZh:Gsabfcofsuhfgs}W. S. Chen and Z. Q. Zhang,
24
{it Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign},
25
Fuzzy Sets and Systems, {bf 161}textbf{(6)} (2010), 821-836.
26
bibitem{DuShYa:Annccltsns}
27
H. B. Du, H. H. Shao and P. J. Yao, {it
28
Adaptive neural network control for a class of
29
low-triangular-structured nonlinear systems}, IEEE Trans. Neural
30
Networks, {bf 17}textbf{(2)} (2006), 509-514.
31
bibitem{FeCaRe:Dfcsgs}G. Feng, S. G. Cao, N. W. Rees and etc., {it Design of fuzzy control systems with guaranteed stability}, Fuzzy Sets and Systems,
32
{bf 85}textbf{(1)} (1997), 1-10.
33
bibitem{FiBoFaDj:Rafmpciaistp}
34
S. Filali, S. Bououden, M. L. Fas and A. Djebebla,{it Robust adaptive fuzzy model predictive control and its application to an industrial surge tank problem}, ICIC Express Letters, {bf 1}textbf{(2)} (2007), 197-202.
35
bibitem{DwLiNi:Anccnptds}
36
D. W. C. Ho, J. M. Li and Y. G. Niu,
37
{it Adaptive neural control for a class of nonlinearly parametric time delay systems}, IEEE Transactions on Neural
38
Networks, {bf 16}textbf{(3)} (2005), 625 - 635.
39
bibitem{HoGeReLe:Raccusfns}
40
F. Hong, S. S. Ge, B. Ren and T. H. Lee, {it Robust adaptive control for a class of uncertain strict-feedback nonlinear systems}, Int. J. Robust Nonlinear Control, {bf 19}textbf{(7)} (2009), 746-767.
41
bibitem{HuWaGu:Afofcdntdsucd}
42
C. C. Hua, Q. G. Wang and X. P. Guan, {it Adaptive fuzzy output-feedback controller
43
design for nonlinear time-delay systems
44
with unknown control direction}, IEEE Trans. Systems Man Cybernet.-Part B, {bf 39}textbf{(2)} (2009), 363-374.
45
bibitem{LiChZhFa:Resusnnddtvd}H. Y. Li, B. Chen, Q. Zhou and S. L. Fang, {it Robust exponential
46
stability for uncertain stochastic neural networks with discrete and
47
distributed time-varying delays},
48
Physics Letters A, {bf 372}textbf{(19)} (2008), 3385-3394.
49
bibitem{LiQi:Acnpsanff} W. Lin and C. J. Qian, {it Adaptive control of nonlinearly
50
parameterized systems: a nonsmooth feedback framework}, IEEE
51
Trans. Automatic Control, {bf 47}textbf{(5)} (2002), 757-774.
52
bibitem{LiChWeTo:Anoftccudtns}Y. J. Liu, C. L. P. Chen,
53
G. X. Wen and S. C. Tong, {it Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems}, IEEE Trans. Neural Networks, {bf 22}textbf{(7)} (2011), 1162-1167.
54
bibitem{LiToLi:Obaftccunms}
55
Y. J. Liu, S. C. Tong and T. S. Li, {it Observer-based adaptive fuzzy tracking control for a
56
class of uncertain nonlinear MIMO systems}, Fuzzy Sets and Systems, {bf 164}textbf{(1)} (2011), 25-44.
57
bibitem{LiToWaLiCh:Anofcdroocunss}
58
Y. J. Liu, S. C. Tong, D. Wang, T. S. Li and C. L. Chen,
59
{it Adaptive neural output feedback controller design with reduced-order observer for a class of uncertain nonlinear SISO systems}, IEEE Trans. Neural Networks, {bf 22}textbf{(8)} (2011), 1328-1334.
60
bibitem{LiToWa: Afotccuns}Y. J. Liu, S. C. Tong and W. Wang, {it Adaptive fuzzy output
61
tracking control for a class of uncertain nonlinear systems},
62
Fuzzy Sets and Systems, {bf 160}textbf{(19)} (2009), 2727 - 2754.
63
bibitem{LiWa:Afcunns}Y. J. Liu and W. Wang, {it Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems}, Information Sciences,
64
{bf 177}textbf{(18)} (2007), 3901-3917.
65
bibitem{LiWaToLi£ºRatcnsbbfap}
66
Y. J. Liu, W. Wang, S. C. Tong and Y. S. Liu, {it Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters}, IEEE Trans. Systems, Man, and Cybernetics, Part A: Systems and Humans, {bf 40}textbf{(1)} (2010), 170-184.
67
bibitem{Ry:Auascns}
68
E. P. Ryan, {it A universal adaptive stabilizer for a class of nonlinear systems}, Syst. Control Lett., {bf 16}textbf{(3)} (1991), 209-218.
69
bibitem{ToLiLi:Faobcmns} S. C. Tong, C. Y. Li and Y. M. Li, {it Fuzzy adaptive observer backstepping control for MIMO nonlinear systems}, Fuzzy Sets and Systems,
70
{bf 160}textbf{(19)} (2009), 2755-2775.
71
bibitem{ToLiLiLi:Obafbccsnsfs}
72
S. C. Tong, Y. Li, Y. M. Li and Y. J. Liu, {it Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems}, IEEE Trans. Systems, Man, and Cybernetics, Part B: Cybernetics, {bf 41}textbf{(6)} (2011), 1693 - 1704.
73
bibitem{ToLi:Obfacsfns}
74
S. C. Tong and Y. M. Li, {it Observer-based fuzzy adaptive control for strict-feedback nonlinear systems}, Fuzzy Sets and Systems,
75
{bf 160}textbf{(12)} (2009), 1749-1764.
76
bibitem{Wa:Afscdsa}L. X. Wang,
77
{it Adaptive fuzzy systems and control design and stability
78
analysis}, NJ: Prentice-Hall, Englewood Cliffs, 1994.
79
bibitem{WaCh:Aftcntdswvcc}
80
M. Wang and B. Chen, {it Adaptive fuzzy tracking control of
81
nonlinear time-delay systems with unknown virtual control
82
coefficients}, Information Sciences, {bf 178}textbf{(22)} (2008), 4326-4340.
83
bibitem{WaCh:Aftccpsfntds} M. Wang and
84
B. Chen, {it Adaptive fuzzy tracking control for a class of perturbed
85
strict-feedback nonlinear time-delay systems}, Fuzzy Sets and
86
Systems, {bf 159}textbf{(8)} (2008), 949-967.
87
bibitem{XiFrSh:Rcddsacc} L. Xie, E. Fridman and U. Shaked, {it Robust $H_{infty}$ control of distributed delay systems with application to the combustion control}, IEEE Trans. Automat. Control, {bf 46}textbf{(12)} (2001), 1930-1935.
88
bibitem{XuCh:Rofcudds}S. Xu and T. Chen, {it Robust $H_{infty}$ output feedback control for uncertain distributed delay systems}, Eur. J. Control,
89
{bf 9}textbf{(6)} (2003), 566-574.
90
bibitem{XuCh:Alafdusdd} S. Xu and T. Chen, {it An LMI approach to the $H_{infty}$ filter design for uncertain systems with distributed delays}, IEEE Trans. Circuits Syst. II, {bf 51}textbf{(4)} (2004), 195-201.
91
bibitem{XuLaChZo:Addarfudds} S. Xu, J. Lam, T. Chen and Y. Zou, {it A delay-dependent approach to robust $H_{infty}$ filtering for uncertain distributed delay systems}, IEEE Trans. Signal Process., {bf 53}textbf{(10)} (2005), 3764-3772.
92
bibitem{YaFeRe:Acbsgarafcsfns} Y. S. Yang,
93
G. Feng and J. S. Ren, {it A combined backstepping and small-gain
94
approach to robust adaptive fuzzy control for strict-feedback
95
nonlinear systems}, IEEE Trans. Systems Man Cybernet.-Part A,
96
{bf 34}textbf{(3)} (2004), 406-420.
97
bibitem{Yu:Alarfustvdd} X. G. Yu, {it An LMI approach to robust $H{infty}$ filtering for uncertain systems with time-varying distributed delays}, Journal of the Franklin Institute, {bf345}textbf{(8)} (2008), 877-890.
98
bibitem{ZhGe:Ancmnstvdsudzgs}T. P. Zhang and S. S. Ge, {it Adaptive neural control of MIMO nonlinear state time-varying
99
delay systems with unknown dead-zones and gain signs}, Automatica, {bf43}textbf{(6)} (2007), 1021-1033.
100
bibitem{ZhYi:Afcamnsudz}T. P. Zhang and Y. Yi, {it Adaptive fuzzy control for a class of MIMO nonlinear systems with
101
unknown dead-zones}, Acta Automatica Sinica, {bf33}textbf{(1)} (2007), 96-99.
