ORIGINAL_ARTICLE
Cover Special Issue vol. 10, no. 2, April 2013
http://ijfs.usb.ac.ir/article_2719_40548fa8cb311bf7e87b5cb4defb8845.pdf
2013-04-29T11:23:20
2017-09-20T11:23:20
0
10.22111/ijfs.2013.2719
ORIGINAL_ARTICLE
RANDOM FUZZY SETS: A MATHEMATICAL TOOL TO
DEVELOP STATISTICAL FUZZY DATA ANALYSIS
Data obtained in association with many real-life random experiments from different fields cannot be perfectly/exactly quantified.\hspace{.1cm}Often the underlying imprecision can be suitably described in terms of fuzzy numbers/\\values. For these random experiments, the scale of fuzzy numbers/values enables to capture more variability and subjectivity than that of categorical data, and more accuracy and expressiveness than that of numerical/vectorial data. On the other hand, random fuzzy numbers/sets model the random mechanisms generating experimental fuzzy data, and they are soundly formalized within the probabilistic setting.This paper aims to review a significant part of the recent literature concerning the statistical data analysis with fuzzy data and being developed around the concept of random fuzzy numbers/sets.
http://ijfs.usb.ac.ir/article_609_5b8567703d17bcd661b10543f43ed47a.pdf
2013-04-30T11:23:20
2017-09-20T11:23:20
1
28
10.22111/ijfs.2013.609
Distances between fuzzy numbers/values
Fuzzy numbers/values
Fuzzy arithmetic
Random fuzzy numbers/sets
Statistical methodology
A.
Blanco-Fernandez
blancoangela@uniovi.es
true
1
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
AUTHOR
M. R.
Casals
rmcasals@uniovi.es
true
2
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
AUTHOR
A.
Colubi
colubi@uniovi.es
true
3
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
AUTHOR
N.
Corral
norbert@uniovi.es
true
4
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
AUTHOR
M.
Garca-Barzana
martagb5@gmail.com
true
5
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
AUTHOR
M. A.
Gil
magil@uniovi.es
true
6
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
LEAD_AUTHOR
G.
Gonzalez-Rodrguez
gil@uniovi.es
true
7
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
AUTHOR
M.T.
Lopez
mtlopez@uniovi.es
true
8
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
AUTHOR
M.
Montenegro
mmontenegro@uniovi.es
true
9
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
AUTHOR
M. A.
Lubiano
lubiano@uniovi.es
true
10
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo,
Spain
AUTHOR
A. B.
Ramos-Guajardo
ramosana@uniovi.es
true
11
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
AUTHOR
S.
de la Rosa de Saa
delarosasara@uniovi.es
true
12
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de
Oviedo, Spain
AUTHOR
B.
Sinova
sinovabeatriz@uniovi.es
true
13
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
Departamento de Estadstica e I.O. y D.M., Universidad de Oviedo, Spain
AUTHOR
[1] M. C. Alonso, T. Brezmes, M. A. Lubiano and C. Bertoluzza, A generalized real-valued
1
measure of the inequality associated with a fuzzy random variable, Int. J. Approx. Reas., 26
2
(2001), 47–66.
3
[2] C. Bertoluzza, N. Corral and A. Salas, On a new class of distances between fuzzy numbers,
4
Mathware & Soft Computing, 2 (1995), 71–84.
5
[3] A. Colubi, Statistical inference about the means of fuzzy random variables: applications to
6
the analysis of fuzzy- and real-valued data, Fuzzy Sets and Systems, 160 (2009), 344–356.
7
[4] A. Colubi, J. S. Dom´ınguez-Menchero, M. L´opez-D´ıaz and D. A. Ralescu, On the formalization
8
of fuzzy random variables, Information Sciences, 133 (2001), 3–6.
9
[5] A. Colubi, G. Gonz´alez-Rodr´ıguez, M. A. Gil and W. Trutschnig, Nonparametric criteria for
10
supervised classification of fuzzy data, Int. J. Approx. Reas., 52 (2011), 1272–1282.
11
[6] A. Colubi, M. L´opez-D´ıaz, J. S. Dom´ınguez-Menchero and M. A. Gil, A generalized strong
12
law of large numbers, Prob. Theor. Rel. Fields, 114 (1999), 401–417.
13
[7] P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets and Systems, 100 (1999),
14
63–71.
15
[8] M. B. Ferraro, R. Coppi, G. Gonz´alez-Rodr´ıguez and A. Colubi, A linear regression model
16
for imprecise response, Int. J. Approx. Reas., 51 (2010), 759–770.
17
[9] D. Garc´ıa, M. A. Lubiano and M. C. Alonso, Estimating the expected value of fuzzy random
18
variables in the stratified random sampling from finite populations, Information Sciences, 138
19
(2001), 165–184.
20
[10] M. A. Gil, M. L´opez-D´ıaz and H. L´opez-Garc´ıa, The fuzzy hyperbolic inequality index associated
21
with fuzzy random variables, Eur. J. Oper. Res., 110 (1998), 377–391.
22
[11] M. A. Gil, M. A. Lubiano, M. Montenegro and M. T. L´opez, Least squares fitting of an affine
23
function and strength of association for interval-valued data, Metrika, 56 (2002), 97–111.
24
[12] M. A. Gil, M. Montenegro, G. Gonz´alez-Rodr´ıguez, A. Colubi and M. R. Casals, Bootstrap
25
approach to the multi-sample test of means with imprecise data, Comp. Stat. Data Anal., 51
26
(2006), 148–162.
27
[13] E. Gin´e and J. Zinn, Bootstrapping general empirical measures, Ann. Probab., 18 (1990),
28
851–869.
29
[14] G. Gonz´alez-Rodr´ıguez, A. Blanco, A. Colubi and M. A. Lubiano, Estimation of a simple
30
linear regression model for fuzzy random variables, Fuzzy Sets and Systems, 160 (2009),
31
[15] G. Gonz´alez-Rodr´ıguez, A. Colubi and M. A. Gil, A fuzzy representation of random variables:
32
an operational tool in exploratory analysis and hypothesis testing, Comp. Stat. Data Anal.,
33
51 (2006), 163–176.
34
[16] G. Gonz´alez-Rodr´ıguez, A. Colubi and M. A. Gil, Fuzzy data treated as functional data. A
35
one-way ANOVA test approach, Comp. Stat. Data Anal., 56 (2012), 943-955.
36
[17] G. Gonz´alez-Rodr´ıguez, A. Colubi, M. A. Gil and P. D’Urso, An asymptotic two dependent
37
samples test of equality of means of fuzzy random variables, In: Proc. COMPSTAT’2006,
38
(2006), http://www.stat.unipg.it/iasc/Proceedings/2006/COMPSTAT/CD/145.pdf.
39
[18] G. Gonz´alez-Rodr´ıguez, M. Montenegro, A. Colubi and M. A. Gil, Bootstrap techniques
40
and fuzzy random variables: Synergy in hypothesis testing with fuzzy data, Fuzzy Sets and
41
Systems, 157 (2006), 2608–2613.
42
[19] G. Gonz´alez-Rodr´ıguez, W. Trutschnig and A. Colubi., Confidence regions for
43
the mean of a fuzzy random variable, In: Abstracts of IFSA-EUSFLAT 2009,
44
http://www.eusflat.org/publications/proceedings/IFSA-EUSFLAT 2009/pdf/tema 1433.pdf.
45
[20] T. Hesketh, R. Pryor and B. Hesketh, An application of a computerized fuzzy graphic rating
46
scale to the psychological measurement of individual differences, Int. J. Man-Machine Studies,
47
29 (1988), 21–35.
48
[21] B. Hesketh, T. Hesketh, J. I. Hansen and D. Goranson, Use of fuzzy variables in developing
49
new scales from the strong interest inventory, J. Counseling Psychology, 42 (1995), 85–99.
50
[22] M. Hukuhara, Int´egration des applications measurables dont la valeur est un compact convexe,
51
Funkcial. Ekvac., 10 (1967), 205-223.
52
[23] E. P. Klement, M. L. Puri and D. A. Ralescu, Limit theorems for fuzzy random variables,
53
Proc. R. Soc. Lond. A, 407 (1986), 171–182.
54
[24] R. K¨orner, An asymptotic -test for the expectation of random fuzzy variables, J. Stat. Plann.
55
Infer., 83 (2000), 331–346.
56
[25] R. K¨orner and W. N¨ather, On the variance of random fuzzy variables, In: C. Bertoluzza,
57
M. A. Gil and D. A. Ralescu, eds., Statistical Modeling, Analysis and Management of Fuzzy
58
Data, Physica-Verlag, Heidelberg, (2002), 22–39.
59
[26] R. Kruse and K. D. Meyer, Statistics with vague data, D. Reidel Publishing Company, Dordrecht,
60
[27] H. Kwakernaak, Fuzzy random variables-I. definitions and theorems, Information Sciences,
61
15 (1978), 1–29.
62
[28] H. Kwakernaak, Fuzzy random variables-II. algorithms and examples for the discrete case,
63
Information Sciences, 17 (1979), 253–278.
64
[29] H. L´opez-Garc´ıa, M. A. Gil, N. Corral and M. T. L´opez, Estimating the fuzzy inequality
65
associated with a fuzzy random variable in random samplings from finite populations, Kybernetika,
66
34 (1998), 149–161.
67
[30] M. A. Lubiano, M. C. Alonso and M. A. Gil, Statistical inferences on the S-mean squared
68
dispersion of a fuzzy random variable, In: B. de Baets, J. Fodor and L. T. Koczy, eds.,
69
Proceedings of EUROFUSE-SIC99, University of Veterinary Science, Budapest, (1999), 532–
70
[31] M. A. Lubiano and M. A. Gil, Estimating the expected value of fuzzy random variables in
71
random samplings from finite populations, Stat. Pap., 40(1999), 277–295.
72
[32] M. A. Lubiano, M. A. Gil and M. L´opez-D´ıaz, On the Rao-Blackwell theorem for fuzzy
73
random variables, Kybernetika, 35 (1999), 167–175.
74
[33] M. A. Lubiano, M. A. Gil, M. L´opez-D´ıaz and M. T. L´opez, The ! -mean squared dispersion
75
associated with a fuzzy random variable, Fuzzy Sets and Systems, 111 (2000), 307–317.
