ORIGINAL_ARTICLE
Cover vol. 9, no.1, February 2012
http://ijfs.usb.ac.ir/article_2816_9276302627a083223f091bfc721de91a.pdf
2012-02-01T11:23:20
2018-05-25T11:23:20
0
10.22111/ijfs.2012.2816
ORIGINAL_ARTICLE
APPLICATION OF TABU SEARCH FOR SOLVING THE
BI-OBJECTIVE WAREHOUSE PROBLEM IN
A FUZZY ENVIRONMENT
The bi-objective warehouse problem in a crisp environment is often not eective in dealing with the imprecision or vagueness in the values of the problem parameters. To deal with such situations, several researchers have proposed that the parameters be represented as fuzzy numbers. We describe a new algorithm for fuzzy bi-objective warehouse problem using a ranking function followed by an application of tabu search. The method is illustrated on a numerical example, demonstrating the eectiveness of the tabu search method. Numerical results are compared for both fuzzy and crisp versions of the problem.
http://ijfs.usb.ac.ir/article_221_2400536ae1bcebd857003631acf8ca86.pdf
2012-02-10T11:23:20
2018-05-25T11:23:20
1
19
10.22111/ijfs.2012.221
Trapezoidal fuzzy numbers
Bi-objective warehouse problem
Ecient
solution
Tabu search
Anila
Gupta
anilasingal@gmail.com
true
1
School of Mathematics and Computer Applications, Thapar Univer-
sity, Patiala-147004, India
School of Mathematics and Computer Applications, Thapar Univer-
sity, Patiala-147004, India
School of Mathematics and Computer Applications, Thapar Univer-
sity, Patiala-147004, India
LEAD_AUTHOR
Amit
Kumar
amit rs iitr@yahoo.com
true
2
School of Mathematics and Computer Applications, Thapar University,
Patiala-147004, India
School of Mathematics and Computer Applications, Thapar University,
Patiala-147004, India
School of Mathematics and Computer Applications, Thapar University,
Patiala-147004, India
AUTHOR
Mahesh
Kumar Sharma
mksharma@thapar.edu
true
3
School of Mathematics and Computer Applications, Thapar
University, Patiala-147004, India
School of Mathematics and Computer Applications, Thapar
University, Patiala-147004, India
School of Mathematics and Computer Applications, Thapar
University, Patiala-147004, India
AUTHOR
bibitem{37-43}
1
S. Abbasbandy and M. Alavi, {it A method for solving fuzzy linear
2
systems}, Iranian Journal of Fuzzy Systems, textbf{2(2)} (2005),
3
bibitem{19-32}
4
T. Allahviranloo, F. H. Lotfi, M. K. Kiasary, N. A. Kiani and L.
5
Alizadeh, {it Solving fully fuzzy linear programming problem by the
6
ranking function}, Applied Mathematical Sciences, {bf
7
2}textbf{(1)} (2008), 19-32.
8
bibitem{141-164}
9
R. E. Bellman and L. A. Zadeh, {it Decision making in a fuzzy
10
environment}, Management Science, {bf 17}textbf{(4)} (1970),
11
bibitem{277-287}
12
U. Bhattacharya, J. R. Rao and R. N. Tiwari, {it Fuzzy
13
multi-criteria facility location problem}, Fuzzy Sets and Systems,
14
{bf 51}textbf{(3)} (1992), 277-287.
15
bibitem{1993}
16
U. Bhattacharya, J. R. Rao and R. N. Tiwari, {it Bi-criteria multi
17
facility location problem in Fuzzy environment}, Fuzzy Sets and
18
Systems, textbf{56}textbf{(2)} (1993), 145-153.
19
bibitem{35-53}
20
J. Buckley and T. Feuring, {it Evolutionary algorithm solution to
21
fuzzy problems: fuzzy linear programming}, Fuzzy Sets and Systems,
22
textbf{109}textbf{(1)} (2000), 35-53.
23
bibitem{1751-1763}
24
R. Caballero, M. Gonzalez, F. M. Guerrero, J. Molina and C.
25
Paralera, {it Solving a multiobjective location routing problem
26
with a metaheuristic based on tabu search: application to a real
27
case in Andalusia}, European Journal of Operational Research,
28
textbf{177}textbf{(3)} (2007), 1751-1763.
29
bibitem{1-21}
30
J. M. Cadenas and J. L. Verdegay, {it A primer on fuzzy
31
optimization models and methods}, Iranian Journal of Fuzzy Systems,
32
textbf{3(1)} (2006), 1-21.
33
bibitem{145-153}
34
L. M. Campos Ibanez and A. Gonzalez Munoz, {it A subjective
35
approach for ranking fuzzy number}, Fuzzy Sets and Systems,
36
textbf{29}textbf{(2)} (1989), 145-153.
37
bibitem{1-11}
38
L. Campos and J. L. Verdegay, {it Linear programming problems and
39
ranking of fuzzy numbers}, Fuzzy Sets and Systems,
40
textbf{32}textbf{(1)} (1989), 1-11.
41
bibitem{1289-1297}
42
S. P. Chen and Y. J. Hsueh, {it A simple approach to fuzzy critical
43
path analysis in project networks}, Applied Mathematical
44
Modelling, textbf{32}textbf{(7)} (2008), 1289-1297.
45
bibitem{687-702}
46
T. C. Chu, {it Facility location selection using fuzzy TOPSIS under
47
group decisions}, International Journal of Uncertainty, Fuzziness
48
and Knowledge-Based Systems, textbf{10}textbf{(6)} (2002),
49
bibitem{331-343}
50
L. Cooper, {it Location-allocation problems}, Operations Research, textbf{11}textbf{(3)} (1963),
51
bibitem{149-154}
52
J. Darzentas, {it A discrete location model with fuzzy
53
accessibility measures}, Fuzzy Sets and Systems,
54
textbf{23}textbf{(1)} (1987), 149-154.
55
bibitem{1689-1709}
56
R. Z. Farahani, M. SteadieSeifi and N. Asgari, {it Multiple
57
criteria facility location problems: a survey}, Applied Mathematical
58
Modelling, textbf{34}textbf{(7)} (2010), 1689-1709.
59
bibitem{305-315}
60
K. Ganesan and P. Veeramani, {it Fuzzy linear programs with
61
trapezoidal fuzzy Numbers}, Annals of Operations Research,
62
textbf{143}textbf{(1)} (2006), 305-315.
63
bibitem{799-809}
64
M. Gen and A. Syarif, {it Hybrid genetic algorithm for multi-time
65
period production/distribution planning}, Computers and Industrial
66
Engineering, textbf{48}textbf{(4)} (2005), 799-809.
67
bibitem{190-206}
68
F. Glover, {it Tabu search-part I}, ORSA Journal on Computing,
69
textbf{1}textbf{(3)} (1989), 190-206.
70
bibitem{4-32}
71
F. Glover, {it Tabu search-part II}, ORSA Journal on Computing,
72
textbf{2}textbf{(1)} (1990), 4-32.
73
bibitem{21-35}
74
T. S. Hale and C. R. Moberg, {it Location science research: a review}, Annals of Operations Research,
75
textbf{123}textbf{(1-4)} (2003), 21-35.
76
bibitem{135-153}
77
C. Kahraman, D. Ruan and I. Dogan, {it Fuzzy group decision-making
78
for facility location selection}, Information Sciences,
79
textbf{157} (2003), 135-153.
80
bibitem{1991}
81
A. Kaufmann and M. M. Gupta, {it Introduction to fuzzy arithmetics:
82
theory and applications}, New York, Van Nostrand Reinhold, 1991.
83
bibitem{143-150}
84
K. Kim and K. S. Park, {it Ranking fuzzy number with index of
85
optimism}, Fuzzy Sets and Systems, textbf{35}textbf{(2)} (1990),
86
bibitem{1833-1849}
87
C. K. Y. Lin and R. C. W. Kwok, {it Multi-objective metaheuristics
88
for a location-routing Problem with multiple use of vehicles on real
89
data and simulated data}, European Journal of Operational Research,
90
textbf{175}textbf{(3)} (2006), 1833-1849.
91
bibitem{601-606}
92
F. T. Lin, {it Time-cost tradeoff in fuzzy critical path analysis
93
based on $(1-alpha)times 100%$ confidence-interval estimates},
94
IEEE International Conference on Systems, Man and Cybernetics,
95
(2008), 601-606.
96
bibitem{247-255}
97
T. S. Liou and M. J. Wang, {it Ranking fuzzy numbers with integral
98
value}, Fuzzy Sets and Systems, textbf{50}textbf{(3)} (1992),
99
bibitem{206-216}
100
N. Mahdavi-Amiri and S. H. Nasseri, {it Duality in fuzzy number
101
linear programming by the use of a certain linear ranking function},
102
Applied Mathematics and Computation, textbf{180}textbf{(1)} (2006),
103
bibitem{643-659}
104
G. S. Mahapatra and T. K. Roy, {it Fuzzy multi-objective
105
mathematical programming on reliability optimization model}, Applied
106
Mathematics and Computation, textbf{174(1)} (2006), 643-659.
107
bibitem{35-45}
108
H. R. Maleki and M. Mashinchi, {it Multiobjective geometric
109
programming with fuzzy parameters}, International Journal of
110
Information Science and Technology, textbf{5(2)} (2007), 35-45.
111
bibitem{21-33}
112
H. R. Maleki, M. Tata and M. Mashinchi, {it Linear programming with
113
fuzzy variables}, Fuzzy Sets and Systems, textbf{109(1)} (2000),
114
bibitem{401-412}
115
M. T. Melo, S. Nickel and F. Saldanha-da-Gama, {it Facility
116
location and supply chain management-a review}, European Journal
117
of Operational Research, textbf{196(2)} (2009), 401-412.
118
bibitem{9-20}
119
H. Mishmast Nehi, H. R. Maleki and M. Mashinchi, {it Solving fuzzy
120
number linear programming problem by lexicographic ranking
121
function}, Italian J. Pure Appl. Math., textbf{16} (2004), 9-20.
122
bibitem{618-628}
123
R. Narasimhan, {it A fuzzy subset characterization of a
124
site-selection problem}, Decision Sciences, textbf{10(4)} (1979),
125
bibitem{1469-1480}
126
A. A. Noora and P. Karami, {it Ranking functions and its
127
application to fuzzy DEA}, International Mathematical Forum,
128
textbf{3(30)} (2008), 1469-1480.
129
bibitem{129-140}
130
S. Okada and T. Soper, {it A shortest path problem on a network
131
with fuzzy arc lengths}, Fuzzy Sets and Systems,
132
textbf{109(1)} (2000), 129-140.
133
bibitem{79-90}
134
P. Pandian and G. Natarajan, {it A new algorithm for finding a
135
fuzzy optimal solution for fuzzy transportation problems}, Applied
136
Mathematical Sciences, textbf{4(2)} (2010), 79-90.