102
ORIGINAL_ARTICLE
Comparing different stopping criteria for fuzzy decision tree induction through IDFID3
Fuzzy Decision Tree (FDT) classifiers combine decision trees with approximate reasoning offered by fuzzy representation to deal with language and measurement uncertainties. When a FDT induction algorithm utilizes stopping criteria for early stopping of the tree's growth, threshold values of stopping criteria will control the number of nodes. Finding a proper threshold value for a stopping criterion is one of the greatest challenges to be faced in FDT induction. In this paper, we propose a new method named Iterative Deepening Fuzzy ID3 (IDFID3) for FDT induction that has the ability of controlling the tree’s growth via dynamically setting the threshold value of stopping criterion in an iterative procedure. The final FDT induced by IDFID3 and the one obtained by common FID3 are the same when the numbers of nodes of induced FDTs are equal, but our main intention for introducing IDFID3 is the comparison of different stopping criteria through this algorithm. Therefore, a new stopping criterion named Normalized Maximum fuzzy information Gain multiplied by Number of Instances (NMGNI) is proposed and IDFID3 is used for comparing it against the other stopping criteria. Generally speaking, this paper presents a method to compare different stopping criteria independent of their threshold values utilizing IDFID3. The comparison results show that FDTs induced by the proposed stopping criterion in most situations are superior to the others and number of instances stopping criterion performs better than fuzzy information gain stopping criterion in terms of complexity (i.e. number of nodes) and classification accuracy. Also, both tree depth and fuzzy information gain stopping criteria, outperform fuzzy entropy, accuracy and number of instances in terms of mean depth of generated FDTs.
http://ijfs.usb.ac.ir/article_1394_2ba9daf85e10827d238087b91e686c5c.pdf
2014-02-25T11:23:20
2017-12-11T11:23:20
27
48
10.22111/ijfs.2014.1394
Fuzzy inference systems
Classification
Fuzzy decision tree
Stopping criteria
Mohsen
Zeinalkhani
zeinalkhani@gmail.com
true
1
Department of Computer Engineering, Shahid Bahonar Uni-
versity of Kerman, Kerman, Iran
Department of Computer Engineering, Shahid Bahonar Uni-
versity of Kerman, Kerman, Iran
Department of Computer Engineering, Shahid Bahonar Uni-
versity of Kerman, Kerman, Iran
LEAD_AUTHOR
Mahdi
Eftekhari
m.eftekhari@mail.uk.ac.ir
true
2
Department of Computer Engineering, Shahid Bahonar University
of Kerman, Kerman, Iran
Department of Computer Engineering, Shahid Bahonar University
of Kerman, Kerman, Iran
Department of Computer Engineering, Shahid Bahonar University
of Kerman, Kerman, Iran
AUTHOR
bibitem{Ref01}
1
J. Alcalá-Fdez, A. Fernandez, J. Luengo, J. Derrac, S. García, L. Sánchez and F. Herrera, textit{KEEL data-mining software tool: data set repository, integration of algorithms and experimental analysis framework}, Journal of Multiple-Valued Logic and Soft Computing, textbf{17} (2011), 255-287.
2
bibitem{Ref02}
3
J. Alcalá-Fdez, L. Sánchez, S. García, M. del Jesus, S. Ventura, J. Garrell, J. Otero, C. Romero, J. Bacardit, V. Rivas, J. Fernández and F. Herrera, textit{KEEL: a software tool to assess evolutionary algorithms for data mining problems}, Soft Computing, textbf{13(3)} (2009), 307-318.
4
bibitem{Ref03}
5
L. Bartczuk and D. Rutkowska, textit{Type-2 fuzzy decision trees}, In: Proceedings of the 9th International Conference on Artificial Intelligence and Soft Computing, Springer-Verlag, Zakopane, Poland, (2008), 197-206.
6
bibitem{Ref04}
7
R. B. Bhatt and M. Gopal, textit{Neuro-fuzzy decision trees}, International Journal of Neural Systems, textbf{16(1)} (2006), 63-78.
8
bibitem{Ref05}
9
B. Chandra, P. Paul Varghese, {it Fuzzy sliq decision tree algorithm}, IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, {bf38} (2008), 1294-1301.
10
bibitem{Ref06}
11
B. Chandra and P. Paul Varghese, textit{Fuzzifying gini index based decision trees}, Expert Systems with Applications, textbf{36(4)} (2009), 8549-8559.
12
bibitem{Ref07}
13
P. C. Chang, C. Y. Fan and W. Y. Dzan, textit{A CBR-based fuzzy decision tree approach for database classification}, Expert Systems with Applications, textbf{37(1)} (2010), 214-225.
14
bibitem{Ref08}
15
Y. L. Chen, T. Wang, B. S. Wang and Z. J. Li, textit{A survey of fuzzy decision tree classifier}, Fuzzy Information and Engineering, textbf{1(2)} (2009), 149-159.
16
bibitem{Ref09}
17
M. E. Cintra, M. C. Monard and H. A. Camargo, textit{Evaluation of the pruning impact on fuzzy C4.5}, In: Anais Congresso Brasileiro de Sistemas Fuzzy, (2010), 257-264.
18
bibitem{Ref10}
19
J. Demšar, textit{Statistical comparisons of classifiers over multiple data sets}, Journal of Machine Learning Research, textbf{7} (2006), 1-30.
20
bibitem{Ref11}
21
A. Frank and A. Asuncion, textit{UCI machine learning repository}, http://archive.ics.uci.edu/ml, Irvine, 2010.
22
bibitem{Ref12}
23
S. Garcia and F. Herrera, textit{An extension on "statistical comparisons of classifiers over multiple data sets" for all pairwise comparisons}, Journal of Machine Learning Research, textbf{9} (2008), 2677-2694.
24
bibitem{Ref13}
25
J. S. R. Jang, C. T. Sun and E. Mizutani, textit{Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence}, Prentice Hall, London, 1997.
26
bibitem{Ref14}
27
C. Z. Janikow, textit{Fuzzy decision trees: issues and methods}, IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics, textbf{28(1)} (1998), 1-14.
28
bibitem{Ref15}
29
R. Jensen and Q. Shen, textit{Fuzzy-rough feature significance for fuzzy decision trees}, In: Proceedings of the 2005 UK Workshop on Computational Intelligence, (2005), 89-96.
30
bibitem{Ref16}
31
U. Khan, H. Shin, J. Choi and M. Kim, textit{wFDT - weighted fuzzy decision trees for prognosis of breast cancer survivability}, In: The Australasian Data Mining Conference, (2008), 141-152.
32
bibitem{Ref17}
33
R. E. Korf, textit{Depth-first iterative-deepening: an optimal admissible tree search}, In: G. R. Peter, ed., Expert Systems, IEEE Computer Society Press, (1990), 380-389.
34
bibitem{Ref18}
35
D. McNeill and P. Freiberger, textit{Fuzzy logic}, Simon & Schuster, New York, 1994.
36
bibitem{Ref19}
37
T. M. Mitchell, textit{Machine learning}, McGraw-Hill, New York, 1997.
38
bibitem{Ref20}
39
W. Pedrycz and Z. A. Sosnowski, textit{Designing decision trees with the use of fuzzy granulation}, IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans, textbf{30(2)} (2000), 151-159.
40
bibitem{Ref21}
41
W. Pedrycz and Z. A. Sosnowski, textit{Genetically optimized fuzzy decision trees}, IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics, textbf{35(3)} (2005), 633-641.
42
bibitem{Ref22}
43
P. Pulkkinen and H. Koivisto, textit{Fuzzy classifier identification using decision tree and multiobjective evolutionary algorithms}, International Journal of Approximate Reasoning, textbf{48(2)} (2008), 526-543.
44
bibitem{Ref23}
45
J. R. Quinlan, textit{C4.5: programs for machine learning}, Morgan Kaufmann Publishers, San Francisco, 1993.
46
bibitem{Ref24}
47
L. Rokach and O. Maimon, textit{Top-down induction of decision trees classifiers - a survey}, IEEE Transactions on Systems, Man and Cybernetics-Part C: Applications and Reviews, textbf{35(4)} (2005), 476-487.
48
bibitem{Ref25}
49
L. Rokach and O. Maimon, textit{Data mining with decision trees: theroy and applications}, World Scientific, Singapore, 2008.
50
bibitem{Ref26}
51
J. Sanz, A. Fernandez, H. Bustince and F. Herrera, textit{IIVFDT: ignorance functions based interval-valued fuzzy decision tree with genetic tuning}, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, in press, 2012.
52
bibitem{Ref27}
53
M. Umano, H. Okamoto, I. Hatono, H. Tamura, F. Kawachi, S. Umedzu and J. Kinoshita, textit{Fuzzy decision trees by fuzzy ID3 algorithm and its application to diagnosis systems}, In: Proceedings of Third IEEE Conference on Fuzzy Systems, (1994), 2113-2118.
54
bibitem{Ref28}
55
T. Wang, Z. Li, Y. Yan and H. Chen, textit{A survey of fuzzy decision tree classifier methodology}, In: B. Y. Cao, ed., Fuzzy Information and Engineering, Springer, Berlin / Heidelberg, (2007), 959-968.
56
bibitem{Ref29}
57
X. Wang and C. Borgelt, textit{Information measures in fuzzy decision trees}, In: Proceedings of 13th IEEE International Conference on Fuzzy Systems, (2004), 85-90.
58
bibitem{Ref30}
59
X. Wang, B. Chen, G. Qian and F. Ye, textit{On the optimization of fuzzy decision trees}, Fuzzy Sets and Systems, textbf{112(1)} (2000), 117-125.
60
bibitem{Ref31}
61
X. Wang and H. Jiarong, textit{On the handling of fuzziness for continuous-valued attributes in decision tree generation}, Fuzzy Sets and Systems, textbf{99(3)} (1998), 283-290.
62
bibitem{Ref32}
63
Y. Yuan and M. J. Shaw, textit{Induction of fuzzy decision trees}, Fuzzy Sets and Systems, textbf{69(2)} (1995), 125-139.