76
[34] M. Montenegro, M. R. Casals, M. A. Lubiano and M. A. Gil, Two-sample hypothesis tests of
77
means of a fuzzy random variable, Information Sciences, 133 (2001), 89–100.
78
[35] M. Montenegro, A. Colubi, M. R. Casals and M. A. Gil, Asymptotic and Bootstrap techniques
79
for testing the expected value of a fuzzy random variable, Metrika, 59 (2004), 31–49.
80
[36] M. Montenegro, M. T. L´opez-Garc´ıa, M. A. Lubiano and G. Gonz´alez-Rodr´ıguez, A dependent
81
multi-sample test for fuzzy means, In: Abst. 2nd Workshop ERCIM WG Comput. & Statist,
82
(2009), 102.
83
[37] T. Nakama, A. Colubi and M. A. Lubiano, Factorial analysis of variance for fuzzy data, In:
84
Abst. CFE’10 & ERCIM’10, (2010), 88.
85
[38] H. T. Nguyen, A note on the extension principle for fuzzy sets, J. Math. Anal. Appl., 64
86
(1978), 369–380.
87
[39] M. L. Puri and D. A. Ralescu, Differentials of fuzzy functions, J. Math. Anal. Appl., 91
88
(1983), 552–558.
89
[40] M. L. Puri and D. A. Ralescu, The concept of normality for fuzzy random variables, Ann.
90
Probab., 11 (1985), 1373–1379.
91
[41] M. L. Puri and D. A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl., 114 (1986),
92
409–422.
93
[42] S. Ramezanzadeh, M. Memariani and S. Saati, Data envelopment analysis with fuzzy random
94
inputs and outputs: a chance-constrained programming approach, Iranian Journal of Fuzzy
95
Systems, 2 (2005), 21–29.
96
[43] A. B. Ramos-Guajardo, A. Colubi, G. Gonz´alez-Rodr´ıguez and M. A. Gil, One sample tests
97
for a generalized Fr´echet variance of a fuzzy random variable, Metrika, 71 (2010), 185–202.
98
[44] A. B. Ramos-Guajardo and M. A. Lubiano, K-sample tests for equality of variances of
99
random fuzzy sets, Comp. Stat. Data Anal., 56 (2012), 956–966.
100
[45] B. Sinova, M. A. Gil, A. Colubi and S. Van Aelst, The median of a random fuzzy number.
101
The 1-norm distance approach, Fuzzy Sets and Systems, 200 (2011), 99-115.
102
[46] B. Sinova, S. de la Rosa de S´aa and M. A. Gil, A generalized L1-type metric between fuzzy
103
numbers for an approach to central tendency of fuzzy data, Information Sciences, under 2nd
104
[47] S. M. Taheri and M. Kelkinnama, Fuzzy linear regression based on least absolutes deviations,
105
Iranian Journal of Fuzzy Systems, 9(1) (2012), 121-140.
106
[48] P. Ter´an, A strong law of large numbers for random upper semicontinuous functions under
107
exchangeability conditions, Statist. Prob. Lett., 65 (2003), 251–258.
108
[49] W. Trutschnig, G. Gonz´alez-Rodr´ıguez, A. Colubi and M. A. Gil, A new family of metrics for
109
compact, convex (fuzzy) sets based on a generalized concept of mid and spread, Information
110
Sciences, 179 (2009), 3964–3972.
111
[50] W. Trutschnig and M. A. Lubiano, SAFD: statistical analysis of fuzzy data, http://cran.rproject.
112
org/web/packages/SAFD/index.html.
113
[51] R. Viertl and D. Hareter, Fuzzy information and stochastics, Iranian Journal of Fuzzy Systems,
114
1 (2004), 43–56.
115
[52] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning,
116
Part 1, Information Sciences, 8 (1975), 199–249; Part 2, Information Sciences, 8 (1975), 301–
117
353; Part 3, Information Sciences, 9 (1975), 43–80.
118
[53] L. A. Zadeh, Discussion: probability theory and fuzzy logic are complementary rather than
119
competitive, Technometrics, 37 (1995), 271–276.
120
ORIGINAL_ARTICLE
AGE REPLACEMENT POLICY IN UNCERTAIN
ENVIRONMENT
Age replacement policy is concerned with finding an optional time tominimize the cost, at which time the unit is replaced even if itdoes not fail. So far, age replacement policy involving random agehas been proposed. This paper will assume the age of the unit is anuncertain variable, and find the optimal time to replace the unit.
http://ijfs.usb.ac.ir/article_610_ee7d15bd6bca31096c32766a55373e15.pdf
2013-04-29T11:23:20
2017-09-20T11:23:20
29
39
10.22111/ijfs.2013.610
Uncertainty theory
Renewal process
Age replacement
Maintenance
Kai
Yao
yaok09@mails.tsinghua.edu.cn
true
1
Department of Mathematical Sciences, Tsinghua University, Beijing 100084,
China
Department of Mathematical Sciences, Tsinghua University, Beijing 100084,
China
Department of Mathematical Sciences, Tsinghua University, Beijing 100084,
China
LEAD_AUTHOR
Dan A.
Ralescu
ralescd@ucmail.uc.edu
true
2
Department of Mathematical Sciences, University of Cincinnati,
Cincinnati, OH 45221-0025, USA
Department of Mathematical Sciences, University of Cincinnati,
Cincinnati, OH 45221-0025, USA
Department of Mathematical Sciences, University of Cincinnati,
Cincinnati, OH 45221-0025, USA
AUTHOR
[1] R. E. Barlow and F. Proschan, Mathematical theory of reliability, Wiley and Sons, New York,
1
[2] P. J. Boland and F. Proschan, Periodic replacement with increasing minimal repair costs at
2
failure, Operations Research, 30(6) (1982), 1183{1189.
3
[3] X. Chen, American option pricing formula for uncertain financial market, International
4
Journal of Operations Research, 8(2) (2011), 32{37.
5
[4] X. Chen and W. Dai, Maximum entropy principle for uncertain variables, International
6
Journal of Fuzzy Systems, 13(3) (2011), 232{236.
7
[5] R. Cleroux, S. Dubuc and C. Tilquin, The age replacement problem with minimal repair and
8
random repair costs, Operations Research, 27(6) (1979), 1158{1167.
9
[6] W. Dai and X. Chen, Entropy of function of uncertain variables, Mathematical and Computer
10
Modelling, 55(3-4) (2012), 754{760.
11
[7] B. Fox, Age replacement with discounting, Operations Research, 14(3) (1966), 533{537.
12
[8] X. Gao, Some properties of continuous uncertain measure, International Journal of Uncer-
13
tainty, Fuzziness and Knowledge-Based Systems, 17(3) (2009), 419{426.
14
[9] J. Gao, Q. Zhang and P. Shen, Coalitional game with fuzzy payoffs and credibilistic Shapley
15
value, Iranian Journal of Fuzzy Systems, 8(4) (2011), 107{117.
16
[10] J. Gao, Uncertain bimatrix game with applications, Fuzzy Optimization and Decision Making,
17
12(1) (2013), 65-78.
18
[11] D. Kahneman and A. Tversky, Prospect theory: An analysis of decisions under risk, Econo-
19
metrica, 47(2) (1979), 263{291.
20
[12] B. Liu, Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin, 2007.
21
[13] B. Liu, Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems,
22
2(1) (2008), 3{16.
23
[14] B. Liu, Theory and Practice of Uncertain Programming, 2nd ed., Springer-Verlag, Berlin,
24
[15] B. Liu, Uncertain set theory and uncertain inference rule with application to uncertain control
25
, Journal of Uncertain Systems, 4(2) (2010), 83{98.
26
[16] B. Liu, Uncertain risk analysis and uncertain reliability analysis, Journal of Uncertain Sys-
27
tems, 4(3) (2010), 163{170.
28
[17] B. Liu, Uncertainty theory: a branch of mathematics for modeling human uncertainty,
29
Springer-Verlag, Berlin, 2011.
30
[18] B. Liu, Uncertain logic for modeling human language, Journal of Uncertain Systems, 5(1)
31
(2011), 3{20.
32
[19] B. Liu, Why is there a need for uncertainty theory?, Journal of Uncertain Systems, 6(1)
33
(2012), 3{10.
34
[20] B. Liu, Extreme value theorems of uncertain process with application to insurance risk model,
35
Soft Computing, accepted.
36
[21] Y.H. Liu and M. Ha, Expected value of function of uncertain variables, Journal of Uncertain
37
Systems, 4(3) (2010), 181{186.
38
[22] V. P. Marathe and K. P. K. Nair, Multistage planned replacement strategies, Operations
39
Research, 14(5) (1966), 874{887.
40
[23] T. Nakagawa, Maintenance theory of reliability, Springer-Verlag, London, 2005.
41
[24] J. Peng and K. Yao, A new option pricing model for stocks in uncertainty markets, Interna-
42
tional Journal of Operations Research, 8(2) (2011), 18{26.
43
[25] Z. Peng and K. Iwamura, A sufficient and necessary condition of uncertainty distribution,
44
Journal of Interdisciplinary Mathematics, 13(3) (2010), 277{285.
45
[26] C. Tilquin and R. Cleroux, Block replacement policies with general cost structures, Techno-
46
metrics, 17(3) (1975), 291{298.
47
[27] C. Tilquin and R. Cleroux, Periodic replacement with minimal repair at failure and adjustment
48
costs, Naval Research Logistics Quarterly, 22(2) (1975), 243{254.
49
[28] X. Wang, Z. Gao and H. Guo, Uncertain hypothesis testing for two experts’ empirical data,
50
Mathematical and Computer Modelling, 55 (2012), 1478{1482.
51
[29] K. Yao, Uncertain calculus with renewal process, Fuzzy Optimization and Decision Making,
52
11(3) (2012), 285{297.
53
[30] K. Yao and X. Li, Uncertain alternating renewal process and its application, IEEE Transac-
54
tions on Fuzzy Systems, 20(6) (2012), 1154-1160.
55
[31] K. Yao, No-arbitrage determinant theorems on mean-reverting stock model in uncertain market
56
, Knowledge-Based Systems, 35 (2012), 259-263.
57
[32] K. Yao, Block repalcement policy in uncertain environment, http://orsc.edu.cn/online/
58
110612.pdf.
59
[33] K. Yao, Some properties of uncertain renewal process, http://orsc.edu.cn/online/110602.pdf.
