ORIGINAL_ARTICLE
Cover vol. 10, no. 3, June 2013
http://ijfs.usb.ac.ir/article_2704_51aafc18f0567f552ac9f68f7bf9771d.pdf
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10.22111/ijfs.2013.2704
ORIGINAL_ARTICLE
ON FUZZY NEIGHBORHOOD BASED CLUSTERING
ALGORITHM WITH LOW COMPLEXITY
The main purpose of this paper is to achieve improvement in thespeed of Fuzzy Joint Points (FJP) algorithm. Since FJP approach is a basisfor fuzzy neighborhood based clustering algorithms such as Noise-Robust FJP(NRFJP) and Fuzzy Neighborhood DBSCAN (FN-DBSCAN), improving FJPalgorithm would an important achievement in terms of these FJP-based meth-ods. Although FJP has many advantages such as robustness, auto detectionof the optimal number of clusters by using cluster validity, independency fromscale, etc., it is a little bit slow. In order to eliminate this disadvantage, by im-proving the FJP algorithm, we propose a novel Modied FJP algorithm, whichtheoretically runs approximately n= log2 n times faster and which is less com-plex than the FJP algorithm. We evaluated the performance of the ModiedFJP algorithm both analytically and experimentally.
http://ijfs.usb.ac.ir/article_806_29d29dbb033397c08126e891f30d1646.pdf
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10.22111/ijfs.2013.806
Clustering
Fuzzy neighborhood relation
Complexity
Modied FJP
Gozde
Ulutagay
gozde.ulutagay@izmir.edu.tr
true
1
Department of Industrial Engineering, Izmir University, Gursel
Aksel Blv 14, Uckuyular, Izmir, Turkey
Department of Industrial Engineering, Izmir University, Gursel
Aksel Blv 14, Uckuyular, Izmir, Turkey
Department of Industrial Engineering, Izmir University, Gursel
Aksel Blv 14, Uckuyular, Izmir, Turkey
LEAD_AUTHOR
Efendi
Nasibov
efendi nasibov@yahoo.com
true
2
Department of Computer Science, Dokuz Eylul University, Izmir,
35160, Turkey, Institute of Cybernetics, Azerbaijan National Academy of Sciences,
Azerbaijan
Department of Computer Science, Dokuz Eylul University, Izmir,
35160, Turkey, Institute of Cybernetics, Azerbaijan National Academy of Sciences,
Azerbaijan
Department of Computer Science, Dokuz Eylul University, Izmir,
35160, Turkey, Institute of Cybernetics, Azerbaijan National Academy of Sciences,
Azerbaijan
AUTHOR
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the clustering structure, In: Proceedings of ACM SIGMOD International Conference on
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Management of Data, Philadelphia, PA, (1999), 49{60.
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F. Murtagh, Validity-guided (re)clustering with applications to image segmentation, IEEE
8
Transactions on Fuzzy Systems, 4 (1996), 112{123.
9
[4] J. C. Bezdek, Fuzzy mathematics in pattern classification, PhD Thesis, Cornell Univ, NY,
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[5] M. H. Chehreghani, H. Abolhassani and M. H. Chehreghani, Improving density-based methods
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for hierarchical clustering of web pages, Data & Knowledge Engineering, 67 (2008), 30{50.
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in large spatial databases with noise, In Proc. 2nd International Conference on Knowledge
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Discovery and Data Mining, (1996), 226{231.
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databases, In: Proceeding ACM SIGMOD International Conference on Management of Data,
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Seattle, WA, (1998), 73{84.
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San Francisco, CA, 2001.
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Data Mining (KDD98), New York, (1998), 58{65.
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e, DBDC: density based distributed clustering, 5th
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(2004a), 88{105.
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[16] E. Januzaj, H. P. Kriegel and M. Pfei
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e, Scalable density based distributed clustering, 15th
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International Conference on Machine Learning (ECML) and the 8th European Conference on
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Principles and Practice of Knowledge Discovery in Databases (PKDD), Pisa, Italy, 2004b.
