ORIGINAL_ARTICLE
Cover vol. 12, no.2, April 2015
http://ijfs.usb.ac.ir/article_2648_7da56e08e1a4fb3a8299936955a993e7.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
0
10.22111/ijfs.2015.2648
ORIGINAL_ARTICLE
A TS Fuzzy Model Derived from a Typical Multi-Layer Perceptron
In this paper, we introduce a Takagi-Sugeno (TS) fuzzy model which is derived from a typical Multi-Layer Perceptron Neural Network (MLP NN). At first, it is shown that the considered MLP NN can be interpreted as a variety of TS fuzzy model. It is discussed that the utilized Membership Function (MF) in such TS fuzzy model, despite its flexible structure, has some major restrictions. After modifying the MF, we introduce a TS fuzzy model whose MFs are tunable near and far from focal points, separately. To identify such TS fuzzy model, an incremental learning algorithm, based on an efficient space partitioning technique, is proposed. Through an illustrative example, the methodology of the learning algorithm is explained. Next, through two case studies: approximation of a nonlinear function for a sun sensor and identification of a pH neutralization process, the superiority of the introduced TS fuzzy model in comparison to some other TS fuzzy models and MLP NN is shown.
http://ijfs.usb.ac.ir/article_1979_0f5c1f01dfef9d988a11fdcb9b404174.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
1
21
10.22111/ijfs.2015.1979
Takagi-Sugeno fuzzy model
Multi layer perceptron
Tunable membership functions
Nonlinear function approximation
pH neutralization process
A.
Kalhor
akalhor@ut.ac.ir
true
1
System Engineering and Mechatronics Group, Faculty of New Sciences
and Technologies, University of Tehran, Tehran, Iran
System Engineering and Mechatronics Group, Faculty of New Sciences
and Technologies, University of Tehran, Tehran, Iran
System Engineering and Mechatronics Group, Faculty of New Sciences
and Technologies, University of Tehran, Tehran, Iran
LEAD_AUTHOR
B. N.
Aarabi
araabi@ut.ac.ir
true
2
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
AUTHOR
C.
Lucas
lucas@ut.ac.ir
true
3
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
AUTHOR
B.
Tarvirdizadeh
bahram@ut.ac.ir
true
4
System Engineering and Mechatronics Group, Faculty of New Sci-
ences and Technologies, University of Tehran, Tehran, Iran
System Engineering and Mechatronics Group, Faculty of New Sci-
ences and Technologies, University of Tehran, Tehran, Iran
System Engineering and Mechatronics Group, Faculty of New Sci-
ences and Technologies, University of Tehran, Tehran, Iran
AUTHOR
[1] P. Angelov and X. Zhou, On line learning fuzzy rule-based system structure from data
1
streams, In 2008 IEEE International Conference on Fuzzy Systems within the IEEE World
2
Congress on Computational Intelligence, Hong Kong., (2008), 915-922.
3
[2] J. F. Baldwin and S. B. Kandarake, Asymmetric triangular fuzzy sets for classication model,
4
In Lecture Notesin Articial Intelligent, (2003), 364-370.
5
[3] J. N. Choi, S. K. Oh and W. Pedrycz., Identication of fuzzy models using a successive tuning
6
method with a variant identication ratio, Fuzzy Sets and Systems, 159 (2008), 2873-2889.
7
[4] B. L. R. De Moor, ed., DaISy: Database for the Identication of Systems, De-
8
partment of Electrical Engineering, 2008, ESAT/SISTA, K.U.Leuven, Belgium, URL:
9
http://homes.esat.kuleuven.be/~smc/daisy/. (visited on Oct. 10, 2010).
10
[5] H. Du and N. Zhang, Application of evolving Takagi-Sugeno fuzzy model to nonlinear system
11
identication, Applied soft computing, 8 (2007), 676-686.
12
[6] A. Fiordaliso, A constrained Takagi-Sugeno fuzzy system that allows for better interpretation
13
and analysis, Fuzzy Sets and Systems, 118 (2001), 307-318.
14
[7] M. Hell, S. P. Campinas, R. Ballini, Jr. P. Costa and F. Gomid, Training neurofuzzy networks
15
with participatory learning, In: proceeding of 5th Conference of the EUSFLAT, (2007), 231-
16
[8] J. S. R. Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Trans. Syst.
17
Man and Cybern, 23 (1993), 665-685.
18
[9] A. Kalhor, B. N. Araabi and C. Lucas, A new systematic design for habitually linear evolving
19
TS fuzzy model, Journal of Expert systems with applications, 39 (2012), 1725-1736.
20
[10] A. Kalhor, B. N. Araabi and C. Lucas, An online predictor model as adaptive habitually
21
linear and transiently nonlinear model, Evolving Systems, 1 (2010), 29-41.
22
[11] A. Kalhor, B. N. Araabi and C. Lucas, A new high-order Takagi-Sugeno fuzzy model based on
23
deformed linear models, Amirkabir Int. J. of Modeling Identication, Simulation and Control,
24
42 (2010), 43-52.
25
[12] A. Kalhor, B. N. Araabi and C. Lucas, Reducing the number of local linear models in neuro{
26
fuzzy modeling: A split-and-merge clustering approach, Applied Soft Computing Journal, 11
27
(2011), 5582{5589.
28
[13] N. Kasabov, DENFIS: Dynamic Evolving Neural-Fuzzy Inference System and its application
29
for time-series prediction, IEEE Trans. Fuzzy Syst., 10 (2012) 144-154.
30
[14] V. Krkov: Kolmogorov's theorem and multilayer neural networks, Neural networks 5: 501-
31
506, 1992.
32
[15] D. H. Lee, Y. H. Joo and M. H. Tak, Local stability analysis of continuous-time Takagi{
33
Sugeno fuzzy systems: A fuzzy Lyapunov function approach, Information Sciences, 257
34
(2014), 163-175.
35
[16] C. H. Lee and H. Y. Pan, Performance enhancement for neural fuzzy systems using asym-
36
metric membership functions, Fuzzy Sets and Systems, 160 (2009), 949-971.
37
[17] C. H. Lee and C. C. Teng, Fine tuning of membership functions for fuzzy neural systems,
38
Asian J. Control, 3 (2001), 216-225.
39
[18] G. Leng, T. M. Mc Ginnity and G. Prasad, An approach for on-line extraction of fuzzy rules
40
using a self-organising fuzzy neural network, Fuzzy Sets and Systems, 150 (2005), 211-243.
41
[19] C. Li C, K. H. Cheng and J. D. Lee, Hybrid learning neuro fuzzy approach for complex
42
modeling using asymmetric fuzzy sets, In: Proc. of the17th IEEE International Conf. on
43
Tools with Articial Intelligence, (2005), 397-401.
44
[20] C. Li, J. Zhou, X. Xiang, Q. Li and X. An, T-S fuzzy model identication based on a novel
45
fuzzy c-regression model clustering algorithm, Engineering Applications of Articial Intelligence,
46
22 (2009), 646-653.
47
[21] C. J. Lin and W. H. Ho, An asymmetric-similarity-measure-based neural fuzzy inference
48
system, Fuzzy Sets and Systems, 152 (2005), 535{551.
49
[22] T. J. Mc Avoy, E. Hsu and S. Lowenthal, Dynamics of pH in controlled stirred tank reactor,
50
Ind. Eng. Chem. Process Des. Develop., 11 (1972), 71-78.
51
[23] O. Nelles, Nonlinear System Identication, In: New York: Springer, (2001), Section 13.3.1,
52
[24] P. Nikdel, M. Hosseinpour, M. A. Badamchizadeh and M. A. Akbari, Improved Takagi{
53
Sugeno fuzzy model-based control of
54
exible joint robot via Hybrid-Taguchi genetic algorithm,
55
Engineering Applications of Articial Intelligence, 33 (2014), 12-20.
56
[25] J. Park and I. W. Sandberg, Universal Approximation Using Radial-Basis-Function Net-
57
works, Neural Computation, 3 (1991), 246-257.
58
[26] K. B. Petersen and M. S. Pedersen, The matrix cookbook, http://matrixcookbook.com, Version:
59
Nov. 14, 2008.