137
bibitem{449-460}
138
S. Prakash, M. K. Sharma and A. Singh, {it Selection of warehouse
139
sites for clustering ration shops to them with two objectives
140
through a heuristic algorithm incorporating tabu search}, Opsearch,
141
textbf{46(4)} (2010), 449-460.
142
bibitem{76-84}
143
T. Uno and H. Katagiri, {it Single and multi-objective defensive
144
location problems on a network}, European Journal of Operational
145
Research, textbf{188(1)} (2008), 76-84.
146
bibitem{360-365}
147
J. R. Yu and T. H. Wei, {it Solving the fuzzy shortest path
148
problem by using a linear programming}, Journal of the Chinese
149
Institute of Industrial Engineers, textbf{24(5)} (2007), 360-365.
150
bibitem{338-353}
151
L. A. Zadeh, {it Fuzzy sets}, Information and Control,
152
textbf{8(3)} (1965), 338-353.
153
bibitem{45-55}
154
H. J. Zimmermann, {it Fuzzy programming and linear programming with
155
several objective functions}, Fuzzy Sets and Systems,
156
textbf{1(1)} (1978), 45-55.
157
ORIGINAL_ARTICLE
FUZZY GRAVITATIONAL SEARCH ALGORITHM AN
APPROACH FOR DATA MINING
The concept of intelligently controlling the search process of gravitational search algorithm (GSA) is introduced to develop a novel data mining technique. The proposed method is called fuzzy GSA miner (FGSA-miner). At first a fuzzy controller is designed for adaptively controlling the gravitational coefficient and the number of effective objects, as two important parameters which play major roles on search process of GSA. Then the improved GSA (namely Fuzzy-GSA) is employed to construct a novel data mining algorithm for classification rule discovery from reference data sets. Extensive experimental results on different benchmarks and a practical pattern recognition problem with nonlinear, overlapping class boundaries and different feature space dimensions are provided to show the powerfulness of the proposed method. The comparative results illustrate that performance of the proposed FGSA-miner considerably outperforms the standard GSA. Also it is shown that the performance of the FGSA-miner is comparable to, sometimes better than those of the CN2 (a traditional data mining method) and similar approach which have been designed based on other swarm intelligence algorithms (ant colony optimization and particle swarm optimization) and evolutionary algorithm (genetic algorithm).
http://ijfs.usb.ac.ir/article_223_8aafe00e6254010a39a49144e87459eb.pdf
2012-02-10T11:23:20
2018-05-25T11:23:20
21
37
10.22111/ijfs.2012.223
Gravitational search algorithm
Fuzzy controller
Data mining
Rule
based classifier
Seyed Hamid
Zahiri
hzahiri@@birjand.ac.ir
true
1
Department of Electrical Engineering, Faculty of Engineering,
Birjand University, Birjand, Iran
Department of Electrical Engineering, Faculty of Engineering,
Birjand University, Birjand, Iran
Department of Electrical Engineering, Faculty of Engineering,
Birjand University, Birjand, Iran
LEAD_AUTHOR
[1] P. Clark and T. Niblet, The CN2 induction algorithm, Mach. Learn., 3(4) (1989), 261-283.
1
[2] A. E. Eiben, R. Hinterding and Z. Michalewicz, Parameter control in evolutionary algorithms,
2
IEEE Transactions on Evolutionary Computation, 3(2) (1999), 124-141.
3
[3] A. Freitas, A survey of evolutionary algorithms for data mining and knowledge discovery, In:
4
A. Ghosh, S. Tsutsui, eds., Advances in Evolutionary Computation, Springer-Verlag, 2001.
5
[4] R. Kohavi and M. Sahami, Error-based and entropy-based discretization of continuous features,
6
Proc. 2nd Int. Conf. Knowledge Discovery and Data Mining, Menlo Park, CA, (1996),
7
[5] B. Liu, H. A. Abbass and B. Mckay Classification rule discovery with ant colony optimization,
8
In Proceeding of the IEEE/WIC International Conference on Intelligent Agent Technology,
9
Beijing, China, (2003), 83-88.
10
[6] P. M. Mary and S. Marimuthu, Minimum time swing up and stabilization ofrotary inverted
11
pendulum using pulse step control, Iranian Journal of Fuzzy Systems, 6(3) (2009), 1-15.
12
[7] E. Mehdizadeh, S. Sadi-nezhad and R. Tavakkoli-moghaddam, Optimization of fuzzy clustering
13
criteria by a hybrid PSO and fuzzy c-mean clustering algorithm, Iranian Journal of
14
Fuzzy Systems, 5(1) (2008), 1-14.
15
[8] F. Moayedi, R. Boostani, A. R. Kazemi, S. Katebi and E. Dashti, Subclass fuzzy-svm classifier
16
an efficient method to enhance the mass detection in mammograms, Iranian Journal of Fuzzy
17
Systems, 7(1) (2010), 15-31.
18
[9] R. S. Parpinelli, H. S. Lopes and A. A. Freitas, Data mining with an ant colony optimization
19
algorithm, IEEE Transactions on evolutionary computing, 6(4) (2002), 321-332.
20
[10] E. Rashedi, H. Nezamabadi-pour, and S. Saryazdi, GSA: A Gravitational Search Algorithm,
21
Information Sciences, 179(13) (2009), 2232-2248.
22
[11] R. Sarkar, H. abbas and C. Newton, Introducing data mining and knowledge discovery,
23
Heuristic and Optimization for Knowledge Discovery, Idea Group Publishing, (2008), 1-23.
24
[12] Y. Shi, R. Eberhart and Y. Chen, Implementation of evolutionary fuzzy systems, IEEE
25
Transactions On Fuzzy Systems, 7(2) (1999), 109-119.
26
[13] T. Sousa, A Silva and A. Neves, Particle swarm based data mining algorithms for classification
27
tasks, Parallel Computing, 30(1) (2004), 767-783.
28
[14] M. Stenes and H. Robous, GA-fuzzy modeling and classification: complexity and performance,
29
IEEE Transactions on Fuzzy Systems, 8(5) (2000), 509-522.
30
[15] S. H. Zahiri, H. Zareie and M. R. Agha-ebrahimi, Automatic target recognition using jet
31
engine modulation on backscattered signals, In the Communication Proc. of 8’th Iranian
32
Conf. on Electrical Engineering, Isfahan, (1996), 296-303.
33
[16] S. H. Zahiri and S. A. Seyedin, Swarm intelligence based classifiers, Int. J. of the Franklin
34
Inst., 344(2) (2007), 362-376.
35
[17] S. H. Zahiri, H. Rajabi Mashhadi and S. A. Seyedin, Intelligent and robust genetic algorithm
36
based classifier, Iranian Journal of Electrical and Electronic Engineering, 1(3) (2005), 1-9.
37
ORIGINAL_ARTICLE
A NEW APPROACH TO STABILITY ANALYSIS OF FUZZY
RELATIONAL MODEL OF DYNAMIC SYSTEMS
This paper investigates the stability analysis of fuzzy relational dynamic systems. A new approach is introduced and a set of sufficient conditions is derived which sustains the unique globally asymptotically stable equilibrium point in a first-order fuzzy relational dynamic system with sumproduct fuzzy composition. This approach is also investigated for other types of fuzzy relational composition.
http://ijfs.usb.ac.ir/article_224_c42486dad4820bcdd105fb3f70d965ff.pdf
2012-02-10T11:23:20
2018-05-25T11:23:20
39
48
10.22111/ijfs.2012.224
Fuzzy relational dynamic system (FRDS)
Fuzzy relational model
(FRM)
Linguistic stability analysis
Fuzzy relational stability
Arya
Aghili Ashtiani
arya.aghili@aut.ac.ir
true
1
Department of Electrical Engineering, Amirkabir University
of Technology (AUT), P. O. Box 15914, Tehran, Iran
Department of Electrical Engineering, Amirkabir University
of Technology (AUT), P. O. Box 15914, Tehran, Iran
Department of Electrical Engineering, Amirkabir University
of Technology (AUT), P. O. Box 15914, Tehran, Iran
LEAD_AUTHOR
Sayyed Kamaloddin
Yadavar Nikravesh
nikravsh@aut.ac.ir
true
2
Department of Electrical Engineering, Amirk-
abir University of Technology (AUT), P. O. Box 15914, Tehran, Iran
Department of Electrical Engineering, Amirk-
abir University of Technology (AUT), P. O. Box 15914, Tehran, Iran
Department of Electrical Engineering, Amirk-
abir University of Technology (AUT), P. O. Box 15914, Tehran, Iran
AUTHOR
[1] J. M. Andjar and A. J. Barragn, A methodology to design stable nonlinear fuzzy control
1
systems, Fuzzy Sets and Systems, 154 (2005), 157-181.
2
[2] A. Aghili Ashtiani and M. B. Menhaj, Introducing a new pair of differentiable fuzzy norms
3
and its application to fuzzy relational function approximation, Proc. 10th Joint Conf. Information
4
Sciences, Salt Lake City, USA: World Scientific Publishing Co. ISBN: 978-981-270-
5
967-7, (2007), 1329-1336.
6
[3] A. Aghili Ashtiani and M. B. Menhaj, Numerical solution of fuzzy relational equations based
7
on smooth fuzzy norms, Soft Computing, 14(6) (2010), 545-557.
8
[4] X. Ban, X. Z. Gao, X. Huang and A. V. Vasilakos, Stability analysis of the simplest Takagi–
9
Sugeno fuzzy control system using circle criterion, Information Sciences, 177(20) (2007),
10
4387-4409.
11
[5] J. Chen and L. Chen, Study on stability of fuzzy closed-loop control systems, Fuzzy Sets and
12
Systems, 57(2) (1993), 159-168.
13
[6] T. Furuhashi, H. Kakami, J. Peters and W. Pedrycz, A stability analysis of fuzzy control
14
system using a generalized fuzzy petri net model, IEEE World Congress on Computational
15
Intelligence, (1998), 95-100.
16
[7] T. Hasegawa and T. Furuhashi, Stability analysis of fuzzy control systems simplified as a
17
discrete system, Int. J. Control and Cybernetics, 27(4) (1998), 565-577.
18
[8] K. Hirota, H. Nobuhara, K. Kawamoto and S. I. Yoshida On a lossy image compression/
19
reconstruction method based on fuzzy relational equation, Iranian Journal of Fuzzy Systems,
20
1(2) (2004), 33-42.
21
[9] J. B. Kiszka, M. M. Gupta and P. N. Nikiforuk, Energetic stability of fuzzy dynamic systems,
22
IEEE Transactions on Systems, Man and Cybernetics, 15 (1985), 783-792.
23
[10] A. Kandel, Y. Luo and Y. Q. Zhang, Stability analysis of fuzzy control systems, Fuzzy Sets
24
and Systems, 105 (1999), 33-48.
25
[11] C. Kolodziej and R. Priemer, Stability analysis of fuzzy systems, Journal of the Franklin
26
Institute, 336 (1999), 851-873.