64
bibitem{Ref33}
65
M. Zeinalkhani and M. Eftekhari, textit{A new measure for comparing stopping criteria of fuzzy decision tree}, In: International Conference on Computer and Knowledge Engineering, Mashhad, (2011), 120-123.
66
bibitem{Ref34}
67
H. Zhang and B. H. Singer, textit{Recursive partitioning and applications}, 2nd ed., Springer, London, 2010.
68
end{thebibliography}
69
ORIGINAL_ARTICLE
Developing Fuzzy Models for Estimating the Quality of VoIP
This paper presents a novel method for modeling the one-way quality prediction of VoIP, non-intrusively. Intrusive measures of voice quality suffer from common deficiency that is the need of reference signal for evaluating the quality of voice. Owing to this lack, a great deal of effort has been recently devoted for modeling voice quality prediction non-intrusively according to quality degradation parameters, while among the past proposed methods, intelligent techniques have been remarkably successful due to their abilities for modeling the non-linear processes. The present study introduces a procedure for developing fuzzy models, employing Genetic Algorithm (GA) and Adaptive Neuro-Fuzzy Inference System (ANFIS). The proposed method is able to generate optimized fuzzy models in terms of accuracy and complexity. The efficiency of this procedure is compared with and contrasted against 13 regression methods implemented in KEEL as one machine learning tool. Moreover, several experimental results are performed over voice data from 10 different languages. In order to complete the experiment, a comprehensive statistical comparison is also drawn between our proposed method and other previous ones. The results apparently show the efficiency and applicability of this novel method in terms of generating accurate and simple fuzzy models for estimating the VoIP quality.
http://ijfs.usb.ac.ir/article_1395_d41d8cd98f00b204e9800998ecf8427e.pdf
2014-02-25T11:23:20
2017-12-11T11:23:20
49
73
10.22111/ijfs.2014.1395
VoIP
Voice quality
Non-intrusive prediction
PESQ
Neuro-fuzzy
GA
KEEL
F.
Rahdari
rahdarifar@icst.ac.ir
true
1
Computer and Information Technology Department, Institute of Sci-
ence and High Technology and Environmental Sciences, Graduate University of Ad-
vanced Technology, Kerman, Iran
Computer and Information Technology Department, Institute of Sci-
ence and High Technology and Environmental Sciences, Graduate University of Ad-
vanced Technology, Kerman, Iran
Computer and Information Technology Department, Institute of Sci-
ence and High Technology and Environmental Sciences, Graduate University of Ad-
vanced Technology, Kerman, Iran
LEAD_AUTHOR
M.
Eftekhari
m.eftekhari@mail.uk.ac.ir
true
2
Computer Engineering Department, Shahid Bahonar University of
Kerman, Kerman, Iran
Computer Engineering Department, Shahid Bahonar University of
Kerman, Kerman, Iran
Computer Engineering Department, Shahid Bahonar University of
Kerman, Kerman, Iran
AUTHOR
A.
Akbari
akbari@iust.ac.ir
true
3
Computer Engineering Department, Iran University of Science and Tech-
nology, Tehran, Iran
Computer Engineering Department, Iran University of Science and Tech-
nology, Tehran, Iran
Computer Engineering Department, Iran University of Science and Tech-
nology, Tehran, Iran
AUTHOR
M.
Zeinalkhani
zeinalkhani@gmail.com
true
4
Computer Engineering Department, Shahid Bahonar University of
Kerman, Kerman, Iran
Computer Engineering Department, Shahid Bahonar University of
Kerman, Kerman, Iran
Computer Engineering Department, Shahid Bahonar University of
Kerman, Kerman, Iran
AUTHOR
bibitem{Alcala-Fdez:KEEL}
1
J. Alcala-Fdez, L. Sanchez, S. Garcia, M. del Jesus, S. Ventura,
2
J. Garrell, J. Otero, C. Romero, J. Bacardit, V. Rivas, J.
3
Fernandez and F. Herrera, {it KEEL: a software tool to assess
4
evolutionary algorithms for data mining problems}, Journal of
5
Soft Computing - A Fusion of Foundations, Methodologies and
6
Applications, {bf 13}textbf{(3)} (2009), 307-318.
7
bibitem{Andersen:iLBC}
8
S. Andersen and A. Duric, {it Internet low bit rate codec (iLBC),IETF draft}, 2002.
9
bibitem{Beerends:PESQ}
10
J. G. Beerends, A. P. Hekstra, A. W. Rix and M. P. Hollier,
11
{it Perceptual evaluation of speech quality (PESQ): the new ITU
12
standard for end-to-end speech quality assessment part II -
13
psychoacoustic model}, Journal of Audio Eng. Soc., {bf
14
50}textbf{(10)} (2002), 765-778.
15
bibitem{Bolot:PLandD}
16
J. Bolot, {it Characterizing end-to-end packet delay and loss
17
in the Internet}, Journal of High-Speed Networks, {bf
18
2}textbf{(3)} (1993), 305-323.
19
bibitem{Borella:MIofPL}
20
M. S. Borella, {it Measurement and interpretation of Internet
21
packet loss}, Journal of Communication and Networking, {bf
22
2} (2000), 93-102.
23
bibitem{Clark:MofBPL}
24
A. D. Clark, {it Modeling the effects of burst packet loss and
25
recency on subjective voice quality}, Proc. of IPTEL2001, New
26
York, USA, (2001), 123-127.
27
bibitem{Cole:VoIP-PM}
28
R. G. Cole and J. Rosenbluth, {it Voice over IP performance
29
monitoring}, Journal of ACM Computing Communication Review, {bf
30
31}textbf{(2)} (2001), 9-24.
31
bibitem{Cox:3NSC}
32
R. Cox, {it Three new speech coders from the ITU cover a range
33
of applications}, Journal of IEEE Communications Magazine, {bf
34
35}textbf{(9)} (1997), 40-47.
35
bibitem{Demsar:SCCoverMDS}
36
J. Demsar, {it Statistical comparisons of classifiers over
37
multiple data sets}, Journal of Machine Learning Research, {bf
38
7} (2006), 1-30.
39
bibitem{Eftekhari:CFRforNSM}
40
M. Eftekhari and S. D. Katebi, {it Extracting compact fuzzy rules
41
for nonlinear system modeling using subtractive clustering, GA
42
and unscented filter}, Journal of Applied Mathematical Modeling,
43
{bf 32} (2008), 2634-2651.
44
bibitem{Eftekhari:TFM-DE}
45
M. Eftekhari, S. D. Katebi, M. Karimi and A. H. Jahanmiri, {it
46
Eliciting transparent fuzzy model using differential evolution},
47
Journal of Applied Soft Computing , {bf 8} (2008), 466-476.
48
bibitem{Garcia:E-SCCoverMDS}
49
S. Garcia and F. Herrera, {it An Extension on statistical
50
comparisons of classifiers over multiple data sets for all
51
pairwise comparisons}, Journal of Machine Learning Research,
52
{bf 9} (2008), 2677-2694.
53
bibitem{Herrera:GFS}
54
F. Herrera, {it Genetic fuzzy systems: taxonomy, current
55
research trends and prospects}, Journal of Evolutionary
56
Intelligence, {bf 1}textbf{(1)} (2008), 27-46.
57
bibitem{ITU:P.50}
58
International Telecommunication Union, {it Objective measuring
59
apparatus, Appendix 1: test signals}, ITU-T Recommendation
60
P.50, 1998.
61
bibitem{ITU:MOS}
62
International Telecommunication Union, {it Mean opinion score (MOS) terminology},
63
ITU-T Recommendation P.800.1, 2003.
64
bibitem{ITU:PESQ}
65
International Telecommunication Union, {it Perceptual
66
evaluation of speech quality (PESQ), an objective method for
67
end-to-end speech quality assessment of narrow-band telephone
68
networks and speech codecs}, ITU-T Recommendation P.862, 2001.
69
bibitem{ITU:H323}
70
International Telecommunication Union, {it Packet based
71
multimedia communications systems}, ITU-T Recommendation H.323,
72
bibitem{ITU:E-MODEL}
73
International Telecommunication Union, {it The E-model, a
74
computational model for use in transmission planning}, ITU-T
75
Recommendation G.107, 2000.
76
bibitem{ITU:P800}
77
International Telecommunication Union, {it Methods for
78
subjective determination of transmission quality}, ITU-T
79
Recommendation P.800, 1996.
80
bibitem{Jang:ANFIS}
81
J. S. R. Jang, {it ANFIS: adaptive network-based fuzzy
82
inference systems}, Journal of IEEE Transactions on System, Man
83
and Cybernetics, {bf 23} (1993), 665-685.
84
bibitem{Jang:NFandSC}
85
J. S. R. Jang, C. T. Sun and E. Mizutani, {it Neuro-fuzzy and soft
86
computing}, Prentice Hall, Engleeood Cliffs, 1977.
87
bibitem{Jiang:PLandD}
88
W. Jiang and H. Schulzrinne, {it Modeling of packet loss and
89
delay and their effect on real-time multimedia service quality},
90
Proc. of Int.Workshop Network and Operating Systems Support for
91
Digital Audio and Video NOSSDAV, Chapel Hill, NC, 2000.
92
bibitem{Kurose:CN-TD}
93
J. F. Kurose and K. W. Ross, {it Computer networking: a top-down
94
approach featuring the Internet}, Pearson Addison-Wesley, 2000.