60
[34] C. You, Some convergence theorems of uncertain sequences, Mathematical and Computer
61
Modelling, 49(3-4) (2009), 482{487.
62
[35] Y. Zhu, Uncertain optimal control with application to a portfolio selection model, Cybernetics
63
and Systems, 41(7) (2010), 535{547.
64
ORIGINAL_ARTICLE
REGION MERGING STRATEGY FOR BRAIN MRI
SEGMENTATION USING DEMPSTER-SHAFER THEORY
Detection of brain tissues using magnetic resonance imaging (MRI) is an active and challenging research area in computational neuroscience. Brain MRI artifacts lead to an uncertainty in pixel values. Therefore, brain MRI segmentation is a complicated concern which is tackled by a novel data fusion approach. The proposed algorithm has two main steps. In the first step the brain MRI is divided to some main and ancillary cluster which is done using Fuzzy c-mean (FCM). In the second step, the considering ancillary clusters are merged with main clusters employing Dempster-Shafer Theory. The proposed method was validated on simulated brain images from the commonly used BrainWeb dataset. The results of the proposed method are evaluated by using Dice and Tanimoto coefficients which demonstrate well performance and robustness of this algorithm.
http://ijfs.usb.ac.ir/article_611_816e9129fa7cd7f854cbf6ff7d8fd94a.pdf
2013-04-29T11:23:20
2017-09-20T11:23:20
49
56
10.22111/ijfs.2013.611
MRI
Fuzzy c-mean
Brain MRI Segmentation
Dempster-Shafer Theory
Jamal
Ghasemi
j.ghasemi@umz.ac.ir
true
1
Faculty of Engineering and Technology, University of Mazan-
daran, Babolsar, Iran
Faculty of Engineering and Technology, University of Mazan-
daran, Babolsar, Iran
Faculty of Engineering and Technology, University of Mazan-
daran, Babolsar, Iran
LEAD_AUTHOR
Mohamad Reza
Karami Mollaei
mkarami@nit.ac.ir
true
2
Faculty of Electrical and Computer Engeniering,
Babol University of Technology, P.O.Box 484, Babol, Iran
Faculty of Electrical and Computer Engeniering,
Babol University of Technology, P.O.Box 484, Babol, Iran
Faculty of Electrical and Computer Engeniering,
Babol University of Technology, P.O.Box 484, Babol, Iran
AUTHOR
Reza
Ghaderi
r_ghaderi@sbu.ac.ir
true
3
Shahid Beheshti University, Tehran, Iran
Shahid Beheshti University, Tehran, Iran
Shahid Beheshti University, Tehran, Iran
AUTHOR
Ali Hojjatoleslami
Hojjatoleslami
s.a.hojjatoleslami@kent.ac.uk
true
4
School of computing, University of Kent, Canterbury,CT2 7PT
UK
School of computing, University of Kent, Canterbury,CT2 7PT
UK
School of computing, University of Kent, Canterbury,CT2 7PT
UK
AUTHOR
[1] W. Abd-Almageed, A. El-Osery and C. Smith, A fuzzy-statistical contour model for MRI
1
segmentation and target tracking, presented at the SPIE, Orlando, FL, USA, (2004), 25{33.
2
[2] M. N. Ahmed, S. M. Yamany, N. Mohamed, A. A. Farag and T. Moriarty, A modied fuzzy c-
3
means algorithm for bias eld estimation and segmentation of MRI data, IEEE transactions
4
on medical imaging, 21(3) (2002), 193{199.
5
[3] S. P. Awate, H. Zhang, T. J. Simon and J. C. Gee, Multivariate segmentation of brain tissues
6
by fusion of MRI and DTI data, presented at the Proceedings of the 2008 IEEE International
7
Symposium on Biomedical Imaging: From Nano to Macro, Paris, France, (2008).
8
[4] M. Balafar, A. Ramli, M. Saripan and S. Mashohor, Review of brain MRI image segmentation
9
methods, Articial Intelligence Review, 33(3) (2010), 261{274.
10
[5] M. Beynon, D. Cosker and D. Marshall, An expert system for multi-criteria decision making
11
using Dempster Shafer theory, Expert Systems with Applications, 20(4) (2001), 357{367.
12
[6] E. Binaghi and P. Madella, Fuzzy DempsterShafer reasoning for rule-based classiers, Inter-
13
national Journal of Intelligent Systems, 14(6) (1999), 559-583.
14
[7] I. Bloch, Some aspects of Dempster-Shafer evidence theory for classication of multi-modality
15
medical images taking partial volume eect into account, Pattern Recognition Letters, 17(8)
16
(1996), 905{919.
17
[8] M. Bomans, K. H. Hohne, U. Tiede and M. Riemer, 3-D segmentation of MR images of the
18
head for 3-D display, IEEE transactions on medical imaging, 9(2) (1990), 177{183.
19
[9] C. Brechbhler, G. Gerig and G. Szkely, Compensation of spatial inhomogeneity in MRI based
20
on a multi-valued image model and a parametric bias estimate, In Visualization in Biomedical
21
Computing, (1996), 141{146.
22
[10] K. S. Chuang, H. L. Tzeng, S. Chen, J. Wu and T. J. Chen, Fuzzy c-means clustering with
23
spatial information for image segmentation, Computerized Medical Imaging and Graphics :
24
the Ocial Journal of the Computerized Medical Imaging Society, 30(1) (2006), 9-151.
25
[11] A. Demirhan and I. Gler, Combining stationary wavelet transform and self-organizing maps
26
for brain MR image segmentation, Engineering Applications of Articial Intelligence, 24(2)
27
(2011), 358{367.
28
[12] J. Ghasemi, R. Ghaderi, M. R. Karami Mollaei and A. Hojjatoleslami, Separation of brain tis-
29
sues in MRI based on multi-dimensional FCM and spatial information, Eighth International
30
Conference on in Fuzzy Systems and Knowledge Discovery (FSKD), (2011), 247{251.
31
[13] J. Ghasemi, M. R. Karami Mollaei, R. Ghaderi and A. Hojjatoleslami, Brain tissue segmen-
32
tation based on spatial information fusion by Dempster-Shafer theory, Journal of Zhejiang
33
University - Science C, 13(7) (2012), 520{533.
34
[14] J. D. Gispert, S. Reig, J. Pascau, J. J. Vaquero, P. Garcia-Barreno and M. Desco, Method for
35
bias eld correction of brain T1-weighted magnetic resonance images minimizing segmenta-
36
tion error, Human brain mapping, 22(2) (2004), 133{144.
37
[15] M. Hasanzadeh and S. Kasaei, Multispectral Brain MRI Segmentation based on Fuzzy Clas-
38
siers and Evidence Theory, presented at the 15th Iranian Conference on Electrical Engi-
39
neering, ICEE, Tehran, Iran, 2007.
40
[16] T. Heinonen, P. Dastidar, H. Eskola, H. Frey, P. Ryymin and E. Laasonen, Applicability of
41
semi-automatic segmentation for volumetric analysis of brain lesions, Journal of Medical
42
Engineering And Technology, 22(4) (1998), 173{178.
43
[17] S. K. Jha and R. D. S. Yadava, Denoising by singular value decomposition and its application
44
to electronic nose data processing, IEEE Sensors Journal, 11(1) (2011), 35{44.
45
[18] L. Ji and H. Yan, An attractable snakes based on the greedy algorithm for contour extraction,
46
Pattern Recognition, 35(4) (2002), 791{806.
47
[19] Z. X. Ji, Q. S. Sun and D. S. Xia, A modied possibilistic fuzzy c-means clustering algo-
48
rithm for bias eld estimation and segmentation of brain MR image, Computerized Medical
49
Imaging and Graphics, 35(5) (2011), 383{397.
50
[20] L. Jui-Hsiang, T. Ming-Feng, C. Lumdo and C. C. P. Chen, Accurate and analytical statistical
51
spatial correlation modeling based on singular value decomposition for VLSI DFM applica-
52
tions, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,
53
29(4) (2010), 580-589.
54
[21] F. Kyoomarsi, H. Khosravi, E. Eslami and M. Davoudi, Extraction-based Text Summarization
55
Using Fuzzy Analysisn, Iranian Journal of Fuzzy Systems, 7(3) (2010), 15{32.
56
[22] Llado, A. Oliver, M. Cabezas, J. Freixenet, J. C. Vilanova, A. Quiles, L. Valls, L. Ramio-
57
Torrent and A. Rovira, Segmentation of multiple sclerosis lesions in brain MRI: a review of
58
automated approaches, Information Sciences, 186(1) (2012), 164{185.
59
[23] A. W. Liew and H. Yan, An adaptive spatial fuzzy clustering algorithm for 3-D MR image
60
segmentation, IEEE transactions on medical imaging, 22(9) (2003), 1063{1075.
61
[24] A. Liew and H. Yan, Current methods in the automatic tissue segmentation of 3D magnetic
62
resonance brain images, Current Medical Imaging Reviews, 2(1) (2006), 91{103.
63
[25] E. G. Mansoori, M. J. Zolghadri and S. D. Katebi, Using distribution of data to enhance
64
prformance of fuzzy classication systems, Iranian Journal of Fuzzy Systems, 4(1) (2007),
65
[26] E. G. Mansoori, M. J. Zolghadri, S. D. Katebi, H. Mohabatkar,R. Boostani and M. H.
66
Sadreddini, Generating fuzzy for protein classication, Iranian Journal of Fuzzy Systems,
67
5(2) (2008), 21{33.
68
[27] T. McInerney and D. Terzopoulos, Deformable models in medical image analysis: a survey,
69
Medical Image Analysis, 1(2) (1996), 91{108.
70
[28] S. B. Mehta, S. Chaudhury, A. Bhattacharyya and A. Jena, Handcrafted fuzzy rules for tissue
71
classication, Magnetic Resonance Imaging, 26(6) (2008), 815{823.
72
[29] F. Moayedi, R. bostani, A. R. Kazemi, S. Katebi and E. Dashti, Subclass Fuzzy-SVM classier
73
as an ecient method to enhance the mass detection in mamograms, Iranian Journal of Fuzzy
74
Systems, 7(1) (2010), 15{31.