27
[12] T. Leephakpreeda and C. Batur, Stability analysis of a fuzzy control system, Thammasat Int.
28
J. Science and Technology, 2(l) (1997), 1-5.
29
[13] W. Pedrycz, An identification algorithm in fuzzy relational systems, Fuzzy Sets and Systems,
30
13 (1984), 153-167.
31
[14] J. N. Ridley, I. S. Shaw and J. J. Kruger, Probabilistic fuzzy model for dynamic systems,
32
Electronics Letters, 24 (1988), 890-892.
33
[15] A. A. Suratgar and S. K. Y. Nikravesh, A new method for linguistic modeling with stability
34
analysis and applications, Intelligent automation and soft computing, 15(3) (2009), 329-342.
35
[16] A. A. Suratgar and S. K. Y. Nikravesh, Potential energy based stability analysis of fuzzy
36
linguistic systems, Iranian Journal of Fuzzy Systems, 2(1) (2005), 67-74.
37
[17] A. A. Suratgar and S. K. Y. Nikravesh, Necessary and sufficient conditions for asymptotic
38
stability of a class of applied nonlinear dynamical systems, Proc. 10th IEEE Int. Conf. Electronics,
39
Circuits and Systems, 3 (ICECS 2003), 1062-1065.
40
[18] A. A. Suratgar and S. K. Y. Nikravesh, A new sufficient condition for stability of fuzzy
41
systems, Proc. of Iranian Conf. Electrical Engineering, (2002), 441-445.
42
[19] E. Sanchez, Resolution of composite fuzzy relation equations, Information and Control, 30(1)
43
(1976), 38-48.
44
[20] T. ˇ Sijak, S. Teˇsnjak and O. Kuljaca, Stability analysis of fuzzy control system using describing
45
function method, Proc. 9th Mediterranean Conf. Control and Automation, 2001.
46
ORIGINAL_ARTICLE
ON SOLUTION OF A CLASS OF FUZZY BVPs
This paper investigates the existence and uniqueness of solutions to rst-order nonlinear boundary value problems (BVPs) involving fuzzy dif- ferential equations and two-point boundary conditions. Some sucient condi- tions are presented that guarantee the existence and uniqueness of solutions under the approach of Hukuhara dierentiability.
http://ijfs.usb.ac.ir/article_225_64b3d7d1d93425ef5d2a6e2adb0af34c.pdf
2012-02-10T11:23:20
2018-05-25T11:23:20
49
60
10.22111/ijfs.2012.225
Fuzzy numbers
Fuzzy dierential equations
Boundary value
problems
Omid
Solaymani Fard
osfard@du.ac.ir, omidsfard@gmail.com
true
1
School of Mathematics and Computer Science, Damghan Uni-
versity, Damghan, Iran
School of Mathematics and Computer Science, Damghan Uni-
versity, Damghan, Iran
School of Mathematics and Computer Science, Damghan Uni-
versity, Damghan, Iran
LEAD_AUTHOR
Amin
Esfahani
amin@impa.br, esfahani@du.ac.ir
true
2
School of Mathematics and Computer Science, Damghan University,
Damghan, Iran
School of Mathematics and Computer Science, Damghan University,
Damghan, Iran
School of Mathematics and Computer Science, Damghan University,
Damghan, Iran
AUTHOR
Ali
Vahidian Kamyad
avkamyad@math.um.ac.ir
true
3
Department of Mathematics, Ferdowsi University of Mashhad,
Mashhad, Iran
Department of Mathematics, Ferdowsi University of Mashhad,
Mashhad, Iran
Department of Mathematics, Ferdowsi University of Mashhad,
Mashhad, Iran
AUTHOR
[1] M. F. Abbod, D. G. Von Keyserlingk, D. A. Linkens and M. Mahfouf, Survey of utilisation of
1
fuzzy technology in medicine and healthcare, Fuzzy Sets and Systems, 120 (2001), 331-349.
2
[2] T. Allahviranloo and M. A. Kermani, Numerical methods for fuzzy linear partial dierential
3
equations under new denition for derivative, Iranian Journal of Fuzzy Systems, 7(3) (2010),
4
[3] S. Bandyopadhyay, An ecient technique for superfamily classication of amino acid se-
5
quences: feature extraction, fuzzy clustering and prototype selection, Fuzzy Sets and Systems,
6
152 (2005), 5-16.
7
[4] S. Barro and R. Marn, Fuzzy logic in medicine, Heidelberg: Physica-Verlag, 2002.
8
[5] B. Bede, Note on "Numerical solutions of fuzzy dierential equations by predictor-corrector
9
method", Information Sciences, 178 (2008), 1917-1922.
10
[6] B. Bede and S. G. Gal, Generalizations of the dierentiability of fuzzy number valued func-
11
tions with applications to fuzzy dierential equation, Fuzzy Sets and Systems, 151 (2005),
12
[7] J. J. Buckley and T. Feuring, Fuzzy dierential equations, Fuzzy Sets and Systems, 110
13
(2000), 43-54.
14
[8] J. Casasnovas and F. Rossell, Averaging fuzzy biopolymers, Fuzzy Sets and Systems, 152
15
(2005), 139-58.
16
[9] Y. Chalco-Cano and H. Roman-Flores, On new solutions of fuzzy dierential equations,
17
Chaos, Solitions and Fractals, 38 (2008), 112-119.
18
[10] B. C. Chang and S. K. Halgamuge, Protein motif extraction with neuro-fuzzy optimization,
19
Bioinformatics, 18 (2002), 1084-1090.
20
[11] P. Diamond, Time-dependent dierential inclusions, cocycle attractors and fuzzy dierential
21
equations, IEEE Trans Fuzzy Syst., 7 (1999), 734-740.
22
[12] D. Dubois and H. Prade, Towards fuzzy dierential calculus: Part 3, dierentiation, Fuzzy
23
Sets and Systems, 8 (1982), 225-233.
24
[13] D. Dubois and H. Prade, Fuzzy numbers: an overview, In: J. Bezdek, ed., Analysis of Fuzzy
25
Information, CRC Press, 1987.
26
[14] O. S. Fard and A. V. Kamyad, Modied kstep method for solving fuzzy initial value prob-
27
lems, Iranian Journal of Fuzzy Systems, 8(1) (2011), 49-63.
28
[15] T. Gnana Bhaskar, V. Lakshmikantham and V. Devi, Revisiting fuzzy dierential equations,
29
Nonlinear Anal., 58 (2004), 351-358.
30
[16] R. Goetschel and W. Voxman, Topological properties of fuzzy number, Fuzzy Sets and Sys-
31
tems, 10 (1983), 87-99.
32
[17] R. Goetschel and W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986),
33
[18] A. Granas and J. Dugundji, Fixed ooint theory, Springer Monographs in Mathematics.
34
Springer-Verlag, New York, 2003.
35
[19] M. Guo, X. Xue and R. Li, The oscillation of delay dierential inclusions and fuzzy biody-
36
namics models, Math. Comput. Model., 37 (2003), 651-658.
37
[20] M. Guo and R. Li, Impulsive functional dierential inclusions and fuzzy population models,
38
Fuzzy Sets and Systems, 138 (2003), 601-615.
39
[21] C. M. Helgason and T. H. Jobe, The fuzzy cube and causal ecacy: representation of con-
40
comitant mechanisms in stroke, Neural Networks, 11 (1998), 549-555.
41
[22] O. Kaleva, Fuzzy dierential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.
42
[23] O. Kaleva, The Cauchy problem for fuzzy dierential equations, Fuzzy Sets and Systems, 35
43
(1990), 389-396.
44
[24] O. Kaleva, A note on fuzzy dierential equations, Nonlinear Analysis, 64 (2006), 895-900.
45
[25] M. Ma, M. Friedman and A. Kandel, A new approach for defuzzication, Fuzzy Sets and
46
Systems, 111 (2000), 351-356.
47
[26] M. S. El Naschie, A review of E-innite theory and the mass spectrum of high energy particle
48
physics, Chaos, Solitons and Fractals, 19 (2004), 209-236.
49
[27] M. S. El Naschie, The concepts of E-innite: an elementary introduction to the Cantorian-
50
fractal theory of quantum physics, Chaos, Solitons and Fractals, 22 (2004), 495-511.
51
[28] M. S. El Naschie, On a fuzzy Khler manifold which is consistent with the two slit experiment,
52
Int. J. Nonlinear Sci. Numer. Simult., 6 (2005), 95-98.
53
[29] J. J. Nieto and R. Rodrguez-Lopez, Bounded solutions for fuzzy dierential and integral
54
equations, Chaos, Solitons and Fractals, 27 (2006), 1376-1386.
55
[30] J. J. Nieto and R. Rodrguez-Lopez, Existence and uniqueness results for fuzzy dierential
56
equations subject to boundary value conditions, AIP Conf. Proc., 1124 (2009), 264-273.
57
[31] J. J. Nieto and A. Torres, Midpoints for fuzzy sets and their application in medicine, Artif.
58
Intell. Med., 27 (2003), 81-101.
59
[32] M. Oberguggenberger and S. Pittschmann, Dierential equations with fuzzy parameters,
60
Math. Mod. Syst., 5 (1999), 181-202.
61
[33] D. ORegan, V. Lakshmikantham and J. Nieto, Initial and boundary value problems for fuzzy
62
dierential equations, Nonlinear Anal., 54 (2003), 405-415.
63
[34] S. C. Palligkinis, G. Stefanidou and P. Efraimidi, RungeKutta methods for fuzzy dierential
64
equations, Applied Mathematics and Computation, 209 (2009), 97-105.
65
[35] M. L. Puri and D. A. Ralescu, Dierentials of fuzzy functions, Journal of Mathematical
66
Analysis and Applications, 91 (1983), 552-558.
67
[36] R. Rodrguez-Lopez, Periodic boundary value problems for impulsive fuzzy dierential equa-
68
tions, Fuzzy Sets and Systems, 159(11) (2008), 1384-1409.
69
[37] S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 (1987), 319-330.
70
[38] Y. Tanaka, Y. Mizuno and T. Kado, Chaotic dynamics in the Friedman equation, Chaos,
71
Solitons and Fractals, 24 (2005), 407-422.
72
[39] D. Vorobiev and S. Seikkala, Toward the theory of fuzzy dierential equations, Fuzzy Sets
73
and Systems, 125 (2002), 231-237.