60
[27] Y. Shi, R. Eberhart and Y. Chen, Implementation of evolutionary fuzzy systems, IEEE Trans.
61
on Fuzzy Sys., 7 (1999), 109-118.
62
[28] T. Takagi and M. Sugeno, Fuzzy identication of systems and its applications to modeling
63
and control, IEEE Trans. Syst., Man, and Cybern., 15 (1985), 116-132.
64
[29] D. Wang, C. Quek and G. S. Ng, MS-TSKfnn: Novel Takagi-Sugeno-Kang fuzzy neural
65
network using ART like clustering., In: proceeding of IEEE international joint conference on
66
Neural Networks., (2004), 2361-2366.
67
[30] X. Xie, L. Lin and S. Zhong, Process Takagi{Sugeno model: A novel approach for han-
68
dling continuous input and output functions and its application to time series prediction,
69
Knowledge-Based Systems, 63 (2014), 46-58.
70
[31] H. Ying, General SISO Takagi{Sugeno fuzzy systems with linear rule consequent are univer-
71
sal approximators, IEEE Trans. on Fuzzy Systems, 6 (1998), 582-587.
72
ORIGINAL_ARTICLE
Modeling of Epistemic Uncertainty in Reliability Analysis of Structures Using a Robust Genetic Algorithm
In this paper the fuzzy structural reliability index was determined through modeling epistemic uncertainty arising from ambiguity in statistical parameters of random variables. The First Order Reliability Method (FORM) has been used and a robust genetic algorithm in the alpha level optimization method has been proposed for the determination of the fuzzy reliability index. The sensitivity level of fuzzy response due to the introduced epistemic uncertainty was also measured using the modified criterion of Shannon entropy. By introducing bounds of uncertainty, the fuzzy response obtained from the proposed method presented more realistic estimation of the structure reliability compared to classic methods. This uncertainty interval is of special importance in concrete structures since the quality of production and implementation of concrete varies in different cross sections in reality. The proposed method is implementable in reliability problems in which most of random variables are fuzzy sets and in problems containing non-linear limit state functions and provides a precise acceptable response. The capabilities of the proposed method were demonstrated using different examples. The results indicated the accuracy of the proposed method and showed that classical methods like FORM cover only special case of the proposed method.
http://ijfs.usb.ac.ir/article_1980_705e7461f624d40c8f31e42874bb83cb.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
23
40
10.22111/ijfs.2015.1980
Fuzzy reliability index
Alpha level optimization method
Genetic Algorithm
First order reliability method
Mansour
Bagheri
mnsrbagheri@gmail.com
true
1
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
AUTHOR
Mahmoud
Miri
mmiri@eng.usb.ac.ir
true
2
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
LEAD_AUTHOR
Naser
Shabakhty
shabakhty@eng.usb.ac.ir
true
3
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
AUTHOR
[1] G. Alefeld and J. Hertzberger, Introduction to interval computations, Academic Press, New
1
York, 1983.
2
[2] D. K. Armen and D. Taleen, Multiple design points in rst and second-order reliability,
3
Journal of Structural Safety, 20 (1998), 37-49.
4
[3] M. S. Arumugam, M. V. C. Rao and R. Palaniappan, New hybrid genetic operators for real
5
coded genetic algorithm to compute optimal control of a class of hybrid systems, Journal of
6
Applied Soft Computing, 6 (2005), 38-52.
7
[4] S. K. Au and J. L. Beck,Estimation of small failure probabilities in high dimension by subset
8
simulation, Journal of Probabilistic Engineering Mechanics, 16(4) (2001), 263-277.
9
[5] B. M. Ayyub and R. H. McCuen, Probability, statistics, and reliability for engineers and
10
scientists, 2nd Ed. Chapman Hall/CRC, Boca Raton, Fla, 2003.
11
[6] Y. Ben-Haim, Robust reliability in mechanical sciences, Springer, Berlin, 1996.
12
[7] K. Breitung, Asymptotic approximations for multinormal integrals, Journal of Engineering
13
Mechanics ASCE, 110(3) (1984), 357-366.
14
[8] A. DerKiureghian and O. Ditlevsen, Aleatory or epistemic? Does it matter?, Journal of
15
Structural Safety, 31 (2009), 105-112.
16
[9] W. Dong and H. Shah, Vertex method for computing functions on fuzzy variables, Journal of
17
Fuzzy Sets and Systems, 24(1) (1978), 65-78.
18
[10] A. H Elhewy, E. Mesbahi and Y. Pu, Reliability analysis of structures using neural network
19
method, Journal of Probability Engineering Mechanics, 21 (2006), 44-53.
20
[11] S. Freitag, W. Graf and M. Kaliske, A material description based on recurrent neural networks
21
for fuzzy data and its application within the nite element method, Journal of Computers
22
and Structures, 124 (2013), 29-37.
23
[12] M. Giuseppe and Q. Giuseppe, A new possibilistic reliability index denition, Journal of
24
ActaMechanica, 210 (2010), 291-303.
25
[13] D. E. Goldberg, Genetic Algorithms in search, optimization and machine learning, Addison-
26
Wesley, 1989.
27
[14] F. Grooteman, Adaptive radial-based importance sampling method for structural reliability,
28
Journal of Structural Safety, 30(6) (2008), 533-542.
29
[15] J. W. Hall and J. Lawry, Fuzzy label methods for constructing imprecise limit state functions,
30
Journal of Structural Safety, 25(4) (2003), 317-341.
31
[16] M. Hanss and S. Turrin, A fuzzy-based approach to comprehensive modeling and analysis of
32
systems with epistemic uncertainties, Journal of Structural Safety, 32(6) (2010), 433-441.
33
[17] A. M. Hasofer and N. C. Lind, Exact and invariant second moment code format, Journal of
34
Engineering Mechanics ASCE, 100 (1974), 111-121.
35
[18] J. C. Helton and W. L. Oberkampf, alternative representations of epistemic uncertainty,
36
Journal of Reliability Engineering and System Safety, 85(1-3) (2004), 1-10.
37
[19] J. E. Hurtado and D. A. Alvarez,Neural network-based reliability analysis: a comparative
38
study, Journal of Computer Methods in Applied Mechanics and Engineering, 191(1-2)
39
(2001), 113-132.
40
[20] J. E. Hurtado, D. A. Alvarez and J. Ramirez, Fuzzy structural analysis based on fundamental
41
reliability concepts, Journal of Computers and Structures, 112 (2012), 183-192.
42
[21] P. Inseok and V. Ramana V Grandhi, Quantication of model-form and parametric uncer-
43
tainty using evidence theory, Journal of Structural Safety, 39 (2012), 44-51.
44
[22] F. Jalayer, I. Iervolino and G. Manfredi, Structural modeling uncertainties and their in
45
on seismic assessment of existing RC structures, Journal of Structural Safety, 32(3) (2010),
46
[23] H. Jinsong and D. V. Griths, Observations on FORM in a simple geomechanics example,
47
Journal of Structural Safety, 33(1) (2011), 115-119.
48
[24] S. D. Koduru and T. Haukaas, Feasibility of FORM in nite element reliability analysis,
49
Journal of Structural Safety, 32(2) (2010), 145-153.
50
[25] H. Kwakernaak, Fuzzy random variables - I. Denitions and Theorems, Journal of Informa-
51
tion Science, 15 (1978), 1-29.
52
[26] H. Kwakernaak, Fuzzy random variables - II.Algorithms and Examples for the Discrete Case,
53
Journal of Information Science, 17 (1979), 253-278.
54
[27] H. O. Madsen, S. Krenk and N. C. Lind, Methods of structural safety, New York: Dover
55
Publications, 2006.
56
[28] F. Massa F, K. Run, T. Tison and B. Lallemand, A complete method for ecient fuzzy
57
modal analysis, Journal of Sound and Vibration, 309(1-2) (2008), 63-85.
58
[29] R. E. Melchers, Structural reliability analysis and prediction, 2nd Ed. Chichester John Wiley
59
and Sons, 1999.