75
[30] W. J. Niessen, K. L. Vincken, J. Weickert, B. M. T. H. Romeny and M. A. Viergever, Multi-
76
scale segmentation of three-dimensional MR brain images, International Journal of Computer
77
Vision, 31(2) (1999), 185{202.
78
[31] D. L. Pham and J. L. Prince, An adaptive fuzzy c-means algorithm for image segmentation in
79
the presence of intensity inhomogeneities, Pattern Recognition Letters, 20(1) (1999), 57{68.
80
[32] D. L. Pham and J. L. Prince, Adaptive fuzzy segmentation of magnetic resonance images,
81
IEEE Transactions on Medical Imaging, 18(9) (1999), 737-752.
82
[33] D. L. Pham, C. Xu and J. L. Prince, A survey of current methods in medical image segmen-
83
tation, Annual Review of Biomedical Engineering, 2 (2000), 315{337.
84
[34] S. Prima, N. Ayache, T. Barrick and N. Roberts, Maximum likelihood estimation of the bias
85
eld in MR brain images: investigating dierent modelings of the imaging process, presented
86
at the Proceedings of the 4th International Conference on Medical Image Computing and
87
Computer-Assisted Intervention, Utrecht, The Netherlands, 2001.
88
[35] S. Ramathilagam, R. Pandiyarajan, A. Sathya, R. Devi and S. R. Kannan, Modied fuzzy c-
89
means algorithm for segmentation of T1-T2-weighted brain MRI, Journal of Computational
90
and Applied Mathematics, 235(6) (2011), 1578{1586.
91
[36] G. Shafer, A mathematical theory of evidence, Princeton University Press, Princeton., 1976.
92
[37] S. Shen, W. Sandham, M. Granat and A. Sterr, MRI fuzzy segmentation of brain tissue using
93
neighborhood attraction with neural-network optimization, IEEE Transactions on Information
94
Technology in Biomedicine : a Publication of the Ieee Engineering in Medicine and Biology
95
Society, 9(3) (2005), 459{67.
96
[38] A. Simmons, P. S. Tofts, G. J. Barker and S. R. Arridge, Sources of intensity nonuniformity
97
in spin echo images at 1.5 T, Magnetic Resonance in Medicine : ocial journal of the Society
98
of Magnetic Resonance in Medicine, 32(1) (1994), 121{8.
99
[39] M. Y. Siyal and L. Yu, An intelligent modied fuzzy c-means based algorithm for bias estima-
100
tion and segmentation of brain MRI, Pattern Recognition Letters, 26(13) (2005), 2052-2062.
101
[40] J. G. Sled, A. P. Zijdenbos and A. C. Evans, A nonparametric method for automatic correc-
102
tion of intensity nonuniformity in MRI data, IEEE Transactions On Medical Imaging, 17(1)
103
(1998), 87{97.
104
[41] P. Smets and R. Kennes, The transferable belief model, Articial Intelligence, 66 (2) (1994),
105
[42] M. Styner, C. Brechbuhler, G. Szekely and G. Gerig, Parametric estimate of intensity inho-
106
mogeneities applied to MRI, IEEE Transactions on Medical Imaging, 19(3) (2000), 153{165.
107
[43] M. Tabassian, R. Ghaderi and R. Ebrahimpour, Combination of multiple diverse classiers
108
using belief functions for handling data with imperfect labels, Expert Systems with Applica-
109
tions, 39(2) (2012), 1698{1707.
110
[44] M. Tabassian, R. Ghaderi and R. Ebrahimpour, Knitted fabric defect classication for uncer-
111
tain labels based on Dempster-Shafer theory of evidence, Expert Systems with Applications,
112
38(5) (2011), 5259{5267.
113
[45] L. Tzu-Chao, Switching-based lter based on Dempsters combination rule for image process-
114
ing, Information Sciences, 180(24) (2010), 4892{4908.
115
[46] v, Pattern recognition with fuzzy objective function algorithms, Plenum Press, New York,
116
[47] F. Valente, Multi-stream speech recognition based on DempsterShafer combination rule,
117
Speech Communication, 52(3) (2010), 213{222.
118
[48] J. Wang, J. Kong, Y. Lu, M. Qi and B. Zhang, A modied FCM algorithm for MRI brain
119
image segmentation using both local and non-local spatial constraints, Computerized Medical
120
Imaging and Graphics : the Ocial Journal of the Computerized Medical Imaging Society,
121
32(8) (2008), 685{698.
122
[49] R. R. Yager, J. Kacprzyk and M. Fedrizzi, Advances in the Dempster-Shafer theory of evi-
123
dence, New York ; Chichester: Wiley, 1994.
124
[50] D. Q. Zhang and S. C. Chen, A novel kernelized fuzzy c-means algorithm with application in
125
medical image segmentation, Articial Intelligence in Medicine, 32(1) (2004), 37-50.
126
ORIGINAL_ARTICLE
An Empirical Comparison between Grade of Membership and Principal Component Analysis
t is the purpose of this paper to contribute to the discussion initiated byWachter about the parallelism between principal component (PC) and atypological grade of membership (GoM) analysis. The author testedempirically the close relationship between both analysis in a lowdimensional framework comprising up to nine dichotomous variables and twotypologies. Our contribution to the subject is also empirical. It relies ona dataset from a survey which was especially designed to study the reward ofskills in the banking sector in Portugal. The statistical data comprisethirty polythomous variables and were decomposed in four typologies using anoptimality criterion. The empirical evidence shows a high correlationbetween the first PC scores and individual GoM scores. No correlation withthe remaining PCs was found, however. In addtion to that, the first PC alsoproved effective to rank individuals by skill following the particularity ofdata distribution meanwhile unveiled in GoM analysis.
http://ijfs.usb.ac.ir/article_612_196563263ef0f06cfe8860854949d512.pdf
2013-04-29T11:23:20
2017-09-20T11:23:20
57
72
10.22111/ijfs.2013.612
Grade of Membership
principal component analysis
Fuzzy partition
Abdul
Suleman
abdul.suleman@iscte.pt
true
1
Department of Quantitative Methods, Instituto Universitario de
Lisboa (ISCTE - IUL), BRU-UNIDE, Av. Forcas Armadas, Lisbon, Portugal
Department of Quantitative Methods, Instituto Universitario de
Lisboa (ISCTE - IUL), BRU-UNIDE, Av. Forcas Armadas, Lisbon, Portugal
Department of Quantitative Methods, Instituto Universitario de
Lisboa (ISCTE - IUL), BRU-UNIDE, Av. Forcas Armadas, Lisbon, Portugal
LEAD_AUTHOR
[1] A. Andreotti, N. Minicuci, P. Kowal and S. Chatterji, Multidimensional proles of health
1
status: an application of the grade of membership model to the world health survey, PLoS
2
ONE 4(2): e4426 (2009) (DOI:10.1371/journal.pone.0004426).
3
[2] L. Berkman, B. Singer and K. Manton, Black / White dierences in health status and mor-
4
tality among eldery, Demography, 26 (1989), 661{678.
5
[3] C. J. Bezdek, Cluster validity with fuzzy sets, Journal of Cybernetics, 3(3) (1974), 58{73.
6
[4] J. R. Brown, Error analysis of some normal approximations to the chi-square distribution,
7
Journal of the Academy of Marketing Science, (DOI: 10.1007/BF02729388), 2(3) (1974),
8
[5] W. Buntine and A. Jakulin, Applying discrete PCA in data analysis, Proceeding UAI '04
9
Proceedings of the 20th Conference on Uncertainty in Articial Intelligence, (available on-line
10
http://portal.acm.org/citation.cfm?id=1036851), (2004), 59{66.
11
[6] Decision System, Inc., User documentation for DSIGoM, Version 1.0, 1999.
12
[7] R. A. Fisher, Statistical methods for research workers, Oliver and Boyd, Edinburgh, 1925.
13
[8] I. T. Jollie, Principal component analysis, Springer-Verlag New York Inc., 2nd Edition,
14
[9] L. T. Kelley, Fundamentals of statistics, Harvard University Press, Cambridge, 1947.
15
[10] K. G. Manton, M. A. Woodbury and D. Tolley, Statistical applications using fuzzy sets, John
16
Wiley & Sons, Inc, 1994.
17
[11] K. G. Manton and X. Gu, Disability declines and trends in medicare expendidure, Ageing
18
Horizons, 2 (2005), 25{34.
19
[12] A. L. McCutcheon, Latent class analysis, Sage Publications, 1987.
20
[13] E. Mehdizadeh, S. Sadi-Nezhad and R. Tavakkoli-Moghaddam, Optimization of fuzzy clus-
21
tering criteria by a hybrid pso and fuzzy c-means clustering algorithm, Iranian Journal of
22
Fuzzy Systems, 5(3) (2008), 1{14.
23
[14] F. Suleman, O valor das compet^encias: um estudo aplicado ao sector bancario, Livros Hori-
24
zonte, Lisboa, 2007.
25
[15] A. Suleman and F. Suleman, Ranking by competence using a fuzzy approach, Quality and
26
Quantity, 46(1) (2012), 323-339.
27
[16] A. Suleman, Grade of membership and principal components analysis: a comparative
28
empirical study, (available on-line http://isi2011.congressplanner.eu/pdfs/950735.pdf ).
29
[17] D. Tolley and K. G. Manton, Large sample properties of estimates of a discrete grade of
30
membership model, Annals of Institute of Statistical Mathematics, 44 (1992), 85{95.
31
[18] R. Viertl and D. Hareter, Fuzzy information and stochastics, Iranian Journal of Fuzzy Sys-
32
tems, 1(1) (2004), 43{56.
33
[19] K. W. Wachter, Grade of membership models in low dimensions, Statistical Papers, 40
34
(1999), 439{457.
35
[20] E. B. Wilson and M. M. Hilferty, The distribution of chi-square, Proceeding of the National
36
Academy of Sciences, 17 (1931), 684{688.
37
[21] M. A.Woodbury and J. Clive, Clinical pure types as a fuzzy partition, Journal of Cybernetics,
38
4 (1974), 111{121.