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using dynamic modeling, IEEE Computer, 32(8) (1999), 68{75.
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John Wiley&Sons, Inc, 1990.
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criteria by a hybrid PSO and fuzzy c-means clustering algorithm, Iranian Journal of
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Fuzzy Systems, 5(3) (2008), 1{14.
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49
points method, Automatic Control and Computer Sciences, 39(6) (2005), 8{17.
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[21] E. N. Nasibov and G. Ulutagay, On the fuzzy joint points method for fuzzy clustering problem,
51
Automatic Control and Computer Sciences, 40(5) (2006), 33{44.
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[23] E. N. Nasibov and G. Ulutagay, Robustness of density-based clustering methods with various
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neighborhood relations, Fuzzy Sets and Systems, 160(24) (2009), 3601{3615.
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data mining, Proceedings of the 23rd Very Large Databases Conference (VLDB 1997), Athens,
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[32] X. Xiaowei, E. Martin, H. P. Kriegel and J. Sander, A distribution-based clustering algorithm
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Engineering (ICDE98), Orlando, Florida, (1998), 324{331.
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[33] A. Z. Xu, J. Chen and J. Wu, Clustering algorithm for intuitionistic fuzzy sets, Information
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of Data, Montreal, Canada, (1996), 103{113.
87
ORIGINAL_ARTICLE
OPTIMAL CONTROL OF FUZZY LINEAR CONTROLLED
SYSTEM WITH FUZZY INITIAL CONDITIONS
In this article we found the solution of fuzzy linear controlled systemwith fuzzy initial conditions by using -cuts and presentation of numbersin a more compact form by moving to the eld of complex numbers. Next, afuzzy optimal control problem for a fuzzy system is considered to optimize theexpected value of a fuzzy objective function. Based on Pontryagin MaximumPrinciple, a constructive equation for the problem is presented. In the lastsection, three examples are used to show that the method in eective to solvefuzzy and fuzzy optimal linear controlled systems.
http://ijfs.usb.ac.ir/article_807_c58b5ba2cb1e2768a9c8c8fc759eb228.pdf
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21
35
10.22111/ijfs.2013.807
Fuzzy linear controlled system
Optimal fuzzy controlled system
PMP
Marzieh
Najariyan
marzieh.najariyan@gmail.com
true
1
Department of Applied Mathematics, Ferdowsi University of
Mashhad, Mashhad, Iran
Department of Applied Mathematics, Ferdowsi University of
Mashhad, Mashhad, Iran
Department of Applied Mathematics, Ferdowsi University of
Mashhad, Mashhad, Iran
LEAD_AUTHOR
Mohamad Hadi
Farahi
farahi@math.um.ac.ir
true
2
Department of Applied Mathematics, Ferdowsi University of
Mashhad, Mashhad, Iran and The center of Excellence on Modelling and Control
Systems (CEMCS)
Department of Applied Mathematics, Ferdowsi University of
Mashhad, Mashhad, Iran and The center of Excellence on Modelling and Control
Systems (CEMCS)
Department of Applied Mathematics, Ferdowsi University of
Mashhad, Mashhad, Iran and The center of Excellence on Modelling and Control
Systems (CEMCS)
AUTHOR
1. T. Allahviranloo and M. A. Kermani, Numerical methods for fuzzy linear partial dierential
1
equations under new denition for derivative, Iranian Journal of Fuzzy Systems, 7 (2010),
2
2. B. Bede, I. J. Rudas and A. L. Bencsik, First order linear fuzzy dierential equation sunder
3
generalized dierentiability, Information Science, 177 (2007), 1648-1662.
4
3. R. C. Dorf and R. H. Bishop, Modern control systems, Person Education, Inc. Upper Saddle
5
River, New Jersey, 07458 (2011).
6
4. P. Diamond and P. E. Kloeden, Metric space of Fuzzy sets, Theory And Applications, World
7
scientic publishing, 1994.
8
5. O. S. Fard and A. V. Kamyad, Modied k-step method for solving fuzzy initial value problems,
9
Iranian Journal of Fuzzy Systems, 8 (2011), 49-63.