60
[30] R. E. Melchers, M. Ahammed and C. Middleton, FORM for discontinuous and truncated
61
probability density functions, Journal of Structural Safety, 25(3) (2003), 305-313.
62
[31] B. Moller and M. Beer, Fuzzy randomness - uncertainty in civil engineering and computa-
63
tional mechanics, Springer Verlag, Berlin, 2004.
64
[32] B. Moller, W. Graf and M. Beer, Fuzzy structural analysis using -level optimization, Journal
65
of Computational Mechanics, 26(6) (2000), 547-565.
66
[33] B. Moller, W. Graf, M. Beer and R. Schneider,Safety assessment of structures in view of
67
fuzzy randomness, Journal of Computers and Structeurs, 81 (2003), 1567-1582.
68
[34] A. S. Nowak and K. R. Collins, Reliability of structures, McGraw-Hill, 2000.
69
[35] M. V. Rama Rao, A. Pownuk, S. Vandewalle and D. Moens, Transient response of structures
70
with uncertain structural parameters, Journal of Structural Safety, 32 (2010), 449-460.
71
[36] M. Rashki, M. Miri and M. AzhdaryMoghaddam, A new ecient simulation method to
72
approximate the probability of failure and most probable point, Journal of Structural Safety,
73
39 (2012), 22-29.
74
[37] T. V. Santosh, R. K. Saraf, A. K. Ghosh and H. S. Kushwaha, Optimum step length selection
75
rule in modied HL-RF method for structural reliability International Journal of Pressure
76
Vessels and Piping, 83 (2006), 742-748.
77
[38] A. Seranska, M. Kaliske, C. Zopf and W. Graf, A multi-objective optimization approach
78
with consideration of fuzzy variables applied to structural tire design, Journal of Computers
79
and Structures, 116(1), (2013), 9-17.
80
[39] M. C. Tae and C. L. Byung, Reliability-based design optimization using convex linearization
81
and sequential optimization and reliability assessment method, Journal of Structural Safety,
82
33(1) (2011), 42-50.
83
[40] J. R. Timothy, (2010), Fuzzy logic with engineering applications, 3rd Ed. Publisher Wiley,
84
[41] G. Wei, S. Chongmin and TL. Francis, Probabilistic interval analysis for structures with
85
uncertainty, Journal of Structural Safety, 32(3) (2010), 191-199.
86
[42] M. William and M. Bulleit, Uncertainty in structural engineering, Journal of Practice Peri-
87
odical on Structural Design and Construction, 13(1) (2008), 24-30.
88
[43] L. N. Xing, Y. W. Chen, K. W. Yang, F. Hou, S. Xue and P. C. Huai, A hybrid approach
89
combining an improved genetic algorithm and optimization strategies for the asymmetric
90
traveling salesman problem, Journal of Engineering Applications of Articial Intelligence, 21
91
(2008), 1370-1380.
92
[44] L. A. Zadeh, Fuzzy sets, Journal of Information Control, 8(3) (1965), 338-553.
93
[45] H. Zhang, Interval importance sampling method for nite element-based structural reliability
94
assessment under parameter uncertainties, Journal of Structural Safety, 38 (2012), 1-10.
95
[46] M. Q. Zhang, M. Beer, S. T. Quek and Y. S. Choo, Comparison of uncertainty models
96
in reliability analysis of oshore structures under marine corrosion, Journal of Structural
97
Safety, 32 (2010), 425-432.
98
[47] Y. G. Zhao and T. Ono, Moment methods for structural reliability, Journal of Structural
99
Safety, 23 (2001), 47-75.
100
[48] H. J. Zimmermann, Fuzzy set theory and its applications, Kluwer Academic Publishers, Lon-
101
don, 1992.
102
ORIGINAL_ARTICLE
EQ-logics with delta connective
In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binaryoperations of fuzzy equality and multiplication. EQ-algebra generalizesresiduated lattices, namely, every residuated lattice is an EQ-algebra but notvice-versa.In this paper, we introduce additional connective $logdelta$ in EQ-logics(analogous to Baaz delta connective in MTL-algebra based fuzzy logics) anddemonstrate that the resulting logic has again reasonable properties includingcompleteness. Introducing $Delta$ in EQ-logic makes it possible to prove alsogeneralized deduction theorem which otherwise does not hold in EQ-logics weakerthan MTL-logic.
http://ijfs.usb.ac.ir/article_1981_f9c205b6a230d24728542018f1b3f176.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
41
61
10.22111/ijfs.2015.1981
EQ-algebra
EQ-logic
Equational logic
Delta connective
Generalized deduction theorem
M.
Dyba
martin.dyba@osu.cz
true
1
University of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech Republic
University of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech Republic
University of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech Republic
LEAD_AUTHOR
V.
Novak
vilem.novak@osu.cz
true
2
University of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech Republic
University of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech Republic
University of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech Republic
AUTHOR
[1] P. Cintula, P. Hajek, R. Horck, Formal systems of fuzzy logic and their fragments, Annals
1
of Pure and Applied Logic, 150 (2007), 40{65.
2
[2] P. Cintula and C. Noguera, A general framework for Mathematical Fuzzy Logic, In: P. Cin-
3
tula, P. Hajek, C. Noguera, eds., Handbook of Mathematical Fuzzy Logic - volume 1, Studies
4
in Logic, Mathematical Logic and Foundations, vol. 37. College Publications, Londres 2011,
5
[3] M. Dyba and V. Novak, EQ-logics: Non-commutative fuzzy logics based on fuzzy equality,
6
Fuzzy Sets and Systems, 172 (2011), 13{32.
7
[4] M. El-Zekey, Representable good EQ-algebras, Soft Computing, 14 (2009), 1011{1023.
8
[5] M. El-Zekey, V. Novak and R. Mesiar, On good EQ-algebras, Fuzzy Sets and Systems, 178
9
(2011), 1{23.
10
[6] F. Esteva and L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous
11
t-norms, Fuzzy Sets and Systems, 124 (2001), 271{288.
12
[7] S. Gottwald, Mathematical fuzzy logics, Bulletin of Symbolic Logic, 14 (2) (2008), 210{239.
13
[8] S. Gottwald and P. Hajek, Triangular norm-based mathematical fuzzy logics, In: E. Kle-
14
ment, R. Mesiar (Eds.), Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular
15
Norms, Elsevier, Amsterdam, (2005), 257{299.
16
[9] D. Gries and F. Schneider, A Logical Approach to Discrete Math, Springer-Verlag, Heidelberg,
17
[10] D. Gries and F. Schneider, Equational propositional logic, Information Processing Letters,
18
53 (1995), 145{152.
19
[11] P. Hajek, Metamathematics of Fuzzy Logic, Dordrecht, Kluwer, 1998.
20
[12] V. Novak, EQ-algebras: primary concepts and properties, In: Proc. Czech-Japan Seminar,
21
Ninth Meeting. Kitakyushu& Nagasaki, August 18{22, 2006, Graduate School of Information,
22
Waseda University, (2006), 219{223.
23
[13] V. Novak, Which logic is the real fuzzy logic?, Fuzzy Sets and Systems, 157 (2006), 635{641.
24
[14] V. Novak, EQ-algebras in progress, In: O. Castillo, ed., Theoretical Advances and Applica-
25
tions of Fuzzy Logic and Soft Computing, Springer, Berlin, (2007), 876{884.
26
[15] V. Novak, EQ-algebra-based fuzzy type theory and its extensions, Logic Journal of the IGPL,
27
19 (2011), 512{542.
28
[16] V. Novak and B. de Baets, EQ-algebras, Fuzzy Sets and Systems, 160 (2009), 2956{2978.
29
[17] G. Tourlakis, Mathematical Logic, New York, J. Wiley & Sons, 2008.