95
bibitem{Markopoulou:VoIPQ-IB}
96
A. P. Markopoulou, F. A. Tobagi and M. Karam, {it Assessment
97
of VoIP quality over Internet backbones}, Proc. of IEEE Infocom,
98
(2002), 150-159.
99
bibitem{Nelles:NSI}
100
O. Nelles, {it Nonlinear system identification: from classical
101
approaches to neural networks and fuzzy models}, Springer, Berlin
102
Heidelberg, 2000.
103
bibitem{Perkins:PLRforSA}
104
C. Perkins, O. Hodson and V. Hardman, {it A survey of packet
105
loss recovery techniques for streaming audio}, Journal of IEEE
106
Network, {bf 12} (1998), 40-48.
107
bibitem{Rahdari:FM-GANF}
108
F. Rahdari and M. Eftekhari, {it Developing fuzzy models for
109
estimating quality of VoIP using a hybrid of GA and
110
neuro-fuzzy}, Proc. of 2nd Int. Conf. on Contemporary Issues in
111
Computer and Information Sciences (CICIS), Zanjan, Iran, (2011),
112
bibitem{Rahdari:VQ-NF}
113
F. Rahdari and M. Eftekhari, {it Modeling the perceived voice
114
quality for VoIP system based on Neuro-Fuzzy}, Proc. of Int.
115
Conferences on Computer and knowledge Engineering (ICCKE),
116
Mashhad, Iran, (2011), 81-86
117
bibitem{Rahdari:BCforQVoIP}
118
F. Rahdari and M.Eftekhari, {it Using bayesian classifiers for
119
estimating quality of VoIP}, Proc. of 16th CSI Int. symposium on
120
Artificial Intelligence and Signal Processing (AISP), Shiraz,
121
Iran, (2012), 348-353.
122
bibitem{Raja:NIQE-GP}
123
A. Raja, R. Azad, C. Flanagan and C. Ryan, {it Non-intrusive
124
quality evaluation of VoIP using genetic programming}, Proc. of
125
1st Int. Conference on Bio- inspired Models of Network,
126
Information and Computing Systems, (2006), 1-8
127
bibitem{Rosenberg:SIP}
128
J. Rosenberg, H. Schulzrinne, G. Camarillo, A. Johnston, J.
129
Peterson, R. Sparks, M. Handley and E. Schooler, {it
130
SIP: Session Initiation Protocol}, RFC 3261, 2002.
131
bibitem{Sanchez:RSMforIFM}
132
L. Sanchez, {it A random sets-based method for identifying
133
fuzzy models}, Journal of Fuzzy Sets and Systems, {bf
134
98}textbf{(3)} (1998), 343-354.
135
bibitem{Sanneek:FMforPL}
136
H. Sanneek, G. Carle and R. Koodli, {it A framework model for
137
packet loss metrics based on run length}, Proc. of SPIE/ACM
138
SIGMM Multimedia Computing and Networking Conf., 2000.
139
bibitem{Schulzrinne:RTP}
140
H. Schulzrinne, S. Casner, R. Frederick and V. Jacobson, {it
141
RTP: a transport protocol for real-time applications}, RFC 1889,
142
bibitem{Sun:SQPforIPNet}
143
L. Sun and E. Ifeachor, {it Perceived speech quality prediction
144
for voice over IP-based networks}, Proc. of IEEE Int. Conf.
145
Communications ICC02, New York, (2002), 2573-2577.
146
bibitem{Sun:VQPinVoIP}
147
L. Sun and E. Ifeachor, {it Voice quality prediction models and
148
their application in VoIP network}, Journal of IEEE Trans. On
149
Multimedia, {bf 8}textbf{(4)} (2006), 809-820.
150
bibitem{Sun:SandOunderBL}
151
L. Sun and E. Ifeachor, {it Subjective and objective speech
152
quality evaluation under bursty losses}, Proc. of on-line
153
Workshop Measurement of Speech and Audio Quality in Networks
154
(MESAQIN), Prague, Czech, (2002), 25-29
155
bibitem{Wang:GFRbyLE}
156
L. X. Wang and J. M. Mendel, {it Generating fuzzy rules by learning
157
from examples}, Journal of IEEE Transactions on Systems, Man and
158
Cybernetics, {bf 22}textbf{(6)} (1992), 1414-1427.
159
bibitem{Wang:MTforPCC}
160
I. Wang and I. H. Witten, {it Induction of model trees for
161
predicting continuous classes}, Proc. of 9th European Conf. on
162
Machine Learning, Czech Republic, (1997), 128-137.
163
ORIGINAL_ARTICLE
Design of an Adaptive Fuzzy Estimator for Force/Position Tracking in Robot Manipulators
This paper presents a stable new algorithm for force/position control in robot manipulators. In this algorithm, position vectors are measured by sensors and then used in the control law. Since using force sensor has some issues such as high costs and technical problems, an approach is presented to overcome these issues. In this respect, force sensor is replaced by an adaptive fuzzy estimator to estimate the external force based on position and velocity measurements. In this approach, force can be properly estimated using universal approximation property of fuzzy systems. Therefore, robots can be controlled in different environments even when no exact mathematical model is available. Since this approach is adaptive, accuracy of the system can be improved with time. Through a theorem the stability of the control system is analyzed using Lyapunov direct method. At last, satisfactory performances of the proposed approach are verified via some numerical simulations and the results are compared with some previous approaches.
http://ijfs.usb.ac.ir/article_1396_5573c6189fbc54601bee32594d6b9478.pdf
2014-02-25T11:23:20
2017-12-11T11:23:20
75
89
10.22111/ijfs.2014.1396
Force/Position control
Adaptive
Fuzzy estimation
Robot manipulator
Stability
Alireza
Naghsh
naghsh a@yahoo.com
true
1
Department of Engineering, Science and Research Branch, Islamic
Azad University, Tehran, Iran
Department of Engineering, Science and Research Branch, Islamic
Azad University, Tehran, Iran
Department of Engineering, Science and Research Branch, Islamic
Azad University, Tehran, Iran
LEAD_AUTHOR
Farid
Sheikholeslam
sheikhsymbol@cc.iut.ac.ir
true
2
Department of Electrical and Computer Engineering, Isfahan
University of Technology, Isfahan, 84156-83111, Iran
Department of Electrical and Computer Engineering, Isfahan
University of Technology, Isfahan, 84156-83111, Iran
Department of Electrical and Computer Engineering, Isfahan
University of Technology, Isfahan, 84156-83111, Iran
AUTHOR
Mohammad
Danesh
danesh@cc.iut.ac.ir
true
3
Department of Mechanical Engineering, Isfahan University of
Technology, Isfahan, 84156-83111, Iran
Department of Mechanical Engineering, Isfahan University of
Technology, Isfahan, 84156-83111, Iran
Department of Mechanical Engineering, Isfahan University of
Technology, Isfahan, 84156-83111, Iran
AUTHOR
bibitem{An:1}
1
C. H. An and J. M. Hollerbach, {it Kinematic stability issues in force control of manipulator}, International Conference on Robotics and Automation, IEEE Robotics and Automation society Raleigh, North Carolina, (1987), 897-903.
2
bibitem{Bernhardt:2}
3
M. Bernhardt, M. Frey, G. Colombo and R. Riener, {it Hybrid force-position control yields cooperative behaviour of the rehabilitation robot LOKOMAT}, IEEE Int. Conf. on Rehabilitation Robotics, (2001), 536-539.
4
bibitem{Briones:3}
5
J. A. Briones, E. Castillo, G. Carbone and M. Ceccarelli, {it Position and force control of the CAPAMAN 2 bis parallel robot for drilling tasks}, IEEE Int. Conf. on Electronics, Robotics and Automotive Mechanics, (2009), 181-186.
6
bibitem{Craig:4}
7
J. J. Craig and M. H. Raibert, {it A systematic method of hybrid position/force control of a manipulator}, In Computer Software and Applications Conference, IEEE Computer Society Chicago, Illinois, (1979), 446-451.
8
bibitem{Danesh:5}
9
M. Danesh, F. Sheikholeslam and M. Keshmiri, {it A force estimator based algorithm for robot control},
10
IEEE Int. Conf. on Mechatronics, (2005), 376-381.
11
bibitem{Danesh:6}
12
M. Danesh, F. Sheikholeslam and M. Keshmiri, {it External force disturbance rejection in robotic arms an adaptive approach}, IEICE Trans. on Fundamentals, {bf E88-A}textbf{(10)} (2005), 2504-2513.
13
bibitem{Danesh:7}
14
M. Danesh, F. Sheikholeslam and M. Keshmiri, {it An adaptive manipulator controller based on force and parameter estimation}, IEICE Trans. on Fundamentals, {bf E89-A}textbf{(10)} (2006), 1-9.
15
bibitem{Dean:8}
16
E. C. Dean-Le´on, L. G. Garc-Valdovinos and V. Parra-Vega , {it Uncalibrated image based position-force adaptive visual servoing for constrained robots under dynamic friction uncertainties}, IEEE Int. Conf. on Mechatronics and Automation, (2006), 1-8.
17
bibitem{Duchemin:9}
18
G. Duchemin, P. Maillet, P. Poignet, E. Dombre and F. Pierrot, {it Hybrid position/force control approach for identification of deformation models of skin and underlying tissues}, IEEE Trans. on Biomedical Engineering, {bf 52}textbf{(2)} (2005), 160-170.