39
ORIGINAL_ARTICLE
HURST EXPONENTS FOR NON-PRECISE DATA
We provide a framework for the study of statistical quantitiesrelated to the Hurst phenomenon when the data are non-precise with boundedsupport.
http://ijfs.usb.ac.ir/article_613_f0dcaa881ca1e193a0d1c159b2545eee.pdf
2013-04-29T11:23:20
2017-09-20T11:23:20
73
81
10.22111/ijfs.2013.613
Hurst phenomenon
Non-precise data
Mayer
Alvo
malvo@uottawa.ca
true
1
Department of Mathematics & Statistics, University of Ottawa, 585
King Edward, Ottawa, ON (K1N 5N1), Canada
Department of Mathematics & Statistics, University of Ottawa, 585
King Edward, Ottawa, ON (K1N 5N1), Canada
Department of Mathematics & Statistics, University of Ottawa, 585
King Edward, Ottawa, ON (K1N 5N1), Canada
LEAD_AUTHOR
Francois
Theberge
ftheberg@uottawa.ca
true
2
Department of Mathematics & Statistics, University of Ottawa,
585 King Edward, Ottawa, ON (K1N 5N1), Canada
Department of Mathematics & Statistics, University of Ottawa,
585 King Edward, Ottawa, ON (K1N 5N1), Canada
Department of Mathematics & Statistics, University of Ottawa,
585 King Edward, Ottawa, ON (K1N 5N1), Canada
AUTHOR
[1] M. Alvo and F. Theberge, The problem of classication when the data are non-precise,
1
Austrian Journal of Statistics, 34 (2005), 375-390.
2
[2] Environment Canada, Archived data for station 02KF005, Ottawa river at Britannia,
3
www.ec.gc.ca/rhc-wsc.
4
[3] W. Feller, The asymptotic distribution of the range of sums of independent random variables,
5
The Annals of Mathematical Statistics, 22 (1951), 427-432.
6
[4] H. E. Hurst, R. P. Black and Y. M. Simaika, Long-term storage: an experimental study,
7
Constable (London), 1965.
8
[5] A. I. McLeod and K. W. Hipel, Preservation of the rescaled adjusted range: A reassessment
9
of the Hurst phenomenon, Water Resources Research, 14(3) (1978), 491-508.
10
[6] J. Valente de Oliveira and W. Pedrycz, Advances in Fuzzy Clustering and its Applications,
11
Chapter 8, Wiley, 2007.
12
[7] R. Viertl, On statistical inference for non-precise data, Environmetrics, 8 (1997), 541-568.
13
ORIGINAL_ARTICLE
ADAPTIVE ORDERED WEIGHTED AVERAGING FOR
ANOMALY DETECTION IN CLUSTER-BASED
MOBILE AD HOC NETWORKS
In this paper, an anomaly detection method in cluster-based mobile ad hoc networks with ad hoc on demand distance vector (AODV) routing protocol is proposed. In the method, the required features for describing the normal behavior of AODV are defined via step by step analysis of AODV and independent of any attack. In order to learn the normal behavior of AODV, a fuzzy averaging method is used for combining one-class support vector machine (OCSVM), mixture of Gaussians (MoG), and self-organizing maps (SOM) one-class classifiers and the combined model is utilized to partially detect the attacks in cluster members. The votes of cluster members are periodically transmitted to the cluster head and final decision on attack detection is carried out in the cluster head. In the proposed method, an adaptive ordered weighted averaging (OWA) operator is used for aggregating the votes of cluster members in the cluster head. Since the network topology, traffic, and environmental conditions of a MANET as well as the number of nodes in each cluster dynamically change, the mere use of a fixed quantifier-based weight generation approach for OWA operator is not efficient. We propose a condition-based weight generation method for OWA operator in which the number of cluster members that participate in decision making may be varying in time and OWA weights are calculated periodically and dynamically based on the conditions of the network. Simulation results demonstrate the effectiveness of the proposed method in detecting rushing, RouteError fabrication, and wormhole attacks.
http://ijfs.usb.ac.ir/article_614_8a447833fe0078753eb1c97cfe7d52f9.pdf
2013-04-29T11:23:20
2017-09-20T11:23:20
83
109
10.22111/ijfs.2013.614
Ordered weighted averaging weight generation
Mobile ad hoc network
Anomaly detection
Mohammad
Rahmanimanesh
rahmanimanesh@modares.ac.ir
true
1
Department of Electrical and Computer Engineering,
Tarbiat Modares University, Tehran, Islamic Republic of Iran
Department of Electrical and Computer Engineering,
Tarbiat Modares University, Tehran, Islamic Republic of Iran
Department of Electrical and Computer Engineering,
Tarbiat Modares University, Tehran, Islamic Republic of Iran
AUTHOR
Saeed
Jalili
sjalili@modares.ac.ir
true
2
Department of Electrical and Computer Engineering, Tarbiat Modares
University, Tehran, Islamic Republic of Iran
Department of Electrical and Computer Engineering, Tarbiat Modares
University, Tehran, Islamic Republic of Iran
Department of Electrical and Computer Engineering, Tarbiat Modares
University, Tehran, Islamic Republic of Iran
LEAD_AUTHOR
[1] B. S. Ahn, Preference relation approach for obtaining OWA operators weights, International
1
Journal of Approximate Reasoning, 47 (2008), 166-178.
2
[2] B. S. Ahn, Parameterized OWA operator weights: an extreme point approach, International
3
Journal of Approximate Reasoning, 51 (2010), 820-831.
4
[3] G. R. Amin and A. Emrouznejad, An extended minimax disparity to determine the OWA
5
operator weights, Computers & Industrial Engineering, 50 (2006), 312-316.
6
[4] V. S. Anitha and M. P. Sebastian, (k, r)-dominating set-based, weighted and adaptive cluster-
7
ing algorithms for mobile ad hoc networks, IET Communications, 5(13) (2011), 1836-1853.
8
[5] T. Avram, S. Oh and S. Hariri, Analyzing attacks in wireless ad hoc network with self-
9
organizing maps, in Proceedings of Fifth Annual Conference on Communication Networks
10
and Services Research (CNSR 07), (2007), 166-175.
11
[6] N. Y. Aydin, E. Kentel and S. Duzgun, GIS-based environmental assessment of wind energy
12
systems for spatial planning: a case study from Western Turkey, Renewable and Sustainable
13
Energy Reviews, 14 (2010), 364-373.
14
[7] K. Bhargavan, C. A. Gunter, M. Kim, I. Lee, D. Obradovic, O. Sokolsky and M. Viswanathan,
15
Verisim: formal analysis of network simulations, IEEE Transactions on Software Engineer-
16
ing, 28(2) (2002), 129-145.
17
[8] C. Bishop, Neural networks for pattern recognition, Oxford University Press, 1995.
18
[9] A. P. Bradley, The use of the area under the ROC curve in the evaluation of machine learning
19
algorithms, Pattern Recognition, 30(7) (1997), 1145-1159.
20
[10] J. B. D. Cabrera, C. Gutierrez and R. K. Mehra, Infrastructures and algorithms for dis-
21
tributed anomaly-based intrusion detection in mobile ad hoc networks, In Proceedings of
22
IEEE Military Communications Conference (MILCOM 2005), (2005), 1831-1837.
23
[11] J. B. D. Cabrera, C. Gutierrez and R. K. Mehra, Ensemble methods for anomaly detection
24
and distributed intrusion detection in mobile ad hoc networks, Information Fusion, 17(8)
25
(2008), 96-119.
26
[12] N. Cagman and S. Enginoglu, Fuzzy soft matrix theory and its application in decision making,
27
Iranian Journal of Fuzzy Systems, 9(1) (2012), 109-119.
28
[13] Z. Chen, Consensus in group decision making under linguistic assessments, Ph.D. Disserta-
29
tion, Kansas State University, 2005.
30
[14] W. Chen, N. Jain and S. Singh, ANMP: ad hoc network management protocol, IEEE Journal
31
on Selected Areas in Communications, 17(8) (1999), 1506-1531.
32
[15] H. Chen and L. Zhou, An approach to group decision making with interval fuzzy prefer-
33
ence relations based on induced generalized continuous ordered weighted averaging operator,
34
Expert Systems with Applications, 38 (2011), 13432-13440.
35
[16] S. Cho, Fuzzy aggregation of modular neural networks with ordered weighted averaging oper-
36
ators, International Journal of Approximate Reasoning, 13 (1995), 359-375.
37
[17] A. De and E. D. Diaz, A fuzzy ordered weighted average (OWA) approach to result merging
38
for meta search using the analytical network process, In Proceedings of Second International
39
Conference on Emerging Applications of Information Technology (EAIT), (2011), 17-20.
40
[18] H. Deng, R. Xu, J. Li, F. Zhang, R. Levy and W. Lee, Agent-based cooperative anomaly
41
detection for wireless ad hoc networks, In Proceedings of the 12th International Conference
42
on Parallel and Distributed Systems (ICPADS 06), 2006.
43
[19] H. Deng, Q. A. Zeng and D. P. Agrawal, SVM-based intrusion detection system for wireless ad
44
hoc networks, In Proceedings of IEEE Vehicular Technology Conference, (2003), 2147-2151.
45
[20] M. Dursun, E. E. Karsak and M. A. Karadayi, A fuzzy multi-criteria group decision mak-
46
ing framework for evaluating health-care waste disposal alternatives, Expert Systems with
47
Applications, 38 (2011), 11453-11462.
48
[21] A. Emrouznejad, MP-OWA: the most preferred OWA operator, Knowledge-Based Systems,
49
21 (2008), 847-851.
50
[22] A. Emrouznejad and G. R. Amin, Improving minimax disparity model to determine the OWA
51
operator weights, Information Sciences, 180 (2010), 1477-1485.
52
[23] D. Filev and R. R. Yager, On the issue of obtaining OWA operator weights, Fuzzy Sets and
53
Systems, 94 (1998), 157-169.
54
[24] R. Fuller and P. Majlender, An analytic approach for obtaining maximal entropy OWA op-
55
erator weights, Fuzzy Sets and Systems, 124 (2001), 53-57.
56
[25] R. Fuller and P. Majlender, On obtaining minimal variability OWA operator weights, Fuzzy
57
Sets and Systems, 136 (2003), 203-215.
58
[26] M. A. Ghaderi, N. Yazdani, B. Moshiri and M. Tayefeh Mahmoudi, A new approach for text
59
feature selection based on OWA operator, In Proceedings of 5th International Symposium on
60
Telecommunications (IST), (2010), 579-583.
61
[27] G. Giacinto, R. Perdisci, M. Del Rio and F. Roli, Intrusion detection in computer networks by
62
a modular ensemble of one-class classiers, Information Fusion, Special Issue on Applications
63
of Ensemble Methods, 9(1) (2008), 69-82.