30
ORIGINAL_ARTICLE
Bifuzzy core of fuzzy automata
The purpose of the present work is to introduce the concept of bifuzzy core of a fuzzy automaton, which induces a bifuzzy topology on the state-set of this fuzzy automaton. This is shown that this bifuzzy topology can be used to characterize the concepts such as bifuzzy family of submachines, bifuzzy separable family and bifuzzy retrievable family of a fuzzy automaton.
http://ijfs.usb.ac.ir/article_1982_23e6f3744366279e9ec0ca3d46e6e982.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
63
73
10.22111/ijfs.2015.1982
Fuzzy automata
Bifuzzy source
Bifuzzy successor
Bifuzzy core
Bifuzzy topology
S. P.
Tiwari
sptiwarimaths@gmail.com
true
1
Department of Applied Mathematics, Indian School of Mines, Dhanbad
826004, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad
826004, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad
826004, India
LEAD_AUTHOR
Anupam K.
Singh
anupam09.bhu@gmail.com
true
2
Department of Applied Mathematics, Indian School of Mines,
Dhanbad-826004, India
Department of Applied Mathematics, Indian School of Mines,
Dhanbad-826004, India
Department of Applied Mathematics, Indian School of Mines,
Dhanbad-826004, India
AUTHOR
Shambhu
Sharan
ssharanfma@kiit.ac.in
true
3
Department of Mathematics, School of Applied Sciences, KIIT Uni-
versity, Bhubaneswar-751024, India
Department of Mathematics, School of Applied Sciences, KIIT Uni-
versity, Bhubaneswar-751024, India
Department of Mathematics, School of Applied Sciences, KIIT Uni-
versity, Bhubaneswar-751024, India
AUTHOR
Vijay K.
Yadav
true
4
Department of Applied Mathematics, Indian School of Mines, Dhanbad
826004, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad
826004, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad
826004, India
AUTHOR
[1] Z. Bavel and J. W. Thomas, On the decomposability of monadic algebras and automata,
1
Proc. of the 8th Annual Symp. on Switching and Automata Theory, (1967), 322-335.
2
[2] P. Das, A fuzzy topology associated with a fuzzy nite state machine, Fuzzy Sets and Systems,
3
105(3) (1999), 469-479.
4
[3] W. M. L. Holcombe, Algebraic automata theory, Cambridge University Press, 1982.
5
[4] J. E. Hopcroft and J. D. Ullman, Introduction to automata theory, languages and computa-
6
tion, Addison-Wesley, New York, 1979.
7
[5] J. Ignjatovic, M. Ciric and V. Simoovic, Fuzzy relation equations and subsystems of fuzzy
8
transition systems, Knowledge-Based Systems, 38 (2013), 48-61.
9
[6] M. Ito, Algebraic structures of automata, Theoretical Computer Science, 429 (2012), 164-168.
10
[7] J. H. Jin, Q. G. Li and Y. M. Li, Algebraic properties of L-fuzzy nite automata, Information
11
Sciences, 234 (2013), 182-202.
12
[8] Y. B. Jun, Intuitionistic fuzzy nite state machines, Journal of Applied Mathematics and
13
Computing, 17 (2005), 109-120.
14
[9] Y. B. Jun, Intuitionistic fuzzy nite switchboard state machines, Journal of Applied Mathe-
15
matics and Computing, 20 (2006), 315-325.
16
[10] Y. B. Jun, Quotient structures of intuitionistic fuzzy nite state machines, Information Sci-
17
ences, 177 (2007), 4977-4986.
18
[11] Y. H. Kim, J. G. Kim and S. J. Cho, Products of T-generalized state machines and T-
19
generalized transformation semigroups, Fuzzy Sets and Systems, 93(3) (1998), 87-97.
20
[12] H. V. Kumbhojkar and S. R. Chaudhri, On proper fuzzication of fuzzy nite state machines,
21
International Journal of Fuzzy Mathematics, 8(4) (2008), 1019-1027.
22
[13] W. Lihua and D. Qiu, Automata theory based on complete residuated lattice-valued logic:
23
Reduction and minimization, Fuzzy Sets and Systems, 161(12) (2010), 1635-1656.
24
[14] R. Lowen, Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis
25
and Applications, 56(3) (1976), 621-633.
26
[15] D. S. Malik, J. N. Mordeson and M. K. Sen, Submachines of fuzzy nite state machine,
27
Journal of Fuzzy Mathematics, 2(4) (1994), 781-792.
28
[16] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages: theory and applications,
29
Chapman and Hall/CRC, London/Boca Raton, 2002.
30
[17] K. Peeva, Finite L-fuzzy acceptors, regular L-fuzzy grammars and syntactic pattern recogni-
31
tion, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(1)
32
(2004), 89-104.
33
[18] D. Qiu, Characterizations of fuzzy nite automata, Fuzzy Sets and Systems, 141(3) (2004),
34
[19] E. S. Santos, Maximin automata, Information and Control, 12(4) (1968), 367-377.
35
[20] W. Shukla and A. K. Srivastava, A topology for automata: A note, Information and Control,
36
32(2) (1976), 163-168.
37
[21] A. K. Srivastava and W. Shukla, A topology for automata II, International Journal of Math-
38
ematics and Mathematical Sciences, 9(3) (1986), 425-428.
39
[22] A. K. Srivastava and S. P. Tiwari, A topology for fuzzy automata, Proc. AFSS International
40
Conference on Fuzzy Systems, Lecture Notes in Articial Intelligence, Springer-verlag, 2275
41
(2002), 485-491.
42
[23] W. G.Wee, On generalizations of adaptive algorithm and application of the fuzzy sets concept
43
to pattern classication, Ph. D. Thesis, Purdue University, 1967.
44
[24] M. S. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39(3) (1991),
45
[25] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
46
[26] Q. Zhang and Y. Huang, Intuitionistic fuzzy automata based on complete residuated lattice-
47
valued logic, International Journal of Materials and Product Technology, 45 (1/2/3/4)
48
(2012), 108-118.
49
ORIGINAL_ARTICLE
Existence and uniqueness of the solution of nonlinear fuzzy Volterra integral equations
In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.
http://ijfs.usb.ac.ir/article_1983_4e17db286a759c153db5a9aa92c5c1e3.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
75
86
10.22111/ijfs.2015.1983
Fuzzy numbers
Fuzzy Volterra integral equations
Existence and uniqueness
T.
Allahviranloo
tofigh@allahviranloo.com
true
1
Department of mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
LEAD_AUTHOR
P.
Salehi
parhamsalehi@rocketmail.com
true
2
Department of mathematics, Hamedan Branch, Islamic Azad University,
Hamedan, Iran
Department of mathematics, Hamedan Branch, Islamic Azad University,
Hamedan, Iran
Department of mathematics, Hamedan Branch, Islamic Azad University,
Hamedan, Iran
AUTHOR
M.
Nejatiyan
maryamnejatiyan@yahoo.com
true
3
Department of mathematics, Science and Research Branch, Islamic
Azad University, Tehran, Iran
Department of mathematics, Science and Research Branch, Islamic
Azad University, Tehran, Iran
Department of mathematics, Science and Research Branch, Islamic
Azad University, Tehran, Iran
AUTHOR
[1] G. A. Anastassiou and S. G. Gal, On a fuzzy trigonometric approximation theorem of
1
Weierstrass-type, J. Fuzzy Math., 9 (3) (2001), 701-708.
2
[2] K. Balachandran and K. Kanagarajan, Existence of solutions of general nonlinear fuzzy
3
Volterra-Fredholm integral equations, J. Appl. Math. Stochast. Anal., 3 (2005), 333-343.
4
[3] K. Balachandran and P. Prakash, Existence of solutions of nonlinear fuzzy Volterra-Fredholm
5
integral equations, Indian J. Pure Appl. Math., 33 (3) (2002), 329-343.
6
[4] K. Balachandran and P. Prakash, Existence of solutions of nonlinear fuzzy integral equations
7
in Banach spaces, Libertas Math., 21 (2001), 91-97.
8
[5] J. J. Buckley and T. Feuring, Fuzzy integral equations, J. Fuzzy Math., 10 (2002), 1011-1024.
9
[6] D. Dubois and H. Prade, Fundamentals of fuzzy sets, Springer Netherlands Publisher, 2000.
10
[7] M. Friedman, M. Ma and A. Kandel, On fuzzy integral equations, Fundam. Inform., 37
11
(1999), 89-99.