19
bibitem{Eom:10}
20
K. S. Eom, I. H. Suh, W. K. Chung and S. R. Oh, {it Disturbance observer based force control of robot manipulator without force sensor}, Proc. of ICRA98, (1998), 3012-3017.
21
bibitem{Huanga:11}
22
Q. Huanga and R. Enomoto, {it Hybrid position, posture, force and moment control of robot manipulators}, IEEE Int. Conf. on Robotics and Biomimetics, (2009), 1444-1450.
23
bibitem{Inoue:12}
24
F. Inoue, T. Murakami and K. Ohnishi, {it A motion control of mobile manipulator with external force}, EEE/ASME Trans. on Mechatronics, {bf 6}textbf{(2)} (2001), 137-142.
25
bibitem{Murakami:13}
26
T. Murakami, R. Nakamura, F. Yau and K. Ohnishi, {it Force sensorless impedance control by disturbance observer}, PCC-Yokohama, (1993), 352-357.
27
bibitem{Roy:16}
28
J. Roy and L. L. Whitcomb, {it Adaptive force control of position/velocity controlled robots: theory and experiment}, IEEE Trans. on Robotics and Automation, {bf 18}textbf{(2)} (2002), 121-137.
29
bibitem{Schutter:18}
30
J. D. Schutter and H. Van Brussel, {it Compliant robot motion II. a control approach based on external control loops}, Int. J. Robot. Res., {bf 7}textbf{(4)} (1988), 18-33.
31
bibitem{Shaung:17}
32
M. Shaung Ju, C. Ching, K. Lin, D. Huang Lin, I. S. Hwang and S. M. Chen, {it A rehabilitation robot with force-position hybrid fuzzy controller: hybrid fuzzy control of rehabilitation robot}, IEEE Trans. on Neural Systems and Rehabilitation Engineering, {bf 13}textbf{(3)} (2005), 349-358.
33
bibitem{Slotine:19}
34
J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, 1991.
35
bibitem{Tsuji:20}
36
T. Tsuji, Y. Kaneko and S. Abe, {it Whole-Body force sensation by force sensor with shell-shaped end-effector}, IEEE Trans. on Industrial Electronics, {bf 56}textbf{(5)} (2009), 1375-1382.
37
bibitem{Wai:14}
38
R. J. Wai and Z. W. Yang, {it Adaptive fuzzy-neural-network control of robot manipulator using T-S fuzzy model design}, IEEE Int. Conf. on Fuzzy Systems, (2008), 90-97.
39
bibitem{Wai:15}
40
R. J. Wai and Z. W. Yang, {it Adaptive fuzzy neural network control design via a T-S fuzzy model for a robot manipulator including actuator dynamics}, IEEE Trans. on Systems, Main, And Cybernetics Part B: Cybernetic, {bf 38}textbf{(5)} (2008), 1326-1346.
41
bibitem{Whitcomb:21}
42
L. L. Whitcomb, S. Arimoto, T. Naniwa and F. Ozaki,, {it Adaptive model-based hybrid control of geometrically constrained robot arms}, IEEE Trans. on Robotics and Automation, (1997), 105-116.
43
bibitem{Zhang:22}
44
H. Zhang, {it Kinematic stability of robot manipulators under force control}, International Conference on Robotics and Automation, IEEE Robotics and Automation Society Scottsdale, Arizona, (1989), 80-85.
45
bibitem{Zhang:23}
46
H. Zhang and R. P. Paul, {it Hybrid control of robot manipulators}, International conference on Robotics and Automation, IEEE Computer Society St. Louis, Missouri, (1985), 602-607.
47
ORIGINAL_ARTICLE
Numerical solution of fuzzy linear Fredholm integro-differential equation by \\fuzzy neural network
In this paper, a novel hybrid method based on learning algorithmof fuzzy neural network and Newton-Cotesmethods with positive coefficient for the solution of linear Fredholm integro-differential equation of the second kindwith fuzzy initial value is presented. Here neural network isconsidered as a part of large field called neural computing orsoft computing. We propose alearning algorithm from the cost function for adjusting fuzzyweights. This paper is one of the first attempts to derive learningalgorithms from fuzzy neural networks with real input, fuzzy output,and fuzzy weights. Finally, we illustrate our approach by numerical examples.
http://ijfs.usb.ac.ir/article_1397_1e44bcaee4c0a281eafa46bae01a2651.pdf
2014-02-25T11:23:20
2017-12-11T11:23:20
91
112
10.22111/ijfs.2014.1397
Fuzzy neural networks
Fuzzy linear Fredholm
integro-differential
Feedforward neural network
Learning algorithm
Maryam
Mosleh
mosleh@iaufb.ac.ir
true
1
Department of Mathematics, Firoozkooh Branch, Islamic Azad Uni-
versity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad Uni-
versity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad Uni-
versity, Firoozkooh, Iran
LEAD_AUTHOR
bibitem{aba} S. Abbasbandy, E. Babolian and M. Alavi, {it Numerical
1
method for solving linear fredholm fuzzy integral equations of
2
the second kind}, Chaos Solitons & Fractals, {bf 31} (2007), 138-146.
3
bibitem{abo} S. Abbasbandy and M. Otadi, {it Numerical solution of fuzzy
4
polynomials by fuzzy neural network}, Applied Mathematics and Computation, {bf 181}
5
(2006), 1084-1089.
6
bibitem{abom} S. Abbasbandy, M. Otadi and M. Mosleh, {it Numerical
7
solution of a system of fuzzy polynomials by fuzzy neural
8
network}, Information Sciences, {bf 178} (2008), 1948-1960.
9
bibitem{al1} G. Alefeld and J. Herzberger, {it Introduction to interval
10
computations}, Academic Press, New York, 1983.
11
bibitem{aaa1} T. Allahviranloo, E. Ahmady and N. Ahmady, {it Nth-order
12
fuzzy linear differential eqations},Information Sciences, {bf 178} (2008),
13
1309-1324.
14
bibitem{aaa2} T. Allahviranloo, N. Ahmady and E. Ahmady, {it Numerical
15
solution of fuzzy differential eqations by predictor-corrector
16
method}, Information Sciences, {bf 177} (2007), 1633-1647.
17
bibitem{at} K. E. Atkinson, {it An introduction to numerical analysis},
18
New York, Wiley, 1987.
19
bibitem{bsa} E. Babolian, H. S. Goghary and S. Abbasbandy, {it Numerical
20
solution of linear fredholm fuzzy integral equations of the
21
second kind by adomian method}, Applied Mathematics and
22
Computation, {bf 161} (2005), 733-744.
23
bibitem{bm} P. Balasubramaniam and S. Muralisankar, {it Existence and uniqueness of fuzzy
24
solution for the nonlinear fuzzy integro-differential equations}, Applied mathematics letters, {bf 14} (2001), 455-462.
25
bibitem{bb} B. Bede, I. J. Rudas and A. L. Bencsik, {it First order linear
26
fuzzy differential eqations under generalized differentiability},
27
Information Sciences, {bf 177} (2007), 1648-1662.
28
bibitem{ber} J. F. Bernard, {it Use of rule-based system for process control}, IEEE Control System Management, {bf 8} (1988), 3-13.
29
bibitem{bf} J. J. Buckley and T. Feuring, {it Fuzzy differential equations}, Fuzzy Sets and Systems, {bf 110} (2000), 69-77.
30
bibitem{by} J. J. Buckley and Y. Hayashi, {it Can fuzzy neural nets
31
approximate continuous fuzzy functions?}, Fuzzy Sets and Systems, {bf 61}
32
(1994), 43-51.
33
bibitem{cz} S. L. Chang and L. A. Zadeh, {it On fuzzy mapping and control},
34
IEEE Transactions Systems Man and Cybernetics, {bf 2} (1972), 30-34.
35
bibitem{che} Y. C. Chen and C. C. Teng, {it A model reference control structure using a fuzzy neural network}, Fuzzy Sets and Systems, {bf 73} (1995), 291-312.
36
bibitem{com} W. Congxin and M. Ming, {it On embedding problem of fuzzy
37
number space}, Fuzzy Sets and Systems, {bf 44} (1991), 33-38.
38
bibitem{dd} D. Dubois and H. Prade, {it Operations on fuzzy numbers}, International Journal of Systems Science, {bf 9} (1978), 613-626.
39
bibitem{dp} D. Dubois and H. Prade, {it Towards fuzzy differential
40
calculus}, Fuzzy Sets and Systems, {bf 8} (1982), 225-233.
41
bibitem{effati} S. Effati and M. Pakdaman, {it Artificial neural network approach for solving fuzzy differential equations}, Information Sciences, {bf 180} (2010), 1434-1457.
42
bibitem{wf} W. Fei, {it Existence and uniqueness of solution for fuzzy random differential equations with non-lipschitz
43
coefficients}, Information Sciences, {bf 177} (2007), 4329-4337.
44
bibitem{fmk} M. Friedman, M. Ma and A. Kandel, {it Numerical solutions
45
of fuzzy differential and integral equations}, Fuzzy Sets and
46
Systems, {bf 106} (1999), 35-48.
47
bibitem{gv} R. Goetschel and W. Voxman, {it Elementary fuzzy calculus},
48
Fuzzy Sets and Systems, {bf 18} (1986), 31-43.