64
[28] F. Herrera, E. Herrera-Viedma and J. L. Verdegay, Direct approach processes in group deci-
65
sion making using linguistic OWA operators, Fuzzy Sets and Systems, 79 (1996), 175-190.
66
[29] Y. C. Hu, A. Perrig and D. B. Johnson, Rushing attacks and defense in wireless ad hoc
67
network routing protocols, in Proceedings of ACM Workshop on Wireless Security (WiSe
68
2003), (2003), 30-40.
69
[30] Y. C. Hu, A. Perrig and D. B. Johnson, Wormhole attacks in wireless networks, IEEE Journal
70
on Selected Areas in Communications, 24(2) (2006), 370-380.
71
[31] Y. Huang, W. Fan, W. Lee and P. Yu, Cross-feature analysis for detecting ad hoc routing
72
anomalies, in Proceedings of the 23rd International Conference on Distributed Computing
73
Systems (ICDCS 03), (2003), 478-487.
74
[32] Y. A. Huang and W. Lee, Attack analysis and detection for ad hoc routing protocols, in
75
Proceedings of Recent Advances in Intrusion Detection, (2004), 125-145.
76
[33] S. Jazebi, A. Tohidi and M. Rahgozar, Application of classier fusion for protein fold recog-
77
nition, In Proceedings of Sixth International Conference on Fuzzy Systems and Knowledge
78
Discovery (FSKD 09), (2009), 171-175.
79
[34] T. Kohonen, self-organizing maps, Springer-Verlag, 3rd edition, 2001.
80
[35] L. I. Kuncheva, Combining pattern classiers, methods and algorithms, John Wiley and Sons,
81
[36] S. Kurosawa, H. Nakayama, N. Kato, A. Jamalipour and Y. Nemoto, A self-adaptive in-
82
trusion detection method for AODV-based mobile ad hoc networks, In Proceedings of IEEE
83
International Conference on Mobile Ad hoc and Sensor Systems (IEEE MASS 05), (2005),
84
[37] X. Li, F. Zhou and X. Yang, A multi-dimensional trust evaluation model for large-scale P2P
85
computing, Journal of Parallel and Distributed Computing, 71 (2011), 837-847.
86
[38] C. X. Ling, J. Huang and H. Zhang, AUC: a statistically consistent and more discriminat-
87
ing measure than accuracy, In Proceedings of 18th International Conference on Articial
88
Intelligence, (2003), 329-341.
89
[39] X. Liu, The solution equivalence of minimax disparity and minimum variance problems for
90
OWA operator, International Journal of Approximate Reasoning, 45 (2007), 68-81.
91
[40] X. Liu, A general model of parameterized OWA aggregation with given orness level, Interna-
92
tional Journal of Approximate Reasoning, 48 (2008), 598-627.
93
[41] B. Llamazares, Choosing OWA operator weights in the eld of social choice, Information
94
Sciences, 177 (2007), 4745-4756.
95
[42] C. Lo and W. Chen, A hybrid information security risk assessment procedure considering
96
interdependences between controls, Expert Systems with Applications, 39 (2012), 247-257.
97
[43] P. Majlender, OWA operators with maximal Renyi entropy, Fuzzy Sets and Systems, 155
98
(2005), 340-360.
99
[44] J. McElroy and P. Gader, Generalized encoding and decoding operators for lattice-based as-
100
sociative memories, IEEE Transactions on Neural Networks, 20(10) (2009), 1674-1678.
101
[45] J. M. Merigo and M. Casanovas, Fuzzy generalized hybrid aggregation operators and its
102
application in decision making, International Journal of Fuzzy Systems, 12(1) (2010), 15-24.
103
[46] J. M. Merigo and M. Casanovas, Decision-making with distance measures and induced ag-
104
gregation operators, Computers & Industrial Engineering, 60 (2011), 66-76.
105
[47] J. M. Merigo and M. Casanovas, Induced aggregation operators in the Euclidean distance and
106
its application in nancial decision making, Expert Systems with Applications, 38 (2011),
107
7603-7608.
108
[48] J. M. Merigo and M. Casanovas, Induced and uncertain heavy OWA operators, Computers
109
& Industrial Engineering, 60 (2011), 106-116.
110
[49] J. M. Merigo and A. M. Gil-Lafuente, The induced generalized OWA operator, Information
111
Sciences, 179(6) (2009),729-741.
112
[50] J. M. Merigo and A. M. Gil-Lafuente, Fuzzy induced generalized aggregation operators and its
113
application in multi-person decision making, Expert Systems with Applications, 38 (2011),
114
9761-9772.
115
[51] H. Nakayama, S. Kurosawa, A. Jamalipour, Y. Nemoto and N. Kato, A dynamic anomaly
116
detection scheme for AODV-based mobile ad hoc networks, IEEE Transactions on Vehicular
117
Technology, 58(5) (2009), 2471-2481.
118
[52] J. Nin, B. Carminati, E. Ferrari and V. Torra, Computing reputation for collaborative pri-
119
vate networks, in Proceedings of 33rd Annual IEEE International Computer Software and
120
Applications Conference (COMPSAC 09), (2009), 246-253.
121
[53] NS-2 (network simulator version 2), URL: http://www.isi.edu/nsnam/ns/ns-documentation,
122
[54] M. O'Hagan, Aggregating template or rule antecedents in real-time expert systems with fuzzy
123
set logic, In Proceedings of 22nd Annual IEEE Asilomar Conference on Signals, Systems,
124
Computers, (1988), 681-689.
125
[55] R. Perdisci, D. Ariu, P. Fogla, G. Giacinto and W. Lee, McPAD : a multiple classier system
126
for accurate payload-based anomaly detection, Computer Networks, Special Issue on Trac
127
Classication and Its Applications to Modern Networks, 5(6) (2009), 864-881.
128
[56] C. Perkins and E. Royer, Ad hoc on demand distance vector routing, In Proceedings of
129
the Second IEEE Workshop on Mobile Computing Systems and Applications (WMCSA 99),
130
(1999), 90-100.
131
[57] C. Perkins, E. Royer and S. Das, Ad hoc on demand distance vector routing, IETF RFC
132
3561, 2003.
133
[58] J. Renaud, E. Levrat and C. Fonteix, Weights determination of OWA operators by parametric
134
identication, Mathematics and Computers in Simulation, 77 (2008), 499-511.
135
[59] R. Sadiq and S. Tesfamariam, Probability density functions-based weights for ordered weighted
136
averaging (OWA) operators: an example of water quality indices, European Journal of Op-
137
erational Research, 182 (2007), 1350-1368.
138
[60] B. Scholkopf, J. C. Platt, J. S. Taylor, A. J. Smola and R. C. Williamson, Estimating the
139
support of a high dimensional distribution, Neural Computation, 13 (2001), 1443-1471.
140
[61] F. Szidarovszky and M. Zarghami, Combining fuzzy quantiers and neat operators for soft
141
computing, Iranian Journal of Fuzzy Systems, 6(1) (2009), 15-25.
142
[62] D. M. J. Tax, One-class classication, Ph.D. Dissertation, Delft University of Technology,
143
[63] D. M. J. Tax, M. V. Breukelen, R. P. W. D. Duin and J. Kittler, Combining multiple classiers
144
by averaging or by multiplying?, Pattern Recognition, 33(9) (2000), 1475-1485.
145
[64] J. A. Torkestani and M. R. Meybodi, Clustering the wireless ad hoc networks: a distributed
146
learning automata approach, Journal of Parallel and Distributed Computing, 70(4) (2010),
147
[65] Y. M. Wang, Y. Luo and X. Liu, Two new models for determining OWA operator weights,
148
Computers & Industrial Engineering, 52 (2007), 203-209.
149
[66] Y. M. Wang and C. Parkan, A minimax disparity approach for obtaining OWA operator
150
weights, Information Sciences, 175 (2005), 20-29.
151
[67] Y. M. Wang and C. Parkan, A preemptive goal programming method for aggregating OWA
152
operator weights in group decision making, Information Sciences, 177 (2007), 1867-1877.
153
[68] Y. Wu and J. Liu, A new method for sh disease diagnosis system based on rough set and
154
classier fusion, In Proceedings of International Conference on Articial Intelligence and
155
Computational Intelligence (AICI 09), (2009), 24-27.
156
[69] J. Wu, B. L. Sun, C. Y. Liang and S. L. Yang, A linear programming model for determining
157
ordered weighted averaging operator weights with maximal Yager's entropy, Computers &
158
Industrial Engineering, 57 (2009), 742-747.
159
[70] Y. Wu, X. Tan and S. Gu, A learning evaluation system based on classier fusion for E-
160
learning, In Proceedings of IEEE International Symposium on IT in Medicine & Education
161
(ITIME 09), (2009), 749-752.
162
[71] Z. Xu, Induced uncertain linguistic OWA operators applied to group decision making, Infor-
163
mation Fusion, 7 (2006), 231-238.
164
[72] R. R. Yager, On ordered weighted averaging aggregation operators in multi-criteria decision
165
making, IEEE Transactions on Systems, Man and Cybernetics, 18 (1988), 183-190.
166
[73] R. R. Yager, Families of OWA operators, Fuzzy Sets and Systems, 59 (1993), 125-148.
167
[74] R. R. Yager, Quantier guided aggregation using OWA operators, International Journal of
168
Intelligent Systems, 11 (1996), 49-73.
169
[75] R. R. Yager, Heavy OWA operators, Fuzzy Optimization and Decision Making, 1(4) (2002),
170
[76] R. R. Yager, Generalized OWA aggregation operators, Fuzzy Optimization and Decision Mak-
171
ing, 3(1) (2004), 93-107.
172
[77] R. R. Yager, OWA aggregation over a continuous interval argument with applications to
173
decision making, IEEE Transactions on Systems, Man, and Cybernetics, Part B 34 (2004),
174
1952-1963.
175
[78] R. R. Yager, Centered OWA operators, Soft Computing, 11 (2007), 631-639.
176
[79] R. R. Yager, On the dispersion measure of OWA operators, Information Sciences, 179 (2009),
177
3908-3919.
178
[80] R. R. Yager and D. P. Filev, Induced ordered weighted averaging operators, IEEE Transaction
179
on Systems, Man and Cybernetics, 29 (1999), 141-150.