74
ORIGINAL_ARTICLE
SECURING INTERPRETABILITY OF FUZZY MODELS FOR
MODELING NONLINEAR MIMO SYSTEMS USING
A HYBRID OF EVOLUTIONARY ALGORITHMS
In this study, a Multi-Objective Genetic Algorithm (MOGA) is utilized to extract interpretable and compact fuzzy rule bases for modeling nonlinear Multi-input Multi-output (MIMO) systems. In the process of non- linear system identi cation, structure selection, parameter estimation, model performance and model validation are important objectives. Furthermore, se- curing low-level and high-level interpretability requirements of fuzzy models is especially a complicated task in case of modeling nonlinear MIMO systems. Due to these multiple and conicting objectives, MOGA is applied to yield a set of candidates as compact, transparent and valid fuzzy models. Also, MOGA is combined with a powerful search algorithm namely Dierential Evolution (DE). In the proposed algorithm, MOGA performs the task of membership function tuning as well as rule base identi cation simultaneously while DE is utilized only for linear parameter identi cation. Practical applicability of the proposed algorithm is examined by two nonlinear system modeling prob- lems used in the literature. The results obtained show the eectiveness of the proposed method.
http://ijfs.usb.ac.ir/article_226_cc28b7c778fbedd749288307752c17c8.pdf
2012-02-10T11:23:20
2018-05-25T11:23:20
61
77
10.22111/ijfs.2012.226
Multi-objective
Evolutionary
Fuzzy identication
Compact
Inter-
pretability
Mojtaba
Eftekhari
m.eftekhari59@gmail.com
true
1
Faculty of Islamic Azad University, Sirjan branch, ,Sirjan, Ker-
man, Iran
Faculty of Islamic Azad University, Sirjan branch, ,Sirjan, Ker-
man, Iran
Faculty of Islamic Azad University, Sirjan branch, ,Sirjan, Ker-
man, Iran
AUTHOR
Mahdi
Eftekhari
m.eftekhari@uk.ac.ir
true
2
Department of Computer Engineering, School of Engineering,
Shahid Bahonar University of Kerman, Kerman, Iran
Department of Computer Engineering, School of Engineering,
Shahid Bahonar University of Kerman, Kerman, Iran
Department of Computer Engineering, School of Engineering,
Shahid Bahonar University of Kerman, Kerman, Iran
LEAD_AUTHOR
Maryam
Majidi
majena67@yahoo.com
true
3
Department of Computer Engineering, School of Engineering, Shahid
Bahonar University of Kerman, Kerman, Iran
Department of Computer Engineering, School of Engineering, Shahid
Bahonar University of Kerman, Kerman, Iran
Department of Computer Engineering, School of Engineering, Shahid
Bahonar University of Kerman, Kerman, Iran
AUTHOR
Hossein
Nezamabadi pour
nezam h@yahoo.com
true
4
Department of Electrical Engineering, School of Engi-
neering, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Electrical Engineering, School of Engi-
neering, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Electrical Engineering, School of Engi-
neering, Shahid Bahonar University of Kerman, Kerman, Iran
AUTHOR
[1] J. Abonyi, Fuzzy Model Identication for Control, Birkhauser, Boston, 2003.
1
[2] K. Debs, Multio-bjective optimization Using Evolutionary Algorithms, John Wiley and Son
2
Ltd, 2001.
3
[3] B. L. R. De Moor and ed., DaISy: Database for the Identication of Systems,
4
Department of Electrical Engineering, ESAT/SISTA, K. U. Leuven, Belgium, URL:
5
http://www.esat.kuleuven.ac.be/sista/daisy/.
6
[4] V. De Oliveira, Semantic constraints for membership function optimization, IEEE Trans.
7
SMC-A, 29(1) (1999), 128-138.
8
[5] M. Eftekhari, S. D. Katebi, M. Karimi and A. H. Jahanmiri, Eliciting transparent fuzzy model
9
using dierential evolution, Applied Soft Computing, 8 (2008), 466-476.
10
[6] M. Eftekhari and S. D. Katebi, Extracting compact fuzzy rules for nonlinear system modeling
11
using subtractive clustering, GA and unscented lter, Applied Mathematical Modelling, 32
12
(2008), 2634-2651.
13
[7] B. Feil, J. Abonyi, J. Madar, S. Nemeth and P. A rva, Identication and analysis of MIMO
14
systems based on clustering algorithm, Acta Agraria Kaposvariensis, 8(3) (2004), 191-203.
15
[8] C. M. Fonseca and P. J. Fleming, Multi-objective optimization and multiple constraint han-
16
dling with evolutionary algorithms-part I: application example, IEEE Trans. Syst. Man and
17
Cybernetics, 28(1) (1998), 26-37.
18
[9] C. M. Fonseca and P. J. Fleming, Multi-objective optimization and multiple constraint han-
19
dling with evolutionary algorithms-part II: a unied formulation, IEEE Trans. Syst. Man and
20
Cybernetics, 28(1) (1998), 38-47.
21
[10] M. J. Gacto, R. Alcala and F. Herrera, Integration of an Index to Preserve the Semantic
22
Interpretability in the Multiobjective Evolutionary Rule Selection and Tuning of Linguistic
23
Fuzzy Systems, IEEE Transactions on Fuzzy Systems, 8(3) (2010), 515-531.
24
[11] S. Y. Ho, H. M. Chen, S. J. Ho and T. K. Cehn, Design of accurate classiers with a compact
25
fuzzy rule base using an evolutionary scatter partition of feature space, IEEE Tans. Systems,
26
Man and Cybernetics, Part B: Cybernetics, 34(2) (2004), 1031-1044.
27
[12] W. H. Ho, J. H. Chou and C. Y. Guo, Parameter identication of chaotic systems using
28
improved dierential evolution algorithm, Nonlinear Dynamics, 61 (2010), 29-41.
29
[13] A. Homaifar and E. McCormick, Simultaneous design of membership functions and rule sets
30
for fuzzy controllers using genetic algorithms, IEEE Trans. Fuzzy Syst., 3 (1995), 129-139.
31
[14] H. Ishibuchi, Multiobjective genetic fuzzy systems: Review and future research directions,
32
Proc. of IEEE InternationalConference on Fuzzy Systems, London, UK, July 23-26, (2007)
33
[15] C. Z. Janikow, A knowledge intensive genetic algorithm for supervised learning, Machine
34
Learning, 13 (1993), 198-228.
35
[16] L. Ljung, System identication toolbox: user's guide, The MathWorks, 2004.
36
[17] S. Medasani, J. Kim and R. Krishnapuram, An overview of membership function generation
37
techniques for pattern recognition, Int. J. Approx. Reasoning, 19(3-4) (1998), 391-417.
38
[18] O. Nelles, Nonlinear System Identication, Springer-Verlag, Berlin Heidelberg, 2001.
39
[19] A. Riid and E. Rustern, Interpretability improvement of fuzzy systems: reducing the number
40
of unique singletons in zeroth order Takagi-Sugeno systems, Proceedings of (2010) IEEE
41
International Conference on Fuzzy Systems, Barcelona, Spain, (2010), 2013-2018.
42
[20] K. Rodriguez-vazquez, Multiobjective evolutionary algorithms in non-linear system identi-
43
cation. PhD thesis, Department of Automatic Control and Systems Engineering, The Uni-
44
versity of Sheeld, 1999.
45
[21] R. Storn and K. Price, Dierential evolution-a simple and ecient adaptive scheme or global
46
optimization over continuous spaces, technical report TR-95-012, International Computer
47
Science Institute, Berkley, 1995.
48
[22] R. Storn and K. Price, Dierential evolution a simple and ecient heuristic for global opti-
49
mization over continuous spaces, J. Global Optim. 11 (1997), 341-359.
50
[23] J. T. Tsai, J. H. Chou and T. K. Liu, Tuning the structure and parameters of a neural
51
network by using hybrid Taguchi-genetic algorithm, IEEE Trans. on Neural Networks, 17
52
(2006), 69-80.
53
[24] H. Wang, S. Kwong, Y. Jin, W. Wei, and K. F. Man, Multi-objective hierarchical genetic
54
algorithm for interpretable fuzzy rule-based knowledge extraction, Fuzzy Sets and Systems,
55
149 (2005), 149-186.
56
[25] H.Wang, S. Kwong, Y. Jin, W.Wei and K. F. Man, Agent-based evolutionary approach for in-
57
terpretable rule-based knowledge extraction, IEEE Trans. on Systems, Man and Cybernetics-
58
Part C, 35 (2005), 143-155.
59
[26] S. M. Zhou and J. Q. Gan, Low-level interpretability and high-level interpretability: a unied
60
view of data-driven interpretable fuzzy system modeling, Fuzzy Sets and Systems, 159 (2008),
61
3091-3131.
62
[27] S. M. Zhou and J. Q. Gan, Extracting Takagi-Sugeno fuzzy rules with interpretable sub-
63
models via regularization of linguistic modiers, IEEE Transactions on Knowledge and Data
64
Engineering, 21(8) (2009), 1191-1204.
65
ORIGINAL_ARTICLE
ESTIMATORS BASED ON FUZZY RANDOM VARIABLES AND
THEIR MATHEMATICAL PROPERTIES
In statistical inference, the point estimation problem is very crucial and has a wide range of applications. When, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. Therefore, the theory of fuzzy sets plays an important role in formulating such situations. In this paper, we rst recall the crisp uniformly minimum variance unbiased (UMVU) and Bayesian estimators and then develop the concept of fuzzy estimators for fuzzy parameters based on fuzzy random variables.
http://ijfs.usb.ac.ir/article_227_b17c576a5e5de627e505d9f09b0d933c.pdf
2012-02-11T11:23:20
2018-05-25T11:23:20
79
95
10.22111/ijfs.2012.227
Fuzzy random variable
Fuzzy parameter
Signed distance
L2- metric
Fuzzy estimator
Fuzzy unbiased estimator
Fuzzy sufficient estimator
Fuzzy risk function
M. G.
Akbari
mga13512@yahoo.com
true
1
Department of Statistics, Faculty of Sciences, University of Birjand,
Southern Khorasan, Birjand
Department of Statistics, Faculty of Sciences, University of Birjand,
Southern Khorasan, Birjand
Department of Statistics, Faculty of Sciences, University of Birjand,
Southern Khorasan, Birjand
LEAD_AUTHOR
M.
Khanjari Sadegh
g_z_akbari@yahoo.com
true
2
Department of Statistics, Faculty of Sciences, University of
Birjand, Southern Khorasan, Birjand
Department of Statistics, Faculty of Sciences, University of
Birjand, Southern Khorasan, Birjand
Department of Statistics, Faculty of Sciences, University of
Birjand, Southern Khorasan, Birjand
AUTHOR
bibitem{A}
1
M. G. Akbari and A. Rezaei, {it An uniformly minimum variance unbiased point estimation using fuzzy observations}, Austrian Journal of Statistics, {bf 36} (2007), 307-317.
2
bibitem{B}
3
M. G. Akbari and A. Rezaei, {it Order statistics using fuzzy
4
random variables}, Statistics and Probability Letters, {bf 79} (2009), 1031-1037.
5
bibitem{au}
6
R. J. Aumann, {it Integrals of set-valued functions}, Journal of Mathematical Analysis and Applications, {bf 12} (1965), 1-12.
7
bibitem{bi}
8
P. Billingsley, {it Probability and measure}, 2nd ed., New York:
9
John Wiley, 1995.