49
bibitem{go} D. Gottlieb and S.A. Orszag, {it Numerical analysis of
50
spectral methods}, Theory and applications, CBMS-NSF Regional
51
Conference Series in Applied Mathematics, SIAM,
52
Philadelphia, {bf 26} (1977).
53
bibitem{hdb} M. T. Hagan, H. B. Demuth and M. Beale, {it Neural network
54
design}, PWS publishing company, Massachusetts, 1996.
55
bibitem{jb2} Y. Hayashi, J. J. Buckley and E. Czogala, {it Fuzzy neural
56
network with fuzzy signals and weights}, International Journal of Intelligent
57
Systems, {bf 8} (1993), 527-537.
58
bibitem{ha} S. Haykin,{it Neural networks: a comprehensive
59
foundation}, Prentice Hall, New Jersey, 1999.
60
bibitem{h} H. Hochstadt, {it Integral equations}, New York: Wiley,
61
bibitem{hsw} K. Hornick, M. Stinchcombe and H. White, {it Multilayer
62
feedforward networks are universal approximators}, Neural Networks,
63
{bf 2} (1989), 359-366.
64
bibitem{dr} H. Ishibuchi, K. Kwon and H. Tanaka, {it A learning algorithm of
65
fuzzy neural networks with triangular fuzzy weights}, Fuzzy Sets
66
and Systems, {bf 71} (1995), 277-293.
67
bibitem{imt} H. Ishibuchi, K. Morioka and I.B. Turksen, {it Learning by
68
fuzzified neural networks}, International Journal of Approximate Reasoning, {bf 13} (1995),
69
bibitem{ism} H. Ishibuchi and M. Nii, {it Numerical analysis of the
70
learning of fuzzified neural networks from fuzzy if-then rules},
71
Fuzzy Sets and Systems, {bf 120} (2001), 281-307.
72
bibitem{wc1} H. Ishibuchi, H. Okada and H. Tanaka, {it Fuzzy neural networks
73
with fuzzy weights and fuzzy biases}, Proceedings ICNN, {bf 93} (1993), 1650-1655.
74
bibitem{ito} H. Ishibuchi, H. Tanaka and H. Okada, {it Fuzzy neural
75
networks with fuzzy weights and fuzzy biases}, IEEE International Conferences on Neural Networks, (1993), 1650-1655.
76
bibitem{kal} O. Kaleva, {it Fuzzy differential equations}, Fuzzy Sets
77
and Systems, {bf 24} (1987), 301-317.
78
bibitem{kh} T. Khanna, {it Foundations of neural networks},
79
Addison-Wesly, Reading, MA, 1990.
80
bibitem{kcy} G. J. Klir, U. S. Clair, B. Yuan, {it Fuzzy set theory:
81
foundations and applications}, Prentice-Hall, 1997.
82
bibitem{kbrh} P. V. Krishnamraju, J. J. Buckley, K. D. Relly and Y.
83
Hayashi, {it Genetic learning algorithms for fuzzy neural nets},
84
IEEE International Conference on Fuzzy
85
Systems, (1994), 1969-1974.
86
bibitem{lag} I. E. Lagaris and A. Likas, {it Artificial neural networks for solving ordinary and partial differential equations}, IEEE Transactions on Neural Networks, September, {bf 9}textbf{(5)} (1998).
87
bibitem{lam} J. D. Lamber, {it Computational methods in ordinary
88
differential equations}, John Wiley & Sons, New York, 1983.
89
bibitem{lf} A. Lapedes and R. Farber, {it How neural nets work?}, Neural Information Processing Systems, AIP, 1988,
90
bibitem{lk} H. Lee and I. S. Kang, {it Neural algorithms for solving
91
differential equations}, Journal of Computational Physics, {bf 91}
92
(1990), 110-131.
93
bibitem{tlee} T. Leephakpreeda, {it Novel determination of
94
differential-equation solutions: universal approximation method},
95
Computational and Applied Mathematics, {bf 146} (2002), 443-457.
96
bibitem{leng} G. Leng, G. Prasad and T. M. McGinnity, {it An on-line algorithm for creating self-organizing fuzzy neural networks}, Neural Networks, {bf 17} (2004), 1477-1493.
97
bibitem{lin1} D. Lin and X. Wang, {it Observer-based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation}, Fuzzy Sets and Systems, {bf 161} (2010), 2066-2080.
98
bibitem{lin3} D. Lin and X. Wang, {it Self-organizing adaptive fuzzy neural control for the synchronization of uncertain chaotic systems with random-varying parameters}, Neurocomputing, {bf 74} (2011), 2241-2249.
99
bibitem{lin2} D. Lin, X. Wang, F. Nian and Y. Zhang, {it Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems}, Neurocomputing, {bf 73} (2010), 2873-2881.
100
bibitem{li} R. P. Lippmann, {it An introduction to computing with
101
neural nets}, IEEE ASSP Magazine, (1987), 4-22.
102
bibitem{mas} A. Malek and R. Shekari Beidokhti, {it Numerical solution
103
for high order differential equations using a hybrid neural
104
network-Optimization method}, Applied Mathematics and Computation, {bf 183} (2006),
105
bibitem{mf} A. J. Meade Jr and A. A. Fernandez, {it The numerical solution
106
of linear ordinary differential equations by feedforward neural
107
networks}, Mathematical and Computer Modelling, {bf 19}textbf{(12)} (1994), 1-25.
108
bibitem{mef} A. J. Meade Jr and A. A. Fernandez, {it Solution of nonlinear
109
ordinary differential equations by feedforward neural networks},
110
Mathematical and Computer Modelling, {bf 20}textbf{(9)} (1994), 19-44.
111
bibitem{mbcrb} M. T. Mizukoshi, L. C. Barros, Y. Chalco-Cano, H. Román-Flores and R. C.
112
Bassanezi, {it Fuzzy differential equations and the extention
113
principle}, Information Sciences, {bf 177} (2007), 3627-3635.
114
bibitem{mto} M. Mosleh, T. Allahviranloo and M. Otadi, {it Evaluation of fully fuzzy regression models by fuzzy neural
115
network}, Neural Comput and Applications, {bf 21} (2012), 105 - 112.
116
bibitem{mom1} M. Mosleh and M. Otadi, {it Minimal solution of fuzzy linear system of differential equations}, Neural Comput and Applications, {bf 21} (2012), 329-336.
117
bibitem{mom} M. Mosleh and M. Otadi, {it Simulation and evaluation of fuzzy differential equations by fuzzy neural network}, Applied Soft Computing, {bf 12} (2012), 2817–2827.
118
bibitem{moa1} M. Mosleh, M. Otadi and S. Abbasbandy, {it Evaluation of fuzzy regression models by fuzzy neural network}, Journal of Computational and Applied
119
Mathematics, {bf 234} (2010), 825-834.
120
bibitem{moa2} M. Mosleh, M. Otadi and S. Abbasbandy, {it Fuzzy polynomial regression with fuzzy neural networks}, Applied Mathematical Modelling, {bf 35} (2011), 5400-5412.
121
bibitem{oma1} M. Otadi and M. Mosleh, {it Simulation and evaluation of dual fully fuzzy linear systems by fuzzy neural network}, Applied Mathematical Modelling, {bf 35} (2011), 5026-5039.
122
bibitem{oma2} M. Otadi, M. Mosleh and S. Abbasbandy, {it Numerical solution of fully fuzzy linear systems
123
by fuzzy neural network}, Soft Computing, {bf 15} (2011), 1513-1522.
124
bibitem{oms} M. Otadi, M. Mosleh, S. Saidanlu and N. A. Aris, {it Fuzzy hyperbolic regression with fuzzy neural networks}, Australian Journal of Basic and Applied Sciences, {bf 5}textbf{(10)} (2011), 838-847.
125
bibitem{pse} G. Papaschinopoulos, G. Stefanidou and P. Efraimidis,
126
{it Existence, uniquencess and asymptotic behavior of the solutions
127
of a fuzzy differential equation with piecewise constant
128
argument}, Information Sciences, {bf 177} (2007), 3855-3870.
129
bibitem{pi} P. Picton, {it Neural Networks}, Second edition, Palgrave,
130
Great Britain, 2000.
131
bibitem{pr} M. L. Puri and D. Ralescu, {it Fuzzy random variables}, Journal of Mathematical Analysis and Applications, {bf 114} (1986), 409-422.
132
bibitem{rrl} R. Rodriguez-Lopez, {it Comparison results for fuzzy
133
differential eqations}, Information Sciences, {bf 178} (2008), 1756-1779.
134
bibitem{ru} D. E. Rumelhart and J. L. McClelland, {it Parallel distributed processing}, MIT Press,
135
Cambridge, MA, 1986.
136
bibitem{sc} R. J. Schalkoff, {it Artificial neural networks},
137
McGraw-Hill, New York, 1997.
138
bibitem{seik} S. Seikkala, {it On the fuzzy initial value problem},
139
Fuzzy Sets and Systems, {bf 24} (1987), 319-330.
140
bibitem{st} J. Stanley, {it Introduction to neural networks}, Sierra Mardre, 1990.
141
bibitem{sb} J. Store and R. Bulirsch, {it Introduction to numerical
142
analysis}, Springer-Verlag, New York, 1993.
143
bibitem{tung} W. L. Tung and C. Quek, {it A generic self-organizing fuzzy neural network}, IEEE Transactions on Neural networks, {bf 13} (2002), 1075-1086.