12
[8] S. G. Gal, Approximation theory in fuzzy setting, in: G. A. Anastassiou (Ed.), Handbook
13
of Analytic-Computational Methods in applied Mathematics, Chapman & Hall, CRC Press,
14
Boca Raton, London, New York, Washington DC, (2000), (Chapter 13).
15
[9] D. N. Georgiou and I. E. Kougias, On fuzzy Fredholm and Volterra integral equations, J.
16
Fuzzy Math., 9 (4) (2001), 943-951.
17
[10] D. N. Georgiou and I. E. Kougias, Bounded solutions for fuzzy integral equation, Int. J. Math.
18
Math. Sci., 31 (2) (2002), 109-114.
19
[11] R. Goetschel and W. Voxman, Elementary fuzzy calculus, Fuzzy Sets Syst., 18 (1986), 31-43.
20
[12] A. Karoui and A. Jawahdou, Existence and approximate Lp and continuous solutions of
21
nonlinear integral equations of the Hammerstein and Volterra types, Appl. Math. Comput.,
22
216 (2010), 2077-2091.
23
[13] J. Mordeson and W. Newman, Fuzzy integral equations, Inform. Sci., 81 (4) (1995), 215-229.
24
[14] J. J. Nieto and R. Rodriguez-lopez, Bounded solutions for fuzzy dierential and integral
25
equations, Chaos Solitons & Fractals, 27 (5) (2006), 1376-1386.
26
[15] J. Y. Park and J. U. Jeong, On the existence and uniquness of solutions of fuzzy Volterra-
27
Fredholm integral equation, Fuzzy Sets Syst., 115 (2000), 425-431.
28
[16] J. Y. Park and J. U. Jeong, A note on fuzzy integral equations, Fuzzy Sets Syst., 108 (1999),
29
[17] J. Y. Park, Y. C. Kwun and J. U. Jeong, Existence of solutions of fuzzy integral equations
30
in Banach spaces, Fuzzy Sets Syst., 72 (1995), 373-378.
31
[18] J. Y. Park, S. Y. Lee and J. U. Jeong, The approximate solutions of fuzzy functional integral
32
equation, Fuzzy Sets Syst., 110 (2000), 79-90.
33
[19] C. Wu and Z. Gong, On Henstock integral of fuzzy-number-valueed functions, Fuzzy Sets
34
Syst., 120 (2001), 523-532.
35
ORIGINAL_ARTICLE
Existence and uniqueness of the solution of fuzzy-valued integral equations of mixed type
In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results.
http://ijfs.usb.ac.ir/article_1984_9ce4534f838ac7a99de3ae4a02061f23.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
87
94
10.22111/ijfs.2015.1984
Fuzzy Volterra-Fredholm integral equation
Two-dimensional integral equation
Fuzzy integral equations of mixed type
Fuzzy valued function
R.
Ezzati
ezati@kiau.ac.ir
true
1
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
LEAD_AUTHOR
F.
Mokhtarnejad
fa_mokhtar@yahoo.com
true
2
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
AUTHOR
[1] S. Abbasbandy, E. Babolian, M. Alavi, Numerical method for solving linear Fredholm integral
1
equations of the second kind, Chaos Solitons Fractals, 31(1) (2007), 138-146.
2
[2] O. A. Anastassiou and S. G. Gal, On a fuzzy trigonometric approximation theorem of
3
Weierstrass-type, Journal of Fuzzy Mathmatics, Los Angles, 9(3) (2001), 701-708.
4
[3] M. A. F. Araghi and N. Parandin, Numerical solution of fuzzy Fredholm integral equations
5
by the Lagrange interpolation based on the extension principle, Soft Computing, 15 (2011),
6
2449-2456.
7
[4] H. Attari and A. Yazdani, A computational method for fuzzy Volterra-Fredholm integarl equa-
8
tions, Fuzzy Information and Engineering, 2 (2011), 147-156.
9
[5] R. J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl., 12 (1965), 1-12.
10
[6] K. Balachandran and K. Kanagarajan, Existence of solutions of general nonlinear fuzzy Volter-
11
raFredholm integral equations, J. Appl. Math. Stoch. Anal., 3 (2005), 333-343.
12
[7] K. Balachandran and P. Prakash, Existence of solutions of nonlinear fuzzy VolterraFredholm
13
integral equations, Indian J. Pure Appl. Math., 33 (2002), 329-343.
14
[8] A. M. Bica, Error estimation in the approximation of the solution of nonlinear fuzzy Fredholm
15
integral equations, Information Sciences, 178 (2008), 1279-1292.
16
[9] A. M. Bica and C. Popescu, Approximating the solution of nonlinear Hammerstein fuzzy
17
integral equations, Fuzzy Sets and Systems, doi.org/10.1016/j.fss.2013.08.005.
18
[10] D. Dubois and H. Prade, Towards fuzzy dierential calculus, Fuzzy Sets and Systems, 8
19
(1982), 1-17.
20
[11] R. Ezzati and S. Ziari, Numerical solution and error estimation of fuzzy Fredholm integral
21
equation using fuzzy Bernstein polynomials, Australian Journal of Basic and Applied Sciences,
22
5(9) (2011), 2072-2082.
23
[12] R. Goetschel and W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986),
24
[13] O. Kaleva, Fuzzy dirential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.
25
[14] A. Molabahrami, A. Shidfar and A. Ghyasi, An analytical method for solving linear Fredholm
26
fuzzy integral equations of the second kind, Computers and Mathematics with Applications,
27
61(9) (2011), 2754-2761.
28
[15] J. Mordeson and W. Newman, Fuzzy integral equations, Information Sciences, 87 (1995),
29
[16] S. Nanda, On integration of fuzzy mapping, Fuzzy Sets and Systems, 32 (1989), 95-101.
30
[17] J. Y. Park, S. J. Lee and J. U. Jeong, On the existence and uniqueness of solutions of fuzzy
31
VolterraFredholm integral equations, Fuzzy sets and systems, 115 (2000), 425-431.
32
[18] M. L. Puri and D. A. Ralescu, Fuzzy random variables, J. Math. Anal.Appl., 114 (1986),
33
[19] D. Ralescu and G. Adams, The fuzzy integrals, J. Math. Anal. Appl., 75 (1980), 562-570.
34
[20] S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 (1987), 319-330.
35
[21] P. V. Subrahmaniam and S. K. Sudarsanam, On some fuzzy functional equations, Fuzzy Sets
36
and Systems, 64 (1994), 333-338.
37
[22] P. V. Subrahmaniam and S. K. Sudarsanam, A note on fuzzy Volterra integral equations,
38
Fuzzy Sets and Systems, 81 (1996), 237-240.
39
[23] M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Dissertation, Tokyo Inst. of
40
Tech., 1974.
41
[24] C. Wu and Z. Gong, On Henstock integral of fuzzy-number- valued functions, Fuzzy sets and
42
systems, 120 (2001), 523-532.
43
[25] Z. Wang, The autocontinuity of set-function and the fuzzy integral, J. Math. Anal. Appl., 99
44
(1984), 195-218.
45
[26] H. C.Wu, The fuzzy Riemann integral and its numerical integration, Fuzzy Sets and Systems,
46
110 (2000), 1-25.
47
[27] L. A. Zadeh, A fuzzy-set-theoretic interpretation of linguistic hedges, Journal of Cybernetics,
48
2 (1972), 4-34.
49
[28] L. A. Zadeh, The concept of the linguistic variable and its application to approximate rea-
50
soning, Information Sciences, 8 (1975), 199-249.
51
[29] S. Ziari, R. Ezzati and S. Abbasbandy, Numerical solution of linear fuzzy fredholm inte-
52
gral equations of the second kind using fuzzy haar wavelet, Communications in Computer and
53
Information Science, 299 (2012), 79-89.
