ORIGINAL_ARTICLE
Cover Special Issue vol. 10, no. 2, April 2013
http://ijfs.usb.ac.ir/article_2719_40548fa8cb311bf7e87b5cb4defb8845.pdf
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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
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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
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the analysis of fuzzy- and real-valued data, Fuzzy Sets and Systems, 160 (2009), 344–356.
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of fuzzy random variables, Information Sciences, 133 (2001), 3–6.
9
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10
supervised classification of fuzzy data, Int. J. Approx. Reas., 52 (2011), 1272–1282.
11
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law of large numbers, Prob. Theor. Rel. Fields, 114 (1999), 401–417.
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63–71.
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variables in the stratified random sampling from finite populations, Information Sciences, 138
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(2001), 165–184.
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with fuzzy random variables, Eur. J. Oper. Res., 110 (1998), 377–391.
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associated with a fuzzy random variable, Fuzzy Sets and Systems, 111 (2000), 307–317.
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means of a fuzzy random variable, Information Sciences, 133 (2001), 89–100.
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for testing the expected value of a fuzzy random variable, Metrika, 59 (2004), 31–49.
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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
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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,
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[2] P. J. Boland and F. Proschan, Periodic replacement with increasing minimal repair costs at
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failure, Operations Research, 30(6) (1982), 1183{1189.
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Journal of Operations Research, 8(2) (2011), 32{37.
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Journal of Fuzzy Systems, 13(3) (2011), 232{236.
7
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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
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Modelling, 55(3-4) (2012), 754{760.
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tainty, Fuzziness and Knowledge-Based Systems, 17(3) (2009), 419{426.
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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
2017-11-22T11:23:20
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
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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
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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
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ONE 4(2): e4426 (2009) (DOI:10.1371/journal.pone.0004426).
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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
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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
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11
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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
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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
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5
operator weights, Computers & Industrial Engineering, 50 (2006), 312-316.
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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
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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
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and Reliability Engineering International, 21(2005), 781{794.
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Journal of Reliability, Quality and Safety Engineering, 12 (2005), 31{49.
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[6] P. Castagliola, G. Celano and S. Fichera, Monitoring process variability using EWMA, Handbook
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of Engineering Statistics, Springer, Berlin, (2006), 291{325.
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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
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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
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ORIGINAL_ARTICLE
Persian-translation Special Issue vol. 10, no. 2, April 2013
http://ijfs.usb.ac.ir/article_2720_c55cc2472dcccd04ee4bbbc841400cfd.pdf
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10.22111/ijfs.2013.2720