10
bibitem{ca}
11
J. J. Buckley, {it Fuzzy probabilities: new approach and applications}, Springer-Verlag, Berlin, Heidelberg, 2005.
12
bibitem{cb}
13
J. J. Buckley, {it Fuzzy probability and statistics}, Springer-Verlag, Berlin, Heidelberg, 2006.
14
bibitem{ch}
15
C. Cheng, {it A new approach for ranking fuzzy numbers by distance
16
method}, Fuzzy Sets and Systems, {bf 95} (1998), 307-317.
17
bibitem{g1}
18
G. Z. Gertner and H. Zhu, {it Bayesian estimation in forest survey
19
when samples or prior information are fuzzy}, Fuzzy Sets an Systems,
20
{bf 77} (1997), 277-290.
21
bibitem{ho}
22
H. Hong-Zhong, J. Z. Ming and S. Zhan-Quan, {it Bayesian
23
reliability analysis for fuzzy lifetime data}, Fuzzy Sets and
24
Systems, {bf 157} (2006), 1674-1686.
25
bibitem{hr}
26
O. Hryniewicz, {it Possibilities approach to the Bayes statistical
27
decisions}, In: P. Grzegorzewski, O. Hryniewicz, M. A. Gil , eds., Soft
28
Methods in Probability, Statistics and Data Analysis. Physica
29
Verlag, Heidelberg-New York, (2002), 207-218.
30
bibitem{k1}
31
R. Kruse, {it Statistical estimation with linguistic data},
32
Information Sciences, {bf 33} (1984), 197-207.
33
bibitem{k2}
34
R. Kruse and K. D. Meyer, {it Statistics with vague data}, Reidel, Dordrecht, {bf 33} (1987).
35
bibitem{kw}
36
H. Kwakernaak, {it Fuzzy random variables I}, Information Sciences, {bf 15} (1978), 1-29.
37
bibitem{mo}
38
M. Modarres and S. Sadi-Nezhad, {it Ranking fuzzy numbers by
39
preference ratio}, Fuzzy Sets and Systems, {bf 118} (2001), 429-436.
40
bibitem{na}
41
W. N$ddot{a}$ther, {it Regression with fuzzy data},
42
Computational Statistics and Data Analysis, {bf 51} (2006), 235-252.
43
bibitem{no}
44
M. Nojavan and M. Ghazanfari, {it A fuzzy ranking method by
45
desirability index}, Journal of Intelligent and Fuzzy Systems,
46
{bf 17} (2006), 27-34.
47
bibitem{p1}
48
M. L. Puri and D. A. Ralescu, {it Differential of fuzzy functions}, Journal of Mathematical Analysis and Applications, {bf 114} (1983), 552-558.
49
bibitem{p2}
50
M. L. Puri and D. A. Ralescu, {it Fuzzy random variables}, Journal of Mathematical Analysis and Applications, {bf 114} (1986), 409-422.
51
bibitem{p3}
52
M. L. Puri and D. A. Ralescu, {it Convergence theorem for fuzzy martingales}, Journal of Mathematical Analysis and Applications, {bf 160} (1991), 107-122.
53
bibitem{sh}
54
J. Shao, {it Mathematical Statistics}, 2nd ed., New York:
55
Springer-Verlag, 2003.
56
bibitem{s11}
57
B. Sadeghpour Gildeh and D. Gien, {it $d_{p,q}$-distance and
58
Rao-Blackwell theorem for fuzzy random variables}, In Proc, of
59
the 8th international Conference of Fuzzy Theory and
60
Technology, Durham, USA, 2002.
61
bibitem{u1}
62
Y. Uemura, {it A decision rule on fuzzy events}, Japanese Journal
63
Fuzzy Theory and Systems, {bf 3} (1991), 291-300.
64
bibitem{u2}
65
Y. Uemura, {it A decision rule on fuzzy events under an
66
observation}, Journal of Fuzzy Mathematics, {bf 1} (1993), 39-52.
67
bibitem{v1}
68
R. Viertl, {it Statistical methods for non-precise data}, CRC
69
Press, Boca Raton, 1996.
70
bibitem{v2}
71
R. Viertl, {it Statistics with one-dimensional fuzzy data}, In C.
72
Bertoluzzi et al., Editor, Statistical Modeling, Analysis and
73
Management of Fuzzy Data, Physica-Verlag, Heidelberg, (2002a), 199-212.
74
bibitem{v3}
75
R. Viertl, {it Statistical inference with non-precise data}, In
76
Encyclopedia of Life Support Systems, UNESCO, Paris, 2002b.
77
bibitem{ac}
78
R. Viertl, {it Univariate statistical analysis with fuzzy data},
79
Computational Statistics and Data Analysis, {bf 51} (2006), 133-147.
80
bibitem{yaa}
81
J. S. Yao and K. Wu, {it Ranking fuzzy numbers based on
82
decomposition principle and signed distance}, Fuzzy Sets and Systems, {bf 11} (2000), 275-288.
83
ORIGINAL_ARTICLE
A NEW METHOD TO REDUCE TORQUE RIPPLE IN
SWITCHED RELUCTANCE MOTOR USING
FUZZY SLIDING MODE
This paper presents a new control structure to reduce torque ripple in switched reluctance motor. Although SRM possesses many advantages in motor structure, it suers from large torque ripple that causes some problems such as vibration and acoustic noise. In this paper another control loop is added and torque ripple is de ned as an objective function. By using fuzzy sliding mode strategy, the DC link voltage is adjusted to optimize the objective function. Simulation results have demonstrated the proposed control method.
http://ijfs.usb.ac.ir/article_228_eda29a4d8485fce43ad3b0b5e35789ed.pdf
2012-02-11T11:23:20
2018-05-25T11:23:20
97
108
10.22111/ijfs.2012.228
Fuzzy sliding control
Switched Reluctance Motor
Torque ripple re-
duction
S. R.
Mousavi-Aghdam
rmousavi@tabrizu.ac.ir
true
1
Faculty of electrical and computer engineering, University
of Tabriz, Tabriz, Iran
Faculty of electrical and computer engineering, University
of Tabriz, Tabriz, Iran
Faculty of electrical and computer engineering, University
of Tabriz, Tabriz, Iran
LEAD_AUTHOR
M. B. B.
Sharifian
sharifian@tabrizu.ac.ir
true
2
Faculty of electrical and computer engineering, University of
Tabriz, Tabriz, Iran
Faculty of electrical and computer engineering, University of
Tabriz, Tabriz, Iran
Faculty of electrical and computer engineering, University of
Tabriz, Tabriz, Iran
AUTHOR
M. R.
Banaei
m.banaei@azaruniv.edu
true
3
Department of electrical engineering, Faculty of engineering, azarbai-
jan, University of tarbiat moallem, Tabriz, Iran
Department of electrical engineering, Faculty of engineering, azarbai-
jan, University of tarbiat moallem, Tabriz, Iran
Department of electrical engineering, Faculty of engineering, azarbai-
jan, University of tarbiat moallem, Tabriz, Iran
AUTHOR
[1] M. R. Akbarzadeh-T and R. Shahnazi, Direct adaptive fuzzy PI sliding mode control of system
1
with unknown but bounded disturbances, Iranian Journal of Fuzzy Systems, 3(2) (2006), 33-
2
[2] D. Cajander and H. Le-Huy, Design and optimization of a torque controller for a switched
3
reluctance motor drive for electric vehicles by simulation, Mathematics and Computers in
4
Simulation, Elsevier, 71 (2006), 333-344.
5
[3] J. Y. Chai and C. M. Liaw, Reduction of speed ripple and vibration for switched reluctance
6
motor drive via intelligent current proling, IET Electric Power Applications, (2010), 380-
7
[4] N. Inanc and V. Ozbulur, Torque ripple minimization of a switched reluctance motor by
8
using continuous sliding mode control technique, Electric power systems research, Elsevier,
9
66 (2003), 241-251.
10
[5] G. John and A. R. Eastham, Speed control of switched reluctance motor using sliding mode
11
control strategy, IEEE International Conference on Industrial Technology, 1 (1995), 263-270.
12
[6] H. Khorashadi-Zadeh and M. R. Aghaebrahimi, A neuro-fuzzy technique for discrimination
13
between internal faults and magnetizing inrush currents in transformers, Iranian Journal of
14
Fuzzy Systems, 2(2) (2005), 45-57.
15
[7] J. Li, X. Song and Y. Cho, Comparison of 12/8 and 6/4 switched reluctance motor: noise
16
and vibration aspects, IEEE Trans. Magn., 44(11) (2008), 4131-4134.
17
[8] J. Li and Y. Cho, Investigation into reduction of vibration and acoustic noise in switched
18
reluctance motors in radial force excitation and frame transfer function aspects, IEEE Trans.
19
Magn., 45(10) (2009), 4664-4667.
20
[9] M. A. A. Morsy, M. Said, A. Moteleb and H. T. Dorrah, Design and implementation of
21
fuzzy sliding mode controller for switched reluctance motor, IEEE International Conference
22
on Industrial Technology, (2008), 1-6.
23
[10] N. Nelvaganesan, D. Raja and S. Srinivasan, Fuzzy based fault detection and control for 6/4
24
switched reluctance motor, Iranian Journal of Fuzzy Systems, 45(1) (2007), 37-51.
25
[11] H. Rouhani, C. Lucas, R. Mohammadi Milasi and M. Nikkhah bahrami, Fuzzy sliding mode
26
control applied to low noise switched reluctance motor control, International Conference on
27
Control and Automation (ICCA), 1 (2005), 325-329.
28
[12] W. Shang, S. Zhao, Y. Shen and Z. Qi, A sliding mode
29
ux-linkage controller with integral
30
compensation for switched reluctance motor, IEEE Trans. Magn., 45(9) (2009), 3322-3328.
31
[13] B. Singh, V. Kumar Sharma and S. S. Murthy, Comparative study of PID, sliding mode and
32
fuzzy logic controllers for four quadrant operation of switched reluctance motor, International
33
Conference on Power Electronic Drives and Energy Systems for Industrial Growth, 1 (1998),
34
[14] H. Vasquez and J. K. Parker, A new simplied mathematical model for a switched reluctance
35
motor in a variable speed pumping application, Mechatronics, Elsevier, 14 (2004), 1055-1068.
36
[15] K. Vijayakumar, R. Karthikeyan, S. Paramasivam, R. Arumugam and K. N. Srinivas,
37
Switched reluctance motor modeling, design, simulation, and analysis: a comprehensive re-
38
view, IEEE Trans. Magn., 44(12) (2008), 4605-4617.
39
[16] Y. Wang, A novel fuzzy controller for switched reluctance motor drive, Second IEEE Inter-
40
national Conference on Information and Computing Science, 2 (2009), 55-58.