54
ORIGINAL_ARTICLE
Fuzzy resolvent equation with $H(cdot,cdot)$-$phi$-$eta$-accretive operator in Banach spaces
In this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $H(cdot,cdot)$-$phi$-$eta$-accretive operator in real uniformly smooth Banach spaces. It is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. This equivalence is used to define an iterative algorithm for solving fuzzy resolvent equation. Some examples are given.
http://ijfs.usb.ac.ir/article_1985_86f566343f7b89986c214aecb2f7d718.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
95
106
10.22111/ijfs.2015.1985
Fuzzy variational-like inclusion
Fuzzy resolvent equation
$H(cdot
cdot)$-$phi$-$eta$-accretive operator
algorithm
Fixed point
Rais
Ahmad
raisain_123@rediffmail.com
true
1
Department of Mathematics, Aligarh Muslim University, Aligarh
202002, India
Department of Mathematics, Aligarh Muslim University, Aligarh
202002, India
Department of Mathematics, Aligarh Muslim University, Aligarh
202002, India
LEAD_AUTHOR
Mohd
Dilshad
mdilshaad@gmail.com
true
2
Department of Mathematics, Aligarh Muslim University, Aligarh
202002, India
Department of Mathematics, Aligarh Muslim University, Aligarh
202002, India
Department of Mathematics, Aligarh Muslim University, Aligarh
202002, India
AUTHOR
[1] Q. H. Ansari, Certain problems concerning variational inequalities, Ph.D Thesis, Aligarh
1
Muslim University, Aligarh, India, 1988.
2
[2] S. S. Chang, Fuzzy quasi-variational inclusions in Banach spaces, Appl. Math. Comput., 145
3
(2003), 805-819.
4
[3] S. S. Chang, Y. Zhu, On variational inequalities for fuzzy mappings, Fuzzy Sets and Systems,
5
32 (1989), 359-367.
6
[4] H. X. Dai, Generalized mixed variational-like inequalities with fuzzy mappings, J. Comput.
7
Appl. Math., 224 (2009), 20-28.
8
[5] X. P. Ding and J. Y. Park, A new class of generalized nonlinear implicit quasivariational
9
inclusions with fuzzy mappings, J. Comp. Math. Appl., 138 (2002) 249-257.
10
[6] X. P. Ding, Algorithm of solutions for mixed implicit quasi-variational inequalities with fuzzy
11
mappings, Comput. Math. Appl., 38 (1999), 231-241.
12
[7] C. F. Hu, Solving variational inequalities in fuzzy environment, J. Math. Anal., 249 (2000),
13
[8] P. Kumam and N. Petrol, Mixed variational-like inequality for fuzzy mappings in re
14
Banach spaces, J. Inequal. Appl., 2009 (2009), 1-15.
15
[9] Z. Liu, L. Debnath, S. M. Kang and J. S. Ume, Generalized mixed quasi-variational inclusions
16
and generalized mixed resolvent equations for fuzzy mappings, Appl. Math. Comput., 149
17
(2004), 879-891.
18
[10] B. S. Lee, M. F. Khan, Salahuddin, Fuzzy nonlinear set-valued variational inclusions, Com-
19
put. Math. Appl., 60 (2010), 1768-1775.
20
[11] Jr. S. B. Nadler, Multivalued contraction mappings, Pacic. J. Math., 30 (1969), 475-488.
21
[12] M. A. Noor, Variational inequalities for fuzzy mappings (II), Fuzzy Sets and System, 110
22
(2000) 101-108.
23
[13] Z. Wu and J. Xu, Generalized convex fuzzy mappings and fuzzy variational-like inequalities,
24
Fuzzy Sets and Systems, 160(11) (2009), 1590-1619.
25
[14] H. K. Xu, Inequalities in Banach spaces and applications, Nonlinear Analysis, Theory Meth-
26
ods and Applications, 16(12) (1991), 1127-1138.
27
[15] L. A. Zadeh, Fuzzy Sets, Inform. Contr., 8 (1965), 338-353.
28
[16] Y. Z. Zou and N. J. Huang, H(; )-accretive operator with an application for solving varia-
29
tional inclusions in Banach spaces, Appl. Math. Comput., 204 (2008), 809-816.
30
ORIGINAL_ARTICLE
Classifying fuzzy normal subgroups of\ finite groups
In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.
http://ijfs.usb.ac.ir/article_1986_41edad298512bef030d02e273bcb6a1c.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
107
115
10.22111/ijfs.2015.1986
Fuzzy normal subgroups
Chains of normal
subgroups
Maximal chains of normal subgroups
Symmetric groups
Dihedral groups
Marius
Tarnauceanu
tarnauc@uaic.ro
true
1
Faculty of Mathematics, "Al.I. Cuza" University, Iasi, Romania
Faculty of Mathematics, "Al.I. Cuza" University, Iasi, Romania
Faculty of Mathematics, "Al.I. Cuza" University, Iasi, Romania
LEAD_AUTHOR
[1] N. Ajmal and K.V. Thomas, The lattice of fuzzy normal subgroups is modu-lar, Inform. Sci.
1
83 (1995), 199{209.
2
[2] G. Gratzer, General lattice theory, Academic Press, New York, 1978.
3
[3] T. Head, A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and
4
Systems 73 (1995), 349-358; 79 (1996), 277{278.
5
[4] M. Mashinchi and M. Mukaidono, A classication of fuzzy subgroups, Ninth Fuzzy System
6
Symposium, Sapporo, Japan, (1992), 649{652.
7
[5] M. Mashinchi and M. Mukaidono, On fuzzy subgroups classication, Research Report of Meiji
8
Univ., 9 (1993), 31{36.
9
[6] J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, Fuzzy group theory, Springer Verlag, Berlin,
10
[7] V. Murali and B. B. Makamba, Normality and congruence in fuzzy subgroups, Inform. Sci.,
11
59 (1992), 121{129.
12
[8] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups, I, Fuzzy Sets and
13
Systems, 123 (2001), 259{264.
14
[9] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups, II, Fuzzy Sets and
15
Systems, 136 (2003), 93{104.
16
[10] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups, III, Int. J. Math. Sci.,
17
36 (2003), 2303{2313.
18
[11] V. Murali and B. B. Makamba, Counting the number of fuzzy subgroups of an abelian group
19
of order pnqm, Fuzzy Sets and Systems, 144 (2004), 459{470.
20
[12] V. Murali and B. B. Makamba, Fuzzy subgroups of nite abelian groups, FJMS, 14 (2004),
21
[13] R. Schmidt, Subgroup lattices of groups, de Gruyter Expositions in Mathematics 14, de
22
Gruyter, Berlin, 1994.
23
[14] M. Suzuki, Group theory, I, II, Springer Verlag, Berlin, (1982), (1986).
24
[15] M. Stefanescu and M. Tarnauceanu, Counting maximal chains of subgroups of nite nilpotent
25
groups, Carpathian J. Math., 25 (2009), 119{127.
26
[16] M. Tarnauceanu and L. Bentea, On the number of fuzzy subgroups of nite abelian groups,
27
Fuzzy Sets and Systems, doi: 10.1016/j.fss.2007.11.014, 159 (2008), 1084{1096.
28
[17] A. C. Volf, Counting fuzzy subgroups and chains of subgroups, Fuzzy Systems & Articial
29
Intelligence, 10 (2004), 191{200.
30
ORIGINAL_ARTICLE
Numerical solutions of nonlinear fuzzy Fredholm integro-differential equations of\ the second kind
In this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy Fredholmintegro-differential equation of the second kindis proposed. This paper presents a method based on Newton-Cotesmethods with positive coefficient. Then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an iterativeapproach.
http://ijfs.usb.ac.ir/article_1987_0cf46298a686ec0a96c8d069d42f41f9.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
117
127
10.22111/ijfs.2015.1987
Nonlinear fuzzy integro-differential equations
Newton-Cotes methods
M.
Mosleh
mosleh@iaufb.ac.ir
true
1
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran
LEAD_AUTHOR
M.
Otadi
mahmoodotadi@yahoo.com
true
2
Department of Mathematics, Firoozkooh Branch, Islamic Azad University,
Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad University,
Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad University,
Firoozkooh, Iran
AUTHOR
[1] S. Abbasbandy and T. Allahviranloo,Numerical solution of fuzzy dierential equation by
1
Runge-Kutta method, Nonlinear studies, 11(1) (2004), 117-129.