180
[81] J. Y. Yu and P. H. J. Chong, A survey of clustering schemes for mobile ad hoc networks,
181
IEEE Communications Surveys & Tutorials, 7(1) (2005), 32-48.
182
[82] Y. Zhang and W. Lee, Intrusion detection in wireless ad hoc networks, In Proceedings of 6th
183
Annual International Conference on Mobile Computing and Networking, (2000), 275-283.
184
[83] Y. Zhang, W. Lee and Y. Huang, Intrusion detection techniques for mobile wireless networks,
185
ACM Wireless Networks, 9(5) (2003), 545-556.
186
[84] L. G. Zhou and H. Y. Chen, Continuous generalized OWA operator and its application to
187
decision making, Fuzzy Sets and Systems, 168 (2011), 18-34.
188
[85] S. M. Zhou, F. Chiclana, R. I. John and J. M. Garibaldi, Type-1 OWA operators for aggre-
189
gating uncertain information with uncertain weights induced by type-2 linguistic quantiers,
190
Fuzzy Sets and Systems, 159 (2008), 3281-3296.
191
[86] S. M. Zhou, F. Chiclana, R. I. John and J. M. Garibaldi, Alpha-level aggregation: a practical
192
approach to type-1 OWA operation for aggregating uncertain information with applications
193
to breast cancer treatments, IEEE Transactions on Knowledge and Data Engineering, 23(10)
194
(2011), 1455-1468.
195
ORIGINAL_ARTICLE
Monitoring Fuzzy Capability Index $\widetilde{C}_{pk}$ by Using
the EWMA Control Chart with Imprecise Data
A manufacturing process cannot be released to production until it has been proven to be stable. Also, we cannot begin to talk about process capability until we have demonstrated stability in our process. This means that the process variation is the result of random causes only and all assignable or special causes have been removed. In complicated manufacturing processes, such as drilling process, the natural instability of the process impedes the use of any control charts for the mean and standard deviation. However, a complicated manufacturing process can be capable in spite of this natural instability.In this paper we discuss the $\widetilde{C}_{pk}$ process capability index. We find the membership function of $\widetilde{C}_{pk}$ based on fuzzy data. Also, by using the definition of classical control charts and the method of V$\ddot{a}$nnman and Castagliola, we propose new control charts that are constructed by the $\alpha$-cut sets of $\widetilde{C}_{pk}$ for the natural instable manufacturing processes with fuzzy normal distributions. The results are concluded for $\alpha=0.6$, that is chosen arbitrarily.
http://ijfs.usb.ac.ir/article_615_56d575b91c8b95769c6051a0f66a4791.pdf
2013-04-29T11:23:20
2017-09-20T11:23:20
111
132
10.22111/ijfs.2013.615
Capability index
$D_{p
q}$-distance
Fuzzy set
Membership Function
EWMA control chart
Bahram
Sadeghpour Gildeh
sadeghpour@umz.ac.ir
true
1
Faculty of Mathematical Science, Department of Sta-
tistics, University of Mazandaran, Babolsar, Iran and School of Mathematical Science,
Department of Statistics, Ferdowsi University of Mashhad, Postal Code : 9177948953,
Mashhad, Iran
Faculty of Mathematical Science, Department of Sta-
tistics, University of Mazandaran, Babolsar, Iran and School of Mathematical Science,
Department of Statistics, Ferdowsi University of Mashhad, Postal Code : 9177948953,
Mashhad, Iran
Faculty of Mathematical Science, Department of Sta-
tistics, University of Mazandaran, Babolsar, Iran and School of Mathematical Science,
Department of Statistics, Ferdowsi University of Mashhad, Postal Code : 9177948953,
Mashhad, Iran
LEAD_AUTHOR
Tala
Angoshtari
tala.angoshtari@gmail.com
true
2
Faculty of Mathematical Science, Department of Statistics, Uni-
versity of Mazandaran, Babolsar, Iran
Faculty of Mathematical Science, Department of Statistics, Uni-
versity of Mazandaran, Babolsar, Iran
Faculty of Mathematical Science, Department of Statistics, Uni-
versity of Mazandaran, Babolsar, Iran
AUTHOR
[1] L. Angstenberger, Dynamic fuzzy pattern recognition with application to finance and engineering,
1
Kluwer Academic Publishers, United States, 2001.
2
[2] E. Baloui Jamkhaneh, B. Sadeghpour Gildeh and G. Yari, Acceptance single sampling plan
3
with fuzzy parameter, Iranian Journal of Fuzzy Systems, 8(2) (2011), 47{55.
4
[3] P. Castagliola, An EWMA control chart for monitoring the logarithm of the process sample
5
variance, Proceedings of the International Conference on Industrial Engineering and Production
6
Management, Glasgow, Scotland, (1999), 371{377.
7
[4] P. Castagliola, A new S2-EWMA control chart for monitoring the process variance, Quality
8
and Reliability Engineering International, 21(2005), 781{794.
9
[5] P. Castagliola, A R-EWMA control chart for monitoring the process range, International
10
Journal of Reliability, Quality and Safety Engineering, 12 (2005), 31{49.
11
[6] P. Castagliola, G. Celano and S. Fichera, Monitoring process variability using EWMA, Handbook
12
of Engineering Statistics, Springer, Berlin, (2006), 291{325.
13
[7] L. K. Chang, S. W. Cheng and F. A. Spiring, A new measure of process capability: Cpm,
14
Journal of Quality Technology, 20 (1988), 162{331.
15
[8] S. Chen and G. Li, Representation, ranking, and distance of fuzzy number with exponential
16
membership function using graded mean integration method, Tamsui Oxford Journal of
17
Mathematical Sciences, 16(2) (2000), 123{131
18
[9] T. W. Chen, K. S. Chen and J. Y. Lin, Fuzzy evaluation of process capability for bigger-thebest
19
type products, International Journal of Advanced Manufacturing Technology, 21 (2003),
20
[10] C. B. Cheng, Fuzzy process control: construction of control charts with fuzzy numbers, Fuzzy
21
Sets and Systems, 154 (2005), 287{303.
22
[11] Y. Deng, Z. Zhenfu and L. Qi, Ranking fuzzy numbers with an area method using radius of
23
gyration, Computers and Mathematics with Applications, 51 (2006), 1127{1136.
24
[12] P. Grzegorzewski, Control charts for fuzzy data, In: Proceedings of the 5th European Congress
25
EUFIT97, Aachen, (1997), 1326{1330.
26
[13] P. Grzegorzewski and O. Hryniewicz, Soft methods in statistical quality control, Control and
27
Cybernetics, 29 (2000), 119{140.
28
[14] O. Hryniewicz, Statistics with fuzzy data in statistical quality control, Soft Computing, 12
29
(2008), 229{234.
30
[15] B. M. Hsu and M. H. Shu, Fuzzy inference to assess manufacturing process capability with
31
imprecise data, European Journal of Operational Research, 186(2) (2008), 652{670.
32
[16] J. M. Juran, Jurans quality control handbook, Third Edition, MacGraw Hill, New York, 1974.
33
[17] A. Kanagawa, F. Tamaki and H. Ohta, Control charts for process average and variability
34
based on linguistic data, International Journal of Production Research, 31 (1993), 913{922.
35
[18] V. E. Kane, Process capability indices, Journal of Quality Technology, 18 (1986), 41{52.
36
[19] I. Kaya and C. Kahraman, Fuzzy process capability analyses: An application to teaching
37
processes, Journal of Intelligent and Fuzzy Systems, 19 (2008), 259{272.
38
[20] S. K. Land, D. B. Smith and J. W. Walz, Practical support for lean six sigma software process
39
definition: using IEEE software engineering standards, Hoboken : Wiley ; Los Alamitos :
40
IEEE computer society, 2008.
41
[21] J. L. Meriam and L. G. Kraige, Engineering mechanics, Third Edition, Wiley, New York,
42
[22] D. C. Montgomery, Introduction to statistical quality control, Third Edition, Wiley, New
43
York, 1996.
44
[23] S. H. Nasseri and M. Sohrabi, Ranking fuzzy numbers by using radius of gyration, Australian
45
Journal of Basic and Applied Sciences, 4 (2010), 658{664.
46
[24] A. Parchami, M. Mashinchi, Fuzzy estimation for process capability indices, Information
47
Sciences, 177 (2007), 1452{1462.
48
[25] W. L. Pearn, S. Kotz and N. L. Johnson, Distributional and inferential properties of process
49
capability indices, Journal of Quality Technology, 24 (1992), 216{231.
50
[26] T. Raz and J. H. Wang, Probabilistic and membership approaches in the construction of
51
control charts for linguistic data, Production Planning and Control, 1 (1990), 147{157.
52
[27] B. Sadeghpour Gildeh and D. Gien, La distance-Dp;q et le coefficient de corrlation entre deux
53
variables alatoires floues, Rencontres Francophones sur la Logique Floue et ses Applications
54
LFA 01, Mons, Belgium, (2001), 97{102.
55
[28] W. A. Shewhart, Economic control of quality of manufactured product, D. Van Nostrand,
56
Inc., Princeton, NJ, 1931.
57
[29] H. Taleb and M. Limam, On fuzzy and probabilistic control charts, International Journal of
58
Production Research, 40 (2002), 2849{2863.
59
[30] J. D. T. Tannock, A fuzzy control charting methods for individuals, International Journal of
60
Production Research, 41 (2003), 1017{1032.
61
[31] C. C. Tsai and C. C. Chen, Making decision to evaluate process capability index Cp with fuzzy
62
numbers, International Journal of Advanced Manufacturing Technology, 30 (2006), 334{339.
63
[32] K. Vannman, A unified approach to capability indices, Statistica Sinica, 5 (1995), 805{820.
64
[33] K. Vannman and P. Castagliola, Monitoring capability indices using an EWMA approach,
65
Quality and Reliability Engineering International, 23 (2008), 769{790.
66
[34] D.Wang, A CUSUM control chart for fuzzy quality data, In: Lawry J, Miranda E, Bugarin A,
67
Li S, Gil MA, Grzegorzewski P, Hryniewicz O, eds., Soft Methods for Integrated Uncertainty
68
Modelling, Springer-Verlag, Heidelberg, (2006), 357{364.