144
bibitem{yuan} X. Wang and J. Zhao, {it Cryptanalysis on a parallel keyed hash function based on chaotic neural network}, Neurocomputing, {bf 73} (2010,) 3224-3228.
145
bibitem{xin} W. Xingyuan, X. Bing and Z. Huaguang, {it A multi-ary number communication system based on hyperchaotic system of 6th-order cellular neural network}, Communications in Nonlinear Science and Numerical Simulation, {bf 15} (2010), 124-133.
146
bibitem{kin} L. A. Zadeh, {it The concept of a liguistic variable and its
147
application to approximate reasoning} Information Sciences, {bf 8}
148
(1975), 199-249, 301-357; {bf 9} (1975), 43-80.
149
bibitem{laz} L. A. Zadeh, {it Is there a need for fuzzy logic?}, Information
150
Sciences, {bf 178} (2008), 2751-2779.
151
bibitem{zhang1} H. G. Zhang and D. R. Liu, {it Fuzzy modeling and fuzzy control}, Boston, 2006.
152
bibitem{zhang2} H. G. Zhang and Y. B. Quan, {it Modeling, identification and control of a class of nonlinear systems}, IEEE Transactions on Fuzzy Systems, {bf 9} (2001), 349-354.
153
ORIGINAL_ARTICLE
Language of General Fuzzy Recognizer
In this note first by considering the notion of general fuzzy automata (for simplicity GFA), we define the notions of direct product, restricted direct product and join of two GFA. Also, we introduce some operations on (Fuzzy) sets and then prove some related theorems. Finally we construct the general fuzzy recognizers and recognizable sets and give the notion of (trim) reversal of a given GFA. In particular, we define the notion of the language of a given general fuzzy $\Sigma$-recognizer and we show that the language of direct product of two $\Sigma$-recognizer is equal to direct product of their languages.
http://ijfs.usb.ac.ir/article_1398_998e413e86612781f35da097555d3bf4.pdf
2014-02-25T11:23:20
2017-12-11T11:23:20
113
134
10.22111/ijfs.2014.1398
(Trim) Reversal general fuzzy automata
Active state set
(Coaccessible) Accessible general fuzzy recognizer
Join
Direct product
K.
Abolpour
abolpor kh@yahoo.com
true
1
Department of Mathematics, Kazerun Branch, Islamic Azad Univer-
sity, Kazerun, Iran
Department of Mathematics, Kazerun Branch, Islamic Azad Univer-
sity, Kazerun, Iran
Department of Mathematics, Kazerun Branch, Islamic Azad Univer-
sity, Kazerun, Iran
LEAD_AUTHOR
M. M.
Zahedi
zahedi mm@mail.uk.ac.ir
true
2
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
AUTHOR
bibitem{[1].} M. A. Arbib, {it From automata theory to brain theory}, Int. J. Man-Machine Stud., {bf7(3)} (1975), 279-295.
1
bibitem{[2].} A. W. Burks, {it Logic, biology and automata -some historical reflections}, Int. J. Man- Machine Stud., {bf7(3)} (1975), 297-312.
2
bibitem{[3].} M. Doostfatemeh and S. C. Kremer, {it New directions in fuzzy automata}, International Journal of Approximate Reasoning, {bf38} (2005), 175-214.
3
bibitem{[4].} M. Horry and M. M. Zahedi, {it On general fuzzy recognizer}, Iranian Journal of Fuzzy Systems, {bf8(3)} (2011), 125-135.
4
bibitem{[5].} H. V. Kumbhojkar and S. R. Chaudhari, {it Fuzzy recognizers and recognizable sets}, Fuzzy Sets and Systems, {bf131} (2002), 381-392.
5
bibitem{[6].} D. S. Malik and J. N. Mordeson, {it Fuzzy discrete structures}, Physica-Verlag, New York, 2000.
6
bibitem{[7].} M. L. Minsky, {it Computation: finite and infinite machines}, Prentice-Hall, Englewood Cliffs, NJ, Chapter 3, (1967), 32-66.
7
bibitem{[8].} J. N. Mordeson and D. S. Malik, {it Fuzzy automata and languages, theory and applications}, Chapman and Hall/CRC, London/Boca Raton, FL, 2002.
8
bibitem{[9].} W. Omlin, C. L. Giles and K. K. Thornber, {it Equivalence in knowledge representation: automata, runs, and dynamical fuzzy systems}, Proc. IEEE, {bf87(9)} (1999), 1623-1640.
9
bibitem{[10].} W. G. Wee, {it On generalization of adaptive algorithm and application of the fuzzy sets concept to pattern classification}, Ph.D. Thesis, Purdue University, Lafayette, IN, 1967.
10
bibitem{[11].} L .A. Zadeh, {it Fuzzy sets}, Information and Control, {bf8} (1965), 338-353.
11
bibitem{[12].} M. M. Zahedi, M. Horry and K. Abolpour, {it Bifuzzy (general) topology on max-min general fuzzy automata}, Advances in Fuzzy Mathematics, {bf3(1)} (2008), 51-68.
12
ORIGINAL_ARTICLE
Numerical solutions of fuzzy nonlinear integral equations of the second kind
In this paper, we use the parametric form of fuzzy numbers, and aniterative approach for obtaining approximate solution for a classof fuzzy nonlinear Fredholm integral equations of the second kindis proposed. This paper presents a method based on Newton-Cotesmethods with positive coefficient. Then we obtain approximatesolution of the fuzzy nonlinear integral equations by an iterativeapproach.
http://ijfs.usb.ac.ir/article_1399_b0bad9e9b8effa0799936bdd34f47202.pdf
2014-02-25T11:23:20
2017-12-11T11:23:20
135
145
10.22111/ijfs.2014.1399
Fuzzy nonlinear Fredholm integral equations
Newton-Cotes methods
Parametric form of a fuzzy number
M.
Otadi
otadi@iaufb.ac.ir
true
1
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
LEAD_AUTHOR
M.
Mosleh
mosleh@iaufb.ac.ir
true
2
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
AUTHOR
bibitem{aba} S. Abbasbandy, E. Babolian and M. Alavi, {it Numerical
1
method for solving linear fredholm fuzzy integral equations of
2
the second kind}, Chaos Solitons & Fractals, {bf 31} (2007), 138-146.
3
bibitem{al1} T. Allahviranloo and M. Otadi, {it Gaussian quadratures for approximate of fuzzy integrals}, Applied Mathematics and Computation, {bf 170} (2005), 874-885.
4
bibitem{al2} T. Allahviranloo and M. Otadi, {it Gaussian quadratures for approximate of fuzzy multiple integrals}, Applied Mathematics and Computation, {bf 172} (2006), 175-187.
5
bibitem{at} K. E. Atkinson, {it An introduction to numerical analysis},
6
New York: Wiley, 1987.
7
bibitem{bsa} E. Babolian, H. S. Goghary and S. Abbasbandy, {it Numerical
8
solution of linear fredholm fuzzy integral equations of the
9
second kind by Adomian method}, Applied Mathematics and
10
Computation, {bf 161} (2005), 733-744.
11
bibitem{baker} C. T. H. Baker, {it A perspective on the numerical
12
treatment of volterra equations}, Journal of Computational and Appllied Mathematics, {bf 125} (2000), 217-249.
13
bibitem{bgggp} M. I. Berenguer, D. Gamez, A. I. Garralda-Guillem, M.
14
Ruiz Galan and M. C. Serrano Perez, {it Biorthogonal systems for solving
15
volterra integral equation systems of the second kind}, Journal of Computational and Appllied Mathematics, {bf 235} (2011), 1875-1883.
16
bibitem{b} A. M. Bica, {it Error estimation in the approximation of
17
the solution of nonlinear fuzzy fredholm integral equations},
18
Information Sciences, {bf 178} (2008), 1279-1292.
19
bibitem{bf} A. H. Borzabadi and O. S. Fard, {it A numerical scheme for
20
a class of nonlinear fredholm integral equations of the second
21
kind}, Journal of Computational and Applied Mathematics, {bf 232} (2009), 449-454.
22
bibitem{cz} S. S. L. Chang and L. Zadeh, {it On fuzzy mapping and control},
23
IEEE Trans. System Man Cybernet, {bf 2} (1972), 30-34.
24
bibitem{ct} Y. Chen and T. Tang, {it Spectral methods for weakly
25
singular volterra integral equations with smooth solutions}, Journal of Computational and Appllied Mathematics, {bf 233} (2009), 938-950.
26
bibitem{cm} W. Congxin and M. Ming, {it On embedding problem of fuzzy
27
number spaces}, Part 1, Fuzzy Sets and Systems, {bf 44} (1991), 33-38.
28
bibitem{dd} D. Dubois and H. Prade, {it Operations on fuzzy numbers}, International Journal of Systems Science, {bf 9} (1978), 613-626.
29
bibitem{dp} D. Dubois and H. Prade, {it Towards fuzzy differential
30
calculus}, Fuzzy Sets and Systems, {bf 8} (1982), 1-7.
31
bibitem{ez} R. Ezzati and S. Ziari, {it Numerical solution and error estimation of fuzzy fredholm integral equation using fuzzy bernstein polynomials}, Australian Journal of Basic and Applied Sciences, {bf 5} (2011), 2072-2082.
32
bibitem{fp} M. A. Fariborzi Araghi and N. Parandin, {it Numerical solution of fuzzy fredholm integral equations
33
by the lagrange interpolation based on the extension principle}, Soft Computing, {bf 15} (2011), 2449-2456.