2
[2] S. Abbasbandy, T. Allaviranloo, O. Lopez-Pouso and J. J. Nieto, Numerical methods for
3
fuzzy dierential inclusions, Computers & mathematics with applications, 48(10-11) (2004),
4
1633-1641.
5
[3] S. Abbasbandy and B. Asady, Newtons method for solving fuzzy nonlinear equations, Applied
6
Mathematics and Computation, 159(2) (2004), 349-356.
7
[4] S. Abbasbandy, E. Babolian and M. Alavi, Numerical method for solving linear Fredholm
8
fuzzy integral equations of the second kind, Chaos Solitons & Fractals, 31(1) (2007), 138-
9
[5] S. Abbasbandy and A. Jafarian, Steepest descent method for solving fuzzy nonlinear equa-
10
tions, Applied Mathematics and Computation, 175(1) (2006), 581-589.
11
[6] S. Abbasbandy, J. J. Nieto and M. Alavi, Tuning of reachable set in one dimensional fuzzy
12
dierential inclusions, Chaos, Solitons & Fractals, 26(5) (2005), 1337-1341.
13
[7] T. Allahviranloo, S. Abbasbandy, N. Ahmady and E. Ahmady, Improved predictorcorrector
14
method for solving fuzzy initial value problems, Information Sciences, 179(7) (2009), 945-955.
15
[8] T. Allahviranloo, N. Ahmady and E. Ahmady, Numerical solution of fuzzy dierential equa-
16
tions by predictorcorrector method, Information Sciences, 177(7) (2007), 1633-1647.
17
[9] T. Allahviranloo, N. A. Kiani and M. Barkhordari,Toward the existence and uniqueness of
18
solutions of second-order fuzzy dierential equations, Information Sciences, 179(8) (2009),
19
1207-1215.
20
[10] T. Allahviranloo, N. A. Kiani and N. Motamedi, Solving fuzzy dierential equations by dif-
21
ferential transformation method, Information Sciences, 179(7) (2009), 956-966.
22
[11] K. E. Atkinson,An introduction to numerical analysis, New York: Wiley, 1987.
23
[12] E. Babolian, H. S. Goghary and S. Abbasbandy,Numerical solution of linear Fredholm fuzzy
24
integral equations of the second kind by Adomian method, Applied Mathematics and Com-
25
putation, 161(3) (2005), 733-744.
26
[13] C. T. H. Baker, A perspective on the numerical treatment of Volterra equations, J. Comput.
27
Appl. Math., 125(1-2) (2000), 217-249.
28
[14] P. Balasubramaniam and S. Muralisankar, Existence and uniqueness of fuzzy solution for the
29
nonlinear fuzzy integro-dierential equations, Applied mathematics letters, 14(4) (2001),
30
[15] M. I. Berenguer, D. Gamez, A. I. Garralda-Guillem, M. Ruiz Galan and M. C. Serrano Perez,
31
Biorthogonal systems for solving Volterra integral equation systems of the second kind, J.
32
Comput. Appl. Math., 235(7) (2011), 1875-1883.
33
[16] A. H. Borzabadi and O. S. Fard, A numerical scheme for a class of nonlinear Fredholm
34
integral equations of the second kind, Journal of Computational and Applied Mathematics,
35
232(2) (2009), 449-454.
36
[17] S. S. L. Chang and L. Zadeh,On fuzzy mapping and control, IEEE Trans. System Man
37
Cybernet, 2(1) (1972), 30-34.
38
[18] Y. Chen and T. Tang, Spectral methods for weakly singular Volterra integral equations with
39
smooth solutions, J. Comput. Appl. Math., 233(4) (2009), 938-950.
40
[19] D. Dubois and H. Prade, Operations on fuzzy numbers, J. Systems Sci., 9(6) (1978), 613-626.
41
[20] D. Dubois and H. Prade, Towards fuzzy dierential calculus, Fuzzy Sets and Systems, 8(1-3)
42
(1982), 1-7.
43
[21] M. Friedman, M. Ma and A. Kandel, Numerical solutions of fuzzy dierential and integral
44
equations, Fuzzy Sets and Systems, 106(1) (1999), 35-48.
45
[22] R. Goetschel and W. Vaxman, Elementary calculus, Fuzzy sets and Systems, 18(1) (1986),
46
[23] H. Hochstadt, Integral equations, New York: Wiley, 1973.
47
[24] A. Kaufmann and M. M. Gupta, Introduction Fuzzy Arithmetic, Van Nostrand Reinhold,
48
New York, 1985.
49
[25] O. Kaleva, Fuzzy dierential equations, Fuzzy Sets and Systems, 24(3) (1987), 301-317.
50
[26] J. P. Kauthen, Continuous time collocation method for Volterra-Fredholm integral equations,
51
Numer. Math., 56(1) (1989), 409-424.
52
[27] G. J. Klir, U. S. Clair and B. Yuan, Fuzzy set theory: foundations and applications, Prentice-
53
Hall Inc., 1997.
54
[28] H. Kwakernaak, Fuzzy random variables. Part I: denitions and theorems, Information Sci-
55
ences, 15(1) (1978), 129.
56
[29] P. Linz, Analytical and numerical methods for Volterra equations, SIAM, Philadelphia, PA,
57
[30] M. T. Malinowski,On random fuzzy dierential equations, Fuzzy Sets and Systems, 160(21)
58
(2009), 3152-3165.
59
[31] M. T. Malinowski, Existence theorems for solutions to random fuzzy dierential equations,
60
Nonlinear Analysis: Theory, Methods & Applications, 73(6) (2010), 1515-1532.
61
[32] M. T. Malinowski, Random fuzzy dierential equations under generalized Lipschitz condition,
62
Nonlinear Analysis: Real World Applications, 13(2) (2012), 860-881.
63
[33] M. Mosleh and M. Otadi, Simulation and evaluation of fuzzy dierential equations by fuzzy
64
neural network, Applied Soft Computing, 12(9) (2012), 2817-2827.
65
[34] M. Mosleh and M. Otadi, Minimal solution of fuzzy linear system of dierential equations,
66
Neural Computing and Applications, 21(1) (2012), 329-336.
67
[35] M. L. Puri and D. Ralescu, Fuzzy random variables, Journal of Mathematical Analysis and
68
Applications, 114(2) (1986), 409-422.
69
[36] M. L. Puri and D. Ralescu, Dierentials of fuzzy functions, Journal of Mathematical Analysis
70
and Applications, 91(2) (1983), 552-558.
71
[37] H. H. Sorkun and S. Yalcinbas, Approximate solutions of linear Volterra integral equation
72
systems with variable coecients, Applied Mathematical Modelling, 34(11) (2010), 3451-
73
[38] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, New York,
74
[39] W. Congxin and M. Ming, Embedding problem of fuzzy number space, Fuzzy Sets and Systems,
75
45(2) (1992), 189-202.
76
[40] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning,
77
Information Sciences, 8(3) (1975), 199-249.
78
ORIGINAL_ARTICLE
Generated $textbf{textit{L}}$-subgroup of an $textbf{textit{L}}$-group
In this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $L$-setting. This construction is illustrated by an example. We also prove that for an $L$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $L$-subset provided the given $L$-subset possesses sup-property.
http://ijfs.usb.ac.ir/article_1988_1a3e3cd32dc886edfac691c6b2b2e9e0.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
129
136
10.22111/ijfs.2015.1988
$L$-algebra
$L$-subgroup
Normal $L$-subgroup
Generated $L$-subgroup
Naseem
Ajmal
nasajmal@yahoo.com
true
1
Department of Mathematics, Zakir Husain Delhi College,, J.N.Marg,
University of Delhi, Delhi-110006, India
Department of Mathematics, Zakir Husain Delhi College,, J.N.Marg,
University of Delhi, Delhi-110006, India
Department of Mathematics, Zakir Husain Delhi College,, J.N.Marg,
University of Delhi, Delhi-110006, India
AUTHOR
Iffat
Jahan
ij.umar@yahoo.com
true
2
Department of Mathematics, Ramjas College,, University of Delhi,,
Delhi-110007, India
Department of Mathematics, Ramjas College,, University of Delhi,,
Delhi-110007, India
Department of Mathematics, Ramjas College,, University of Delhi,,
Delhi-110007, India
LEAD_AUTHOR
[1] N. Ajmal, Set product and fuzzy subgroups, Proc. IFSA World Cong., Belgium, ( 1991 ), 3-7.