41
ORIGINAL_ARTICLE
FUZZY SOFT MATRIX THEORY AND ITS APPLICATION IN
DECISION MAKING
In this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. We then define products of $fs$-matrices andstudy their properties. We finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.
http://ijfs.usb.ac.ir/article_229_b6d292816ccde2e91d91920714cb6245.pdf
2012-02-11T11:23:20
2018-05-25T11:23:20
109
119
10.22111/ijfs.2012.229
Fuzzy soft sets
Fuzzy soft matrix
Products of fuzzy soft matrices
Fuzzy soft max-min decision making
Naim
Cagman
ncagman@gop.edu.tr
true
1
Department of Mathematics, Faculty of Arts and Sciences, Gazios-
manpasa University, 60250 Tokat, Turkey
Department of Mathematics, Faculty of Arts and Sciences, Gazios-
manpasa University, 60250 Tokat, Turkey
Department of Mathematics, Faculty of Arts and Sciences, Gazios-
manpasa University, 60250 Tokat, Turkey
LEAD_AUTHOR
Serdar
Enginoglu
serdarenginoglu@gop.edu.tr
true
2
Department of Mathematics, Faculty of Arts and Sciences, Gazios-
manpasa University, 60250 Tokat, Turkey
Department of Mathematics, Faculty of Arts and Sciences, Gazios-
manpasa University, 60250 Tokat, Turkey
Department of Mathematics, Faculty of Arts and Sciences, Gazios-
manpasa University, 60250 Tokat, Turkey
AUTHOR
bibitem{aca-ea-10} U. Acar, F. Koyuncu and B. Tanay, {it Soft sets and soft rings},
1
Computers and Mathematics with Applications, {bf59} (2010), 3458-3463.
2
bibitem{ahm-kha-09} B. Ahmad and A. Kharal, {it On fuzzy soft sets}, Advances in Fuzzy
3
Systems, (2009), 1-6.
4
bibitem{akt-cag-07} H. Aktad{s} and N. d{C}au{g}man, {it Soft sets and soft groups}, Information
5
Sciences, {bf 1(77)} (2007), 2726-2735.
6
bibitem{ali-ea-09} M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, {it On some new
7
operations in soft set theory}, Computers and Mathematics with
8
Applications, {bf57}(2009), 1547-1553.
9
bibitem{ata-sez-11} A. O. Atag"{u}n and A. Sezgin, {it Soft substructures of rings, fields and modules},
10
Comput. Math. Appl., {bf61(3)} (2011), 592-601.
11
bibitem{cag-eng-10a} N. d{C}au{g}man and S. Enginou{g}lu, {it Soft set theory and uni-int decision
12
making}, European Journal of Operational Research, {bf 207} (2010), 848-855.
13
bibitem{cag-eng-10b} N. d{C}au{g}man and S. Enginou{g}lu, {it Soft matrix theory and its decision making},
14
Computers and Mathematics with Applications, {bf59} (2010), 3308-3314.
15
bibitem{cag-ea-10a} N. d{C}au{g}man, F. C{i}tak and S. Enginou{g}lu, {it Fuzzy parameterized fuzzy soft set
16
theory and its applications}, Turkish Journal of Fuzzy Systems, {bf 1(1)} (2010), 21-35.
17
bibitem{cag-ea-10b} N. d{C}au{g}man, S. Enginou{g}lu and F. C{i}tak,
18
{it Fuzzy soft set theory and its applications}, Iranian Journal of Fuzzy
19
Systems, {bf 8(3)} (2011), 137-147.
20
bibitem{fen-ea-10} F. Feng, Y. B. Jun, X. Liu and L. Li, {it An adjustable approach to
21
fuzzy soft set based decision making}, Journal of Computational and
22
Applied Mathematics, {bf 234} (2010), 10-20.
23
bibitem{fen-ea-08} F. Feng, Y. B. Jun and X. Zhao, {it Soft semirings}, Fuzzy Sets and
24
Systems: Theory and Applications, {bf 56(10)} (2008), 2621-2628.
25
bibitem{her-ea-09} T. Herawan, A. N. M. Rose and M. M. Deris, {it Soft set theoretic
26
approach for dimensionality reduction}, In Database Theory and
27
Application, Springer Berlin Heidelberg, {bf 64} (2009), 171-178.
28
bibitem{jia-ea-10} Y. Jiang, Y. Tang, Q. Chen, J. Wang and S. Tang, {it Extending soft
29
sets with description logics}, Computers and Mathematics with
30
Applications, {bf 59} (2010), 2087-2096.
31
bibitem{jun-08}Y. B. Jun, {it Soft BCK/BCI-algebras}, Computers and Mathematics with
32
Applications, {bf56} (2008), 1408-1413.
33
bibitem{jun-par-08} Y. B. Jun and C. H. Park, {it Applications of soft sets in ideal theory
34
of BCK/BCI-algebras}, Information Sciences, {bf178} (2008), 2466-2475.
35
bibitem{jun-par-09}Y. B. Jun and C. H. Park, {it Applications of soft sets in Hilbert
36
algebras}, Iranian Journal of Fuzzy Systems, {bf6(2)} (2009), 55-86.
37
bibitem{jun-ea-09a}Y. B. Jun, H. S. Kim and J. Neggers, {it Pseudo d-algebras}, Information
38
Sciences, {bf179} (2009), 1751-1759.
39
bibitem{jun-ea-10a} Y. B. Jun, K. J. Lee and A. Khan, {it Soft ordered semigroups},
40
Mathematical Logic Quarterly, {bf56(1)} (2010), 42-50.
41
bibitem{jun-ea-08} Y. B. Jun, K. J. Lee and C. H. Park, {it Soft set theory applied to
42
commutative ideals, in BCK--algebras}, Journal of Applied Mathematics
43
Informatics, {bf26(3-4)} (2008), 707-720.
44
bibitem{jun-ea-09b} Y. B. Jun, K. J. Lee and C. H. Park, {it Soft set theory applied to
45
ideals in d-algebras}, Computers and Mathematics with Applications, {bf 57} (2009), 367-378.
46
bibitem{jun-ea-10b} Y. B. Jun, K. J. Lee and C. H. Park, {it Fuzzy soft set theory applied
47
to BCK/BCI-algebras}, Computers and Mathematics with Applications, {bf 59} (2010), 3180-3192.
48
bibitem{jun-ea-09c} Y. B. Jun, K. J. Lee and J. Zhan, {it Soft p-ideals of soft
49
BCI-algebras}, Computers and Mathematics with Applications, {bf58} (2009), 2060-2068.
50
bibitem{kal-ea-10} S. J. Kalayathankal and G. S. Singh, {it A fuzzy soft flood alarm model},
51
Mathematics and Computers in Simulation, {bf 80} (2010), 887-893.
52
bibitem{kha-ahm-09} A. Kharal and B. Ahmad, {it Mappings on fuzzy soft classes}, Advances in
53
Fuzzy Systems, (2009), 1-6.
54
bibitem{kon-ea-08} Z. Kong, L. Gao, L. Wang and S. Li, {it The normal parameter reduction
55
of soft sets and its algorithm}, Computers and Mathematics with
56
Applications, {bf56} (2008), 3029-3037.
57
bibitem{kov-ea-07} D. V. Kovkov, V. M. Kolbanov and D. A. Molodtsov, {it Soft sets
58
theory-based optimization}, Journal of Computer and Systems Sciences
59
International, {bf46(6)} (2007), 872-880.
60
bibitem{maj-ea-01a} P. K. Maji, R. Biswas and A. R. Roy, {it Fuzzy soft sets}, Journal of Fuzzy
61
Mathematics, {bf9(3)} (2001), 589-602.
62
bibitem{maj-ea-01b} P. K. Maji, R. Biswas and A. R. Roy, {it Intuitionistic fuzzy soft sets},
63
Journal of Fuzzy Mathematics, {bf 9(3)} (2001), 677-691.
64
bibitem{maj-ea-03} P. K. Maji, R. Biswas and A. R. Roy, {it Soft set theory}, Computers and
65
Mathematics with Applications, {bf45} (2003), 555-562.
66
bibitem{maj-ea-02} P. K. Maji, A. R. Roy and R. Biswas, {it An application of soft sets in a
67
decision making problem}, Computers and Mathematics with
68
Applications, {bf44} (2002), 1077-1083.
69
bibitem{maj-sam-08} P. Majumdar and S. K. Samanta, {it Similarity measure of soft sets}, New
70
Mathematics and Natural Computation, {bf4(1)} (2008), 1-12.
71
bibitem{maj-sam-10} P. Majumdar and S. K. Samanta, {it Generalised fuzzy soft sets}, Computers
72
and Mathematics with Applications, {bf 59} (2010), 1425-1432.
73
bibitem{mol-99} D. A. Molodtsov, {it Soft set theory-first results}, Computers and
74
Mathematics with Applications, {bf37} (1999), 19-31.
75
bibitem{muk-cha-08} A. Mukherjee and S. B. Chakraborty, {it On intuitionistic fuzzy soft
76
relations}, Bulletin of Kerala Mathematics Association, {bf5(1)} (2008), 35-42.
77
bibitem{mus-ea-06} M. M. Mushrif, S. Sengupta and A. K. Ray, {it Texture classification using
78
a novel}, Soft-Set Theory Based Classification, Algorithm. Lecture
79
Notes in Computer Science., {bf3851} (2006), 246-254.
80
bibitem{par-ea-08} C. H. Park, Y. B. Jun and M. A. "{O}zt"{u}rk, {it Soft WS-algebras},
81
Communications of the Korean Mathematical Society, {bf23(3)} (2008), 313-324.
82
bibitem{pei-mia-05} D. Pei and D. Miao, {it From soft sets to information systems}, In:
83
Proceedings of Granular Computing (eds: X. Hu, Q. Liu, A. Skowron,
84
T. Y. Lin, R. R. Yager, B. Zhang) IEEE 2005, {bf 2} (2005), 617- 621.
85
bibitem{qin-hon-10} K. Qin and Z. Hong, {it On soft equality}, Journal of Computational and
86
Applied Mathematics, {bf 234} (2010), 1347-1355.
87
bibitem{roy-maj-07} A. R. Roy and P. K. Maji, {it A fuzzy soft set theoretic approach to
88
decision making problems}, Journal of Computational and Applied
89
Mathematics, {bf203} (2007), 412-418.
90
bibitem{sez-ata-11} A. Sezgin and A. O. Atag"{u}n, {it On operations of soft sets},
91
Comput. Math. Appl., {bf61(5)} (2011), 1457-1467.
92
bibitem{sez-ea-11} A. Sezgin, A. O. Atag"{u}n and E. Ayg"{u}n, {it A note on soft near-rings
93
and idealistic soft near-rings}, Filomat, {bf25} (2011), 53-68.
94
bibitem{som-06} T. Som, {it On the theory of soft sets soft relation and fuzzy soft
95
relation}, Proc. of the National Conference on Uncertainty: A
96
Mathematical Approach, UAMA-06, Burdwan, (2006), 1{-}9.
97
bibitem{son-07} M. J. Son, {it Interval-valued fuzzy soft sets}, Journal of Fuzzy Logic
98
and Intelligent Systems, {bf17(4)} (2007), 557-562.