69
[35] J. H. Wang and T. Raz, On the construction of control charts using linguistic variables,
70
International Journal of Production Research, 28 (1990), 477{487.
71
[36] C. W.Wu, Decision-making in testing process performance with fuzzy data. European Journal
72
of Operational Research, 193(2) (2009), 499{509.
73
[37] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.
74
ORIGINAL_ARTICLE
ON INTERRELATIONSHIPS BETWEEN FUZZY
METRIC STRUCTURES
Considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. This paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology.We study interrelationships between this theory and other fuzzy theories suchas intuitionistic fuzzy metric spaces, Kramosil and Michalek's spaces, Kalevaand Seikkala's spaces, probabilistic metric spaces, probabilisticmetric co-spaces, Menger spaces and intuitionistic probabilistic metricspaces, determining their position in the framework of theses different theories.
http://ijfs.usb.ac.ir/article_616_cf1477dfb706555ef5cc5a5ccacc6742.pdf
2013-04-29T11:23:20
2017-09-20T11:23:20
133
150
10.22111/ijfs.2013.616
Fuzzy metric
Fuzzy metric space
Fuzzy number
Fuzzy topology
Links between dierent models
Antonio
Roldan
afroldan@ujaen.es
true
1
Department of Statistics and Operations Research, University of
Jaen, Campus Las Lagunillas, s/n, E-23071, Jaen, Spain
Department of Statistics and Operations Research, University of
Jaen, Campus Las Lagunillas, s/n, E-23071, Jaen, Spain
Department of Statistics and Operations Research, University of
Jaen, Campus Las Lagunillas, s/n, E-23071, Jaen, Spain
LEAD_AUTHOR
Juan
Martnez-Moreno
jmmoreno@ujaen.es
true
2
Department of Mathematics, University of Jaen, Campus Las
Lagunillas, s/n, E-23071, Jaen, Spain
Department of Mathematics, University of Jaen, Campus Las
Lagunillas, s/n, E-23071, Jaen, Spain
Department of Mathematics, University of Jaen, Campus Las
Lagunillas, s/n, E-23071, Jaen, Spain
AUTHOR
Concepcion
Roldan
iroldan@ugr.es
true
3
Department of Statistics and Operations Research, University
of Granada, Campus Fuentenueva s/n, E-18071, Granada, Spain
Department of Statistics and Operations Research, University
of Granada, Campus Fuentenueva s/n, E-18071, Granada, Spain
Department of Statistics and Operations Research, University
of Granada, Campus Fuentenueva s/n, E-18071, Granada, Spain
AUTHOR
[1] H. Adibi, Y. J. Cho, D. O'Regan and R. Saadati, Common xed point theorems in L-fuzzy
1
metric spaces, Appl. Math. Comput., 182 (2006), 820{828.
2
[2] C. Alaca, D. Turkoglu and C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos
3
Soliton Fract, 29 (2006), 1073{1078.
4
[3] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87{96.
5
[4] F. Castro-Company and S. Romaguera, Experimental results for information system based
6
on accesses locality via intuicionist fuzzy metrics, Open Cybern. Syst. J., 2 (2008), 158{172.
7
[5] Y. J. Cho, M. T. Grabiec and V. Radu, On nonsymmetric topological and probabilistic struc-
8
tures, Nova Science Publishers, Inc., New York, 2006.
9
[6] Z. Deng, Fuzzy pseudo metric spaces, J. Math. Anal. Appl., 86 (1982), 74{95.
10
[7] G. Deschrijver and E. E. Kerre, On the position of intuitionistic fuzzy set theory in the
11
framework of theories modelling imprecision, Information Sciences, 177 (2007), 1860{1866.
12
[8] D. Dubois and H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci., 9(6) (1978), 613{
13
[9] M. S. El Naschie, On the verications of heteritic strings theory and (1) theory, Chaos
14
Soliton Fract, 11(2) (2000), 2397{2407.
15
[10] M. A. Erceg, Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69 (1979), 205{230.
16
[11] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,
17
64 (1994), 395{399.
18
[12] D. Gomez, J. Montero and J. Ya~nez, A coloring fuzzy graph approach for image classication,
19
Information Sciences, 176(24) (2006), 3645{3657.
20
[13] M. T. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994),
21
[14] M. T. Grabiec, Y. J. Cho and R. Saadati, Families of quasi-pseudo-metrics generated by
22
probabilistic quasi-pseudo-metric spaces, Surveys in Mathematics and its Applications, 2
23
(2007), 123{143.
24
[15] V. Gregori, S. Morillas and A. Sapena, Examples of fuzzy metrics and applications, Fuzzy
25
Sets and Systems, 170 (2011), 95{111.
26
[16] V. Gregori, S. Romaguera and P. Veereamani, A note on intuitionistic fuzzy metric spaces,
27
Chaos Soliton Fract, 28 (2006), 902{905.
28
[17] H. L. Huang and F. G. Shi, L-fuzzy numbers and their properties, Information Sciences, 178
29
(2008), 1141{1151.
30
[18] H. Huang and C. Wu, On the triangle inequalities in fuzzy metric spaces, Information Sciences,
31
177(4) (2007), 1063{1072.
32
[19] M. Imdad, J. Ali and M. Hasan, Common xed point theorems in modied intuitionistic fuzzy
33
metric spaces, Iranian Journal of Fuzzy Systems, 9(5) (2012), 77-92.
34
[20] O. Kaleva, On the convergence of fuzzy sets, Fuzzy Sets Syst., 17(1985), 53{65.
35
[21] O. Kaleva, A comment on the completion of fuzzy metric spaces, Fuzzy Sets and Systems,
36
159 (2008), 2190{2192.
37
[22] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
38
[23] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika 11
39
(1975), 336{344.
40
[24] H. Y. Li, CLM-Fuzzy topological spaces, Iranian Journal of Fuzzy Systems, to appear.
41
[25] J. Martnez-Moreno, A. Roldan and C. Roldan, A note on the L-fuzzy Banach's contraction
42
principle, Chaos Soliton Fract, 41(5) (2009), 2399{2400.
43
[26] J. Martnez-Moreno, A. Roldan and C. Roldan, KM-Fuzzy approach space, Proceedings of
44
the International Fuzzy Systems Association World Conference, (2009), 1702{1705.
45
[27] K. Menger, Statistical metrics, Proc National Acad Sci of the United States of America, 28
46
(1942), 535{537.
47
[28] N. N. Morsi, On fuzzy pseudo-normed vector spaces, Fuzzy Sets and Systems, 27 (1988),
48
[29] E. Pap, Pseudo-analysis and nonlinear equations, Soft Comput., 6 (2002), 21{32.
49
[30] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Soliton Fract, 22 (2004), 1039{1046.
50
[31] S. Romaguera and P. Tirado, Contraction maps on IFQM-spaces with application to recur-
51
rence equations of quicksort, Electronic Notes in Theoretical Computer Science, 225 (2009),
52
[32] R. Saadati, Notes to the paper xed points in intuitionistic fuzzy metric spaces" and its
53
generalization to L-fuzzy metric spaces, Chaos Soliton Fract, 35 (2008), 176{180.
54
[33] R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Soliton Fract,
55
27 (2006), 331{44.
56
[34] R. Saadati, S. Mansour Vaezpour and Y. J. Cho, Quicksort algorithm: application of a xed
57
point theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words, J. Comput.
58
Appl. Math., 228 (2009), 219{225.
59
[35] R. Saadati, A. Razani and H. Adibi, A common xed point theorem in L-fuzzy metric spaces,
60
Chaos Soliton Fract, 33 (2007), 358{363.
61
[36] R. Saadati, S. Sedghi and N. Shobe, Modied intuitionistic fuzzy metric spaces and some
62
xed point theorems, Chaos Soliton Fract, 38 (2008), 36{47.
63
[37] B. Schweizer and A. Sklar, Probabilistic metric spaces, Dover Publications, New York, 2005.
64
[38] F. G. Shi, (L;M)-Fuzzy metric spaces, Indian Journal of Mathematics, 52(2) (2010), 231{
65
[39] F. G. Shi, Regularity and normality of (L;M)-Fuzzy topological spaces, Fuzzy Sets and Systems,
66
182 (2011), 37{52.
67
[40] L. H. Son, B. C. Cuong, P. L. Lanzi and N. T. Thong, A novel intuitionistic fuzzy clustering
68
method for geo-demographic analysis, Expert Syst. Appl., doi:10.1016/j.eswa.2012.02.167,
69
[41] P. Tirado, On compactness and G-completeness in fuzzy metric spaces, Iranian Journal of
70
Fuzzy Systems, 9(4) (2012), 151-158.
71
[42] Z. S. Xu, J. Chen and J. Wu, Clustering algorithm for intuitionistic fuzzy sets, Information
72
Sciences, 178 (2008), 3775{3790.
73
[43] Z. Xu, A method based on distance measure for interval-valued intuitionistic fuzzy group
74
decision making, Information Sciences, 180 (2010), 181{190.
75
[44] Y. Xu and H. Wang, The induced generalized aggregation operators for intuitionistic fuzzy
76
sets and their application in group decision making, Appl. Soft. Comput., 12 (2012), 1168{
77
[45] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.
78
[46] D. Zhang, A natural topology for fuzzy numbers, J. Math. Anal. Appl., 264(2) (2001), 344{
79
[47] S. F. Zhang and S. Y. Liu, A GRA-based intuitionistic fuzzy multi-criteria group decision
80
making method for personnel selection, Expert Syst. Appl., 38 (2011), 11401{11405.
81
[48] Z. Zhanga, J. Yanga, Y. Yea, Y. Huc and Q. Zhang, A type of score function on intuitionistic
82
fuzzy sets with double parameters and its application to pattern recognition and medical
83
diagnosis, Procedia Engineering, 29 (2012), 4336{4342.
84
[49] Z. Zhao and C. Wu, The equivalence of convergences of sequences of fuzzy numbers and
85
its applications to the characterization of compact sets, Information Sciences, 179 (2009),
86
3018{3025.
87
ORIGINAL_ARTICLE
Persian-translation Special Issue vol. 10, no. 2, April 2013
http://ijfs.usb.ac.ir/article_2720_c55cc2472dcccd04ee4bbbc841400cfd.pdf
2013-04-29T11:23:20
2017-09-20T11:23:20
153
160
10.22111/ijfs.2013.2720