1
[2] N. Ajmal, The lattice of fuzzy normal subgroups is modular, Inform. Sci., 83 (3-4) (1995),
2
[3] N. Ajmal, Fuzzy groups with sup property, Inform. Sci., 93 (3-4) (1996), 247-264.
3
[4] N. Ajmal and K. V. Thomas, Fuzzy lattices, Inform. Sci., 79 (3-4) (1994), 271-291.
4
[5] N. Ajmal and K. V. Thomas, The lattices of fuzzy ideals of a ring, Fuzzy Sets and Systems,
5
74 (3) (1995), 371-379.
6
[6] N. Ajmal and K. V. Thomas, A complete study of the lattices of fuzzy congruences and fuzzy
7
normal subgroups, Inform. Sci., 82 (3-4) (1995), 197-218.
8
[7] N. Ajmal and K. V. Thomas, The join of fuzzy algebraic substructures of a group and their
9
lattices, Fuzzy Sets and Systems, 99 (2) (1998), 213-224.
10
[8] N. Ajmal and K. V. Thomas, A new blueprint for fuzzication : An application to lattices
11
of fuzzy congruences, J. Fuzzy Math., 7 (2) (1999), 499-512.
12
[9] N. Ajmal and K. V. Thomas, Fuzzy latticesI, J. Fuzzy Math., 10 (2) (2002), 255-274.
13
[10] N. Ajmal and K. V. Thomas, Fuzzy lattices II, J. Fuzzy Math., 10 (2) (2002), 275-296.
14
[11] N. Ajmal and Sunil Kumar, Lattices of subalgebras in the category of fuzzy groups, Fuzzy
15
Mathematics, 10 (2) (2002), 359-369.
16
[12] N. Ajmal and I. Jahan, A study of normal fuzzy subgroups and characteristic fuzzy subgroups
17
of a fuzzy group, Fuzzy Information and Engineering, 4 (2) (2012), 123-143.
18
[13] N. Ajmal and A. Jain, Some constructions of the join of fuzzy subgroups and certain lattices
19
of fuzzy subgroups with sup property, Inform. Sci., 179 (23) (2009), 4070-4082.
20
[14] L. Biacino and G. Gerla, Closure systems and L-subalgebras, Inform. Sci., 33 (3) (1984),
21
[15] V. N. Dixit, R. Kumar and N. Ajmal, Level subgroups and union of fuzzy subgroups, Fuzzy
22
Sets and Systems, 37 (3) (1990), 359-371.
23
[16] J. A. Goguen, L fuzzy sets, J. Math. Anal. Appl., 18 (1) (1967), 145-174.
24
[17] T. Head,A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and
25
Systems, 73 (3) (1995), 349-358.
26
[18] R. Kumar, Fuzzy subgroups, fuzzy ideals and fuzzy cosets : Some properties, Fuzzy Sets and
27
Systems, 48 (2) (1992), 267-271.
28
[19] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (2) (1982),
29
[20] M. Mashinchi, S. Salili and M. M. Zahedi, Lattice structures on fuzzy subgroups, Bull. Iranian
30
Math. Soc., 18 (2) (1992), 17-29.
31
[21] S. Ray, Generated and cyclic fuzzy subgroups, Information Sciences, 69 (3) (1993), 185-200.
32
[22] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35(3)(1971), 512-517.
33
[23] N. Sultana and N. Ajmal, Generated fuzzy subgroups: a modication, Fuzzy Sets Systems,
34
107 (2) (1999), 241-243.
35
[24] Y. Yu, J. N. Mordeson and S. C. Cheng, Elements of algebra, lecture notes in fuzzy math-
36
ematics and computer science, Center for Research in Fuzzy Mathematics and Computer
37
Science, Creighton University, USA, 1994.
38
ORIGINAL_ARTICLE
A New Approach to Caristi's Fixed Point Theorem on Non-Archimedean Fuzzy Metric Spaces
In the present paper, we give a new approach to Caristi's fixed pointtheorem on non-Archimedean fuzzy metric spaces. For this we define anordinary metric $d$ using the non-Archimedean fuzzy metric $M$ on a nonemptyset $X$ and we establish some relationship between $(X,d)$ and $(X,M,ast )$%. Hence, we prove our result by considering the original Caristi's fixedpoint theorem.
http://ijfs.usb.ac.ir/article_1989_f8d6aae87a58b7c8804d05459ea70ac5.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
137
143
10.22111/ijfs.2015.1989
Fixed point
Caristi map
Fuzzy metric space
S.
Sedghi
sedghi.gh@qaemshahriau.ac.ir
true
1
Department of Mathematics, Qaemshahr Branch, Islamic Azad University,
Qaemshahr, Iran
Department of Mathematics, Qaemshahr Branch, Islamic Azad University,
Qaemshahr, Iran
Department of Mathematics, Qaemshahr Branch, Islamic Azad University,
Qaemshahr, Iran
AUTHOR
N.
Shobkolaei
nabi_shobe@yahoo.comg
true
2
Department of Mathematics, Babol Branch, Islamic Azad University,
Babol, Iran
Department of Mathematics, Babol Branch, Islamic Azad University,
Babol, Iran
Department of Mathematics, Babol Branch, Islamic Azad University,
Babol, Iran
AUTHOR
I.
Altun
ishakaltun@yahoo.com
true
3
Department of Mathematics, Faculty of Science and Arts, Kirikkale Uni-
versity, 71450 Yahsihan, Kirikkale, Turkey
Department of Mathematics, Faculty of Science and Arts, Kirikkale Uni-
versity, 71450 Yahsihan, Kirikkale, Turkey
Department of Mathematics, Faculty of Science and Arts, Kirikkale Uni-
versity, 71450 Yahsihan, Kirikkale, Turkey
LEAD_AUTHOR
[1] S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung and S. M. Kang, Coincidence point and
1
minimization theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 88 (1997), 119-128.
2
[2] Y. J. Cho, Fixed points in fuzzy metric spaces, Journal of Fuzzy Mathematics, 5 (1997),
3
[3] J. X. Fang, On xed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 46
4
(1992), 107-113.
5
[4] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,
6
64 (1994), 395-399.
7
[5] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389.
8
[6] V. Gregori and A. Sapena, On xed-point theorem in fuzzy metric spaces, Fuzzy Sets and
9
Systems, 125 (2002), 245-252.
10
[7] O. Hadzic and E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Academic
11
Publishers, Dordrecht, 2001.
12
[8] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
13
[9] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11
14
(1975), 326-334.
15
[10] D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems,
16
158 (2007) 915-921.
17
[11] D. Mihet, Fuzzy -contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets
18
and Systems, 159 (2008), 739-744.
19
[12] S. N. Mishra , S. N. Sharma and S. L. Singh, Common xed points of maps in fuzzy metric
20
spaces, Internat. J. Math. Math. Sci., 17 (1994), 253-258.
21
[13] V. Radu, Some remarks on the probabilistic contractions on fuzzy Menger spaces, In: The
22
Eighth International Conference on Appl. Math. Comput. Sci., Cluj-Napoca, 2002, Automat.
23
Comput. Appl. Math., 11 (2002), 125-131.
24
[14] B. Schweizer and A. Sklar, Statistical metric spaces, Pacic Journal of Mathematics, 10
25
(1960), 313-334.
26
ORIGINAL_ARTICLE
Persian-translation vol. 12, no.2, April 2015
http://ijfs.usb.ac.ir/article_2649_c4b7501bfa4858c0dbecc382a6043f85.pdf
2015-04-29T11:23:20
2018-02-21T11:23:20
147
157
10.22111/ijfs.2015.2649