99
bibitem{sun-ea-08} Q. M. Sun, Z. L. Zhang and J. Liu, {it Soft sets and soft modules},
100
Proceedings of Rough Sets and Knowledge Technology, Third
101
International Conference, RSKT 2008, 17-19 May, Chengdu, China, (2008), 403-409.
102
bibitem{xia-ea-09}Z. Xiao, K. Gong and Y. Zou, {it A combined forecasting approach based
103
on fuzzy soft sets}, Journal of Computational and Applied
104
Mathematics, {bf 228} (2009), 326-333.
105
bibitem{xia-ea-10}Z. Xiao, K. Gong, S. Xia and Y. Zou, {it Exclusive disjunctive soft
106
sets}, Computers and Mathematics with Applications, {bf 59} (2010), 2128-2137.
107
bibitem{xia-ea-03}Z. Xiao, Y. Li, B. Zhong and X. Yang, {it Research on synthetically
108
evaluating method for business competitive capacity based on soft
109
set}, Statistical Research, (2003), 52-54.
110
bibitem{xu-ea-10}W. Xu, W. J. Ma, S. Wang and G. Hao, {it Vague soft sets and their
111
properties}, Computers and Mathematics with Applications, {bf 59} (2010), 787-794.
112
bibitem{yan-ea-09} X. Yang, T. Y. Lin, J. Yang, Y. Li and D. Yu, {it Combination of
113
interval-valued fuzzy set and soft set}, Computers and Mathematics
114
with Applications, {bf58} (2009), 521-527.
115
bibitem{zha-jun-10} J. Zhan and Y. B. Jun, {it Soft BL-algebras based on fuzzy sets}, Computers
116
and Mathematics with Applications, {bf 59} (2010), 2037-2046.
117
bibitem{zou-xia-08} Y. Zou and Z. Xiao, {it Data analysis approaches of soft sets under
118
incomplete information}, Knowledge-Based Systems, {bf21} (2008), 941-945.
119
bibitem{zad-65} L. A. Zadeh, {it Fuzzy sets}, Information and Control, {bf8} (1965), 338-353.
120
ORIGINAL_ARTICLE
FUZZY LINEAR REGRESSION BASED ON
LEAST ABSOLUTES DEVIATIONS
This study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. A least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. The proposed approach, which can deal with both symmetric and non-symmetric fuzzy observations, is compared with several existing models by three goodness of t criteria. Three well-known data sets including two small data sets as well as a large data set are employed for such comparisons.
http://ijfs.usb.ac.ir/article_230_d59e96e289e06159aecc01cdcd61a9dd.pdf
2012-02-11T11:23:20
2018-05-25T11:23:20
121
140
10.22111/ijfs.2012.230
Fuzzy regression
Least absolutes deviations
Metric on fuzzy numbers
Similarity measure
Goodness of fit
S. M.
Taheri
sm_taheri@yahoo.com
true
1
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran and Department of Statistics, School of Mathematical
Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran and Department of Statistics, School of Mathematical
Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran and Department of Statistics, School of Mathematical
Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
LEAD_AUTHOR
M.
Kelkinnama
m_ kelkinnama@yahoo.com
true
2
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran
AUTHOR
bibitem{tata}
1
A. R. Arabpour and M. Tata, {it Estimating the parameters of a
2
fuzzy linear regression model}, Iranian Journal of Fuzzy Systems,
3
{bf 5} (2008), 1-20.
4
bibitem{bar2007}
5
A. Bargiela, W. Pedrycz and T. Nakashima, {it Multiple regression
6
with fuzzy data}, Fuzzy Sets and Systems, {bf 158} (2007),
7
2169-2188.
8
bibitem{cel87}
9
A. Celmins, {it Least squares model fitting to fuzzy vector
10
data}, Fuzzy Sets and Systems, {bf 22} (1987), 260-269.
11
bibitem{ctISI2011}
12
J. Chachi and S. M. Taheri, {it A least-absolutes approach to multiple
13
fuzzy regression}, In: Proc. of
14
58th ISI Congress, Dublin, Ireland, (2011), CPS077-01.
15
bibitem{ctr}
16
J. Chachi, S. M. Taheri and R. H. Rezaei Pazhand, {it An interval-based approach
17
to fuzzy regression for fuzzy input-output data}, In: Proc. of
18
the IEEE Int. Conf. Fuzzy Syst. (FUZZ-IEEE 2011), Taipei, Taiwan, (2011), 2859-2863.
19
bibitem{lee94}
20
P. T. Chang and C. H. Lee, {it Fuzzy least absolute deviations
21
regression based on the ranking of fuzzy numbers}, In: Proc. of
22
the Third IEEE World Congress on Computaional Intelligence, Orlando, FL, {bf 2} (1994), 1365-1369.
23
bibitem{hsueh}
24
L. H. Chen and C. C. Hsueh, {it A mathematical programming method
25
for formulating a fuzzy regression model based on distance
26
criterion}, IEEE Transactions on Systems, Man, Cybernetics B, {bf 37} (2007), 705-712.
27
bibitem{hsueh-ls}
28
L. H. Chen and C. C. Hsueh, {it Fuzzy regression models using the least-squares method based on the concept of distance}, IEEE Transactions on Fuzzy Systems, {bf 17} (2009), 1259-1272.
29
bibitem{buk8}
30
S. H. Choi and J. J. Buckley, {it Fuzzy regression using least
31
absolute deviation estimators}, Soft Computing, {bf 12} (2008), 257-263.
32
bibitem{dong}
33
S. H. Choi and K. H. Dong, {it Note on fuzzy regression model}, In: Proc.
34
of the 7th Iranian Statistical Conference, Allameh-Tabatabaie
35
Univ., Tehran, (2004), 51-55.
36
bibitem{coppi}
37
R. Coppi, P. D'urso, P. Giordani and A. Santoro, {it Least
38
squares estimation of a linear regression model with LR fuzzy
39
response}, Computational Statistics and Data Analysis, {bf 51} (2006), 267-286.
40
bibitem{diamond}
41
P. Diamond, {it Least squares fitting of several fuzzy
42
variables}, In: Proc. of Second IFSA Congress, Tokyo, (1987), 20-25.
43
bibitem{dodge}
44
Y. Dodge and ed., {it Statistical data analysis based on the L1-Norm
45
and related methods}, Elsevier Science Publishers B. V., Netherlands, 1987.
46
bibitem{durso}
47
P. D'Urso and A. Santoro, {it Goodness of fit and variable selecion in
48
the fuzzy multiple linear regression},
49
Fuzzy Sets and Systems, {bf 157} (2006), 2627-2647.
50
bibitem{fth}
51
S. Fattahi, S. M. Taheri and S. A. Hoseini Ravandi, {it Cotton yarn engineering via fuzzy
52
least squares regression},
53
Fibers and Polymers, to appear.
54
bibitem{guo}
55
P. Guo and H. Tanaka, {it Dual models for posibilistic regression
56
analysis}, Computational Statistics and Data Analysis, {bf 51} (2006), 253-266.
57
bibitem{hasanpour}
58
H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, {it A goal programming approach to fuzzy linear regresion with non-fuzzy input and fuzzy output data}, Asia-Pacific Journal of Operational Research, {bf26} (2009), 587-604.
59
bibitem{hasanpour2010}
60
H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, {it Fuzzy linear regression model with crisp coefficients: a goal programming approach}, Iranian Journal of Fuzzy Systems, {bf7} (2010), 19-39.
61
bibitem{kao}
62
C. Kao and C. L. Chyu, {it A fuzzy linear regesion model with
63
better explanatory power}, Fuzzy Sets and Systems, {bf126} (2002), 401-409.
64
bibitem{bishu}
65
B. Kim and R. R. Bishu, {it Evalaution of fuzzy linear
66
regresssion models by comparing membership functions}, Fuzzy Sets
67
and Systems, {bf 100} (1998), 343-352.
68
bibitem{kimetal}
69
K. J. Kim, D. H. Kim and S. H. Choi, {it Least absolute deviation
70
estimator in fuzzy regression}, Journal of Applied Mathematics and Computing, {bf18} (2005), 649-656.
71
bibitem{korner}
72
R. K"orner and W. N"ather, {it Linear regression with random
73
fuzzy variables extended classical estimates, best linear
74
estimates, least squares estimates}, Information Sciences, {bf109} (1998), 95-118.
75
bibitem{mohamadi}
76
J. Mohammadi and S. M. Taheri, {it Pedomodels fitting with fuzzy least squares regression}, Iranian Journal of Fuzzy Systems,
77
{bf 1} (2004), 45-61.
78
bibitem{pappis}
79
C. P. Pappis and N. I. Karacapilidis, {it A comparative
80
assessment of measure of similarity of fuzzy values}, Fuzzy Sets
81
and Systems, {bf 56} (1993), 171-174.
82
bibitem{porahmad1}
83
S. Pourahmad, S. M. T. Ayatollahi and S. M. Taheri, {it Fuzzy logistic regression: a new possibilistic model and its application in clinical vague status}, Iranian Journal of Fuzzy Systems,
84
{bf 8} (2011), 1-17.
85
bibitem{porahmad2}
86
S. Pourahmad, S. M. T. Ayatollahi, S. M. Taheri and Z. Habib Agahi, {it Fuzzy logistic regression based on the least squares approach with application in clinical studies}, Computers and Mathematics with Applications, {bf 62} (2011), 3353-3365.
87
bibitem{rezaee}
88
H. Rezaei, M. Emoto and M. Mukaidono, {it New similarity measure
89
between two fuzzy sets}, Journal of Advanced Computational Intelligence and Intelligent Informatics, {bf 10} (2006), 946-953.
90
bibitem{rosu}
91
P. J. Rosseeuw and A. M. Leroy, {it Robust regression and outlier
92
detection}, Wiley, 1987.
93
bibitem{sakawa}
94
M. Sakawa and H. Yano, {it
95
Multiobjective fuzzy linear regression analysis for fuzzy
96
input-output data}, Fuzzy Sets and Systems, {bf 47} (1992), 173-181.
97
bibitem{kelkin}
98
S. M. Taheri and M. Kelkinnama, {it Fuzzy least absolutes regression}, In: Proc. 4th Internatinal IEEE Conferance on Intelligent Systems, Varna, Bulgaria, (2008), 55-58.
99
%bibitem{robust}
100
%W. Stahel and S. Weisberg, (ed.s), {it Directions in robust
101
%Statistics and Diagnistics}, Springer- Verlag, New York, 1991.
102
bibitem{tanakaGuo}
103
H. Tanaka and P. Guo, {it Possibilistic data analysis for operations
104
research}, Springer-Verlag, New York, 1999.
105
bibitem{tanaka}
106
H. Tanaka, S. Vejima and K. Asai, {it Linear regression analysis
107
with fuzzy model}, IEEE Transactions on Systems, Man, Cybernetics, {bf12} (1982), 903-907.