34
bibitem{fmk} M. Friedman, M. Ma and A. Kandel, {it Numerical solutions
35
of fuzzy differential and integral equations}, Fuzzy Sets and
36
Systems, {bf 106} (1999), 35-48.
37
bibitem{fmk2} M. Friedman, M. Ma and A. Kandel, {it Solution to the fuzzy
38
integral equations with arbitrary kernels}, International Journal of Approximate Reasoning, {bf 20} (1999), 249-262.
39
bibitem{gv} R. Goetschel and W. Vaxman, {it Elementary fuzzy calculus}, Fuzzy
40
Sets and Systems, {bf 18} (1986), 31-43.
41
bibitem{h} H. Hochstadt, {it Integral equations}, New York: Wiley,
42
bibitem{kg} A. Kaufmann and M. M. Gupta, {it Introduction fuzzy
43
arithmetic}, Van Nostrand Reinhold, New York, 1985.
44
bibitem{kal}O. Kaleva, {it Fuzzy differential equations}, Fuzzy Sets and
45
Systems, {bf 24} (1987), 301-317.
46
bibitem{kauthen} J. P. Kauthen, {it Continuous time collocation method
47
for volterra-fredholm integral equations}, Numerische Math., {bf 56} (1989),
48
bibitem{kcy} G. J. Klir, U. S. Clair and B. Yuan, {it Fuzzy set theory:
49
foundations and applications}, Prentice-Hall, 1997.
50
bibitem{linz} P. Linz, {it Analytical and numerical methods for
51
volterra equations}, SIAM, Philadelphia, PA, 1985.
52
bibitem{mfk} M. Ma, M. Friedman and A. Kandel, {it A new fuzzy
53
arithmetic}, Fuzzy Sets and Systems, {bf 108} (1999), 83-90.
54
bibitem{mola} A. Molabahrami, A. Shidfar and A. Ghyasi, {it An analytical method for solving linear fredholm fuzzy integral equations of the second kind}, Computers & Mathematics with Applications, {bf 61} (2011), 2754-2761.
55
bibitem{mo11} M. Mosleh and M. Otadi, {it Numerical solution of fuzzy integral equations using Bernstein polynomials}, Australian Journal of Basic Applied Sciences, {bf 5} (2011), 724-728.
56
bibitem{pf1} N. Parandin and M. A. Fariborzi Araghi, {it The approximate solution of linear fuzzy fredholm integral equations of the second kind by using iterative interpolation}, World Academy of Science, Engineering and Technology, {bf 49} (2009), 947-984.
57
bibitem{pf2} N. Parandin and M. A. Fariborzi Araghi, {it The numerical solution of linear fuzzy fredholm integral equations of the second kind by using finite and divided differences methods}, Soft Computing, {bf 15} (2010), 729-741.
58
bibitem{pr} M. L. Puri and D. Ralescu, {it Fuzzy random variables}, Journal of
59
Mathematical Analysis and Applications, {bf 114} (1986), 409-422.
60
bibitem{fard} O. Solaymani Fard and M. Sanchooli, {it Two successive schemes for numerical solution of linear fuzzy fredholm integral equations of the second kind}, Australian Journal of Basic Applied Sciences, {bf 4} (2010), 817-825.
61
bibitem{sy} H. H. Sorkun and S. Yalcinbas, {it Approximate solutions of
62
linear volterra integral equation systems with variable
63
coefficients}, Applied Mathematical Modelling, {bf 34} (2010), 3451-3464.
64
bibitem{sb} J. Stoer and R. Bulirsch, {it Introduction to numerical
65
analysis}, Springer-Verlag,New York, 1993.
66
bibitem{laz} L. A. Zadeh, {it The concept of a linguistic variable
67
and its application to approximate reasoning}, Information Sciences, {bf 8} (1975), 199-249.
68
ORIGINAL_ARTICLE
Boundedness and Continuity of Fuzzy Linear Order-Homomorphisms on $I$-Topological\\ Vector Spaces
In this paper, a new definition of bounded fuzzy linear orderhomomorphism on $I$-topological vector spaces is introduced. Thisdefinition differs from the definition of Fang [The continuity offuzzy linear order-homomorphism. J. Fuzzy Math. {\bf5}\textbf{(4)}(1997), 829--838]. We show that the ``boundedness"and `` boundedness on each layer" of fuzzy linear orderhomomorphisms do not imply each other. On the basis,characterizations of continuity of fuzzy linearorder-homomorphisms, and the relation between continuity andboundedness are studied.
http://ijfs.usb.ac.ir/article_1400_24ff2fd4695152cdc861a3e7cec945fe.pdf
2014-02-25T11:23:20
2017-12-11T11:23:20
147
157
10.22111/ijfs.2014.1400
$I$-topological vector spaces
Bounded fuzzy set
Bounded fuzzy
linear order-homomorphism
Jin Xuan
Fang
jxfang@njnu.edu.cn
true
1
School of Mathematical Science, Nanjing Normal University, Nan-
jing, Jiangsu 210023, P. R. China
School of Mathematical Science, Nanjing Normal University, Nan-
jing, Jiangsu 210023, P. R. China
School of Mathematical Science, Nanjing Normal University, Nan-
jing, Jiangsu 210023, P. R. China
LEAD_AUTHOR
Hui
Zhang
zh9907084@sohu.com
true
2
Department of Mathematics, Anhui NormalUniversity, Wuhu, Anhui 241000,
P. R. China
Department of Mathematics, Anhui NormalUniversity, Wuhu, Anhui 241000,
P. R. China
Department of Mathematics, Anhui NormalUniversity, Wuhu, Anhui 241000,
P. R. China
AUTHOR
bibitem{Fang1} J. X. Fang, {it Fuzzy linear order-homomorphism and its
1
structures}, J. Fuzzy Math., {bf 4}textbf{(1)} (1996), 93--102.
2
bibitem{Fang2} J. X. Fang, {it The continuity of fuzzy linear
3
order-homomorphism}, J. Fuzzy Math., {bf 5}textbf{(4)} (1997),
4
bibitem{Fang3} J. X. Fang, {it On local bases of fuzzy topological vector
5
spaces}, Fuzzy Sets and Systems, {bf 87} (1997), 341--347.
6
bibitem{HR} U. H"ohle and S. E. Rodabaugh, eds., {it Mathematics
7
of fuzzy sets: logic, topology, and measure theory}, The Handbooks
8
of Fuzzy Sets Series, Kluwer Academic Publishers,
9
Dordrecht, {bf 3} (1999).
10
bibitem{JY} S. Q. Jiang and C. H. Yan, {it Fuzzy bounded sets and
11
totally fuzzy bounded sets in $I$-topological vector spaces},
12
Iranian Journal of Fuzzy Systems, {bf 6}textbf{(3)} (2009), 73--90.
13
bibitem{KL} A. K. Katsaras and D. B. Liu, {it Fuzzy vector spaces and fuzzy
14
topological vector spaces}, J. Math. Anal. Appl., {bf 58} (1977),
15
bibitem{Ka1} A. K. Katsaras, {it Fuzzy topological vector spaces I}, Fuzzy
16
Sets and Systems, {bf 6} (1981), 85--95.
17
bibitem{Ka2} A. K. Katsaras, {it Fuzzy topological vector spaces II}, Fuzzy
18
Sets and Systems, {bf 12} (1984), 143--154.
19
bibitem{Lo} R. Lowen, {it Fuzzy topological spaces and fuzzy
20
compactness}, J. Math. Anal. Appl., {bf 56} (1976), 621--633.
21
bibitem{PL} P. M. Liu, {it Fuzzy topology I, neighborhood
22
structures of a fuzzy points and Moore-Smith convergence}, J.
23
Math. Anal. Appl., {bf 76} (1980), 571--599.
24
bibitem{Ro1} S. E. Rodabaugh, {it Point-set lattice-theoretic
25
topology}, Fuzzy Sets and Systems, {bf 40} (1991), 297--347.
26
bibitem{Ro2} S. E. Rodabaugh, {it Powerset operator based foundation for
27
point-set lattice-theoretic (POSLAT) fuzzy set theories and
28
topologies}, Quaestiones Mathematicae, {bf 20} (1997), 463--530.
29
bibitem{Wang} G. J. Wang, {it Order-homomorphisms of fuzzes}, Fuzzy Sets and
30
Systems, {bf 12} (1984), 281--288.
31
bibitem{Wa} R. H. Warren, {it Neighborhoods, bases and continuity in fuzzy
32
topological spaces}, Rocky Mountain J. Math., {bf 8} (1978),
33
bibitem{WF} C. X. Wu and J. X. Fang, {it Boundedness and locally bounded
34
fuzzy topological vector spaces}, Fuzzy Math. (China), (in Chinese), {bf
35
5}textbf{(4)} (1985), 87--94.
36
bibitem{ZF} H. P. Zhang and J. X. Fang, {it A note on locally bounded
37
$L$-topological vector spaces}, Information Sciences, {bf 179}
38
(2009), 1792--1794.
39
ORIGINAL_ARTICLE
Persian-translation vol. 11, no. 1, February 2014
http://ijfs.usb.ac.ir/article_2692_f0227535d3d0e8df719bab08ce5f3bc8.pdf
2014-03-01T11:23:20
2017-12-11T11:23:20
161
168
10.22111/ijfs.2014.2692