108
bibitem{torabi}
109
H. Torabi and J. Behboodian, {it Fuzzy least-absolutes estimates
110
in linear models}, Communications in Statistics-Theory and
111
Methods, {bf 36} (2007), 1935-1944.
112
%bibitem[Yang and Ko]{}
113
%M.S. Yang,
114
bibitem{ko}
115
M. S. Yang and C. H. Ko, {it On a class of fuzzy c-numbers
116
clustering procedures for fuzzy data}, Fuzzy Sets and Systems,
117
{bf 84} (1996), 49-60.
118
bibitem{koccc}
119
M. S. Yang and C. H. Ko, {it On cluster-wise fuzzy regression
120
analysis}, IEEE Transactions on Systems, Man, Cybernetics B, {bf 27} (1997), 1-13.
121
bibitem{lin}
122
M. S. Yang and T. S. Lin, {it Fuzzy least-squares linear
123
regression analysis for fuzzy input-output data}, Fuzzy Sets and
124
Systems, {bf 126} (2002), 389-399.
125
bibitem{yen}
126
K. K. Yen, G. Ghoshray and G. Roig, {it A linear regression
127
model using triangular fuzzy number coefficient}, Fuzzy Sets and
128
Systems, {bf 106} (1999), 167-177.
129
bibitem{z}
130
H. J. Zimmermann, {it Fuzzy set theory and its applications},
131
Kluwer, Dodrecht, 3rd ed., 1995.
132
ORIGINAL_ARTICLE
TRANSPORT ROUTE PLANNING MODELS BASED
ON FUZZY APPROACH
Transport route planning is one of the most important and frequent activities in supply chain management. The design of information systems for route planning in real contexts faces two relevant challenges: the complexity of the planning and the lack of complete and precise information. The purpose of this paper is to nd methods for the development of transport route planning in uncertainty decision making contexts. The paper uses an approximation that integrates a speci c fuzzy-based methodology from Soft Computing. We present several fuzzy optimization models that address the imprecision and/or exibility of some of its components. These models allow transport route planning problems to be solve with the help of metaheuristics in a concise way. A simple numerical example is shown to illustrate this approach.
http://ijfs.usb.ac.ir/article_231_7ebf6519fbcb9484fdaa9a6e8d293100.pdf
2012-02-11T11:23:20
2018-05-25T11:23:20
141
158
10.22111/ijfs.2012.231
Fuzzy optimization
Route planning
Soft computing
Julio
Brito
jbrito@ull.es
true
1
I. U. D. R., University of La Laguna, E-38271 Tenerife, Spain
I. U. D. R., University of La Laguna, E-38271 Tenerife, Spain
I. U. D. R., University of La Laguna, E-38271 Tenerife, Spain
LEAD_AUTHOR
Jose A.
Moreno
jamoreno@ull.es
true
2
I. U. D. R., University of La Laguna, E-38271 Tenerife, Spain
I. U. D. R., University of La Laguna, E-38271 Tenerife, Spain
I. U. D. R., University of La Laguna, E-38271 Tenerife, Spain
AUTHOR
Jose L.
Verdegay
verdegay@decsai.ugr.es
true
3
Department C. C. I. A., University of Granada, E-18071 Granada,
Spain
Department C. C. I. A., University of Granada, E-18071 Granada,
Spain
Department C. C. I. A., University of Granada, E-18071 Granada,
Spain
AUTHOR
[1] E. Avineri, Soft computing applications in trac and transport systems: a review, Advances
1
in Soft Computing, 1 (2005), 17-25.
2
[2] A. Baykasoglu and T. Gocken, Review and classication of fuzzy mathematical programs,
3
Journal of Intelligent & Fuzzy Systems, 19 (2008), 205-229.
4
[3] R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Management
5
Science, 17(B)(4) (1970), 141-164.
6
[4] J. M. Cadenas and J. L. Verdegay, Using fuzzy numbers in linear programming, IEEE Transactions
7
on Systems, Man and Cybernetics, 27(B)(6) (1997), 1017-1022.
8
[5] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,
9
Iranian Journal of Fuzzy Systems, 3(1) (2006), 1-21.
10
[6] R. Cheng and M. Gen, Vehicle routing problem with fuzzy due-time using genetic algorithm,
11
Japanese Journal of Fuzzy Theory and Systems, 7(5) (1995), 1050-1061.
12
[7] J. F. Cordeau, G. Laporte, M. Savelsbergh and D. Vigo, Vehicle Routing, Handbook in OR
13
& MS, 14(6) (2007), 367-427.
14
[8] M. Delgado, J. L. Verdegay and M. A. Vila, Imprecise costs in mathematical programming
15
problems, Control and Cybernet, 16(2) (1987), 113-121.
16
[9] M. Delgado, J. L. Verdegay and M. A. Vila, A general model for fuzzy linear programming,
17
Fuzzy Sets and Systems, 29 (1989), 21-29.
18
[10] M. Djadane, G. Goncalves, T. Hsu and R. Dupas, Dynamic vehicle routing problems under
19
exible time windows and fuzzy travel times, Proceedings of 2006 International Conference
20
on Service Systems and Service Management, 2 (2006), 1519-1524.
21
[11] C. Erbao and L. Mingyong, A hybrid dierential evolution algorithm to vehicle routing prob-
22
lem with fuzzy demands, Journal of Computational and Applied Mathematics, 231 (2009),
23
[12] K. Ganesh, A. S. Nallathambi and T. T. Narendran, Variants, solution approaches and ap-
24
plications for Vehicle Routing Problems in supply chain: agile framework and comprehensive
25
review, International Journal of Agile Systems and Management, 2(1) (2007), 50-75.
26
[13] M. Gendreau, G. Laporte and R. Seguin, Stochastic vehicle routing, European Journal of
27
Operational Research, 88(1) (1996), 312.
28
[14] J. Y. Guo and J. Li, A hybrid genetic algorithm to the vehicle routing problem with fuzzy
29
traveling time, Journal of Industrial Engineering Management, 19 (2006), 13-17.
30
[15] L. Hong and M. Xu, A model of MDVRPTW with fuzzy travel time and time-dependent and
31
its solution, Proceeding of Fifth International Conference on Fuzzy Systems and Knowledge
32
Discovery, 3 (2008), 473-478.
33
[16] L. Hong and M. Xu, Real vehicle routing and dispatching with dynamic fuzzy travel times,
34
Proceeding of Second International Conference on Genetic and Evolutionary Computing,
35
doi:10.1109/WGEC.2008.28, (2008), 32-37,
36
[17] J. Jia, N. Liu and R. Wang, Genetic algorithm for fuzzy logistics distribution vehicle rout-
37
ing problem, Proceeding International Conference on Service Operations and Logistics, and
38
Informatics, doi:10.1109/SOLI.2008.4686625, (2008), 1427-1432.
39
[18] M. Ko, A. Tiwari and J. Mehnen, A review of soft computing applicactions in supply chain
40
management, Applied Soft Computing, 10 (2010), 661-674.
41
[19] R. J. Kuo, C. Y. Chiu and Y. J. Lin, Integration of fuzzy theory and ant algorithm for vehicle
42
routing problem with time window, International Conference of the North American Fuzzy
43
Information Processing Society, 23 (2004), 925-930.
44
[20] C. S. Liu and M. Y. Lai, The vehicle routing problem with uncertain demand at nodes,
45
Transportation Research Part E: Logistics and Transportation Review, 5(4) (2009), 517-524.
46
[21] P. Lucic and D. Teodorovic, Vehicle routing problem with uncertain demand at nodes: the bee
47
system and fuzzy logic approach, In Fuzzy Sets Based Heuristics for Optimization, Springer
48
Verlag, Berlin, (2003), 67-82.
49
[22] P. Lucic and D. Teodorovic, The fuzzy ant system for the vehicle routing problem when
50
demand at nodes is uncertain, Journal on Articial Intelligence Tools (IJAIT), 16(5) (2007),
51
[23] M. R. Sa, H. R. Maleki and E. Zaeimazad, A note on the Zimmermann method for solving
52
fuzzy linear programming problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 31-45.
53
[24] W. R. Stewart Jr. and B. L. Golden, Stochastic vehicle routing: a comprehensive approach,
54
European Journal of Operational Research, 14(4) (1983), 371-385.
55
[25] L. Tang, W. Cheng, Z. Xhang and B. Zhong, Ant colony algorithm based on information
56
entropy theory to fuzzy vehicle routing problem, Proceedings ISKE, Series: Advances in Intelligent
57
Systems Research, 2007.
58
[26] D. Teodorovic and S. Kikuchi, Application of fuzzy sets theory to the saving based vehicle
59
routing algorithm, Civil Engineering Systems, 8 (1991), 87-93.
60
[27] D. Teodorovic and G. Pavkovic, The fuzzy set theory approach to the vehicle routing problem
61
when demand at nodes is uncertain, Fuzzy Sets and Systems, 82 (1996), 307-317.
62
[28] D. Teodorovi, Fuzzy logic systems for transportation engineering: the state of the art, Transportation
63
Research, 33(A) (1999), 337-364.
64
[29] F. Tillman, The multiple terminal problem with probabilistic demands, Transportation Science,
65
3(3) (2002), 192-204.
66
[30] P. Toth and D. Vigo, The vehicle routing problem, Monographs on Discrete Mathematics and
67
Applications, SIAM, 9 (2002).
68
[31] J. L. Verdegay, Fuzzy mathematical programming, In: M. M. Gupta, E. Sanchez, eds., Fuzzy
69
Information and Decision Processes, 1982.
70
[32] J. L. Verdegay, Fuzzy optimization: models, methods and perspectives, Proceding 6thIFSA-95
71
World Congress, (1995), 39-71.
72
[33] J. L. Verdegay, R. R. Yager and P. Bonissone, On heuristics as a fundamental constituent of
73
Soft Computing, Fuzzy Sets and Systems, 159 (2008), 846-855.
74
[34] R. Viertl and D. Hareter, Fuzzy information and stochastics, Iranian Journal of Fuzzy Systems,
75
1(1) (2004), 43-56.
76
[35] J. Y. Zhang and J. Li, Study on logistics distribution vehicle routing problem with fuzzy due-
77
time, International Conference on Management Science & Engineering, doi: 10. 1109/ICMSE.
78
2007. 4421866, (2007), 311-317.
79
[36] Y. S. Zheng and B. D. Liu, Fuzzy vehicle routing model with credibility measure and its hybrid
80
intelligent algorithm, Applied Mathematics and Computation, 176 (2006), 673-683.
81
[37] H. J. Zimmermann, Description and optimization of fuzzy system, International Journal of
82
general System, 2 (1976), 209-216.
83
ORIGINAL_ARTICLE
Persian-translation vol. 9, no.1, February 2012
http://ijfs.usb.ac.ir/article_2817_2daa4ebcebc8bddd67ee46bf11e33390.pdf
2012-02-01T11:23:20
2018-05-25T11:23:20
161
170
10.22111/ijfs.2012.2817