10
6. D. Filev and P. Angelove, Fuzzy optimal control, Fuzzy Sets and Systems, 47 (1992), 151-56.
11
7. D. N. Georgiou, J. J. Nieto and R. Rodriguez-Lopez, Initial value problems for higher-order
12
fuzzy dierential equations, Nonlinear Analysis, 63 (2005), 587-600.
13
8. A. Khastan, J. J. Nieto and R. Rodriguez-Lopez, Variation of constant formula for rst order
14
fuzzy dierential equations, Fuzzy Sets and Systems, 177 (2011), 20-33.
15
9. A. Khastan and J. J. Nieto, A boundary value problem for second order fuzzy dierential
16
equations, Nonlinear Analysis, 72 (2010), 3583-3593.
17
10. J. J. Nieto, R. Rodriguez-Lopez and M. Villanueva-Pesqueira, Exact solution to the periodic
18
boundary value problem for a rst-order linear fuzzy dierential equation with impulses, Fuzzy
19
Optimization Decision Making, 10 (2011), 323-339.
20
11. J. J. Nieto, A. Khastan and K. Ivaz, Numerical solution of fuzzy dierential equations under
21
generalized dierentiability, Nonlinear Analysis: Hybrid Systems, 3 (2009), 700-707.
22
12. J. H. Park, J. S. Park and Y. C. Kwun, Controllability for the semilinear fuzzy integrodier-
23
ential equations with nonlocal conditions, Lecture Notes in Articial Intelligence, LNAI 4223
24
(2006), 221-230.
25
13. D. W. Pearson, A property of linear fuzzy dierential equations, Appl. Math. Lett., 10 (1997),
26
14. E. R. Pinch, Optimal control and the calculuse of variations, Oxford University Press Inc.,
27
New Yourk, 1995.
28
15. Z. Qin, Time-homogeneous fuzzy optimal control problems, http://www.orsc.edu.cn/process/
29
080415.pdf.
30
16. S. Ramezanzadeh and A. Heydari, Optimal control with fuzzy chance constraint, Iranian
31
Journal of fuzzy systems, 8 (2011), 35-43.
32
17. S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 (1987), 319-330.
33
18. J. Xu, Z. Liao and J. J. Nieto, A class of dierential dynamical systems with fuzzy matrices,
34
Math. Anal. Appl., 368 (2010), 54-68.
35
19. J. Xu, Z. Liao and Z. Hu, A class of linear dierential dynamical systems with fuzzy initial
36
condition, Fuzzy Sets and Systems, 158 (2007), 2339-2358.
37
20. Y. Zhu, A fuzzy optimal control model, Journal of uncertain systems, 3 (2009), 270-279.
38
21. Y. Zhu, Fuzzy optimal control with application to portfolio selection, http://www.orsc.edu.cn/
39
process/080117.pdf.
40
ORIGINAL_ARTICLE
$\mathcal{I}_2$-convergence of double sequences of\\ fuzzy numbers
In this paper, we introduce and study the concepts of $\mathcal{I}_2$-convergence, $\mathcal{I}_2^{*}$-convergence for double sequences of fuzzy real numbers, where $\mathcal{I}_2$ denotes the ideal of subsets of $\mathbb N \times \mathbb N$. Also, we study some properties and relations of them.
http://ijfs.usb.ac.ir/article_809_803b6897c706fdbec4081baf755af3ca.pdf
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50
10.22111/ijfs.2013.809
Ideal
Double sequences
$mathcal{I}$-Convergence
Fuzzy number sequences
Erdinc.
Dundar
erdincdundar79@gmail.com
true
1
Department of Mathematics, Afyon Kocatepe University, 03200
Afyonkarahisarn,Turkey
Department of Mathematics, Afyon Kocatepe University, 03200
Afyonkarahisarn,Turkey
Department of Mathematics, Afyon Kocatepe University, 03200
Afyonkarahisarn,Turkey
LEAD_AUTHOR
Ozer
Talo
ozertalo@hotmail.com
true
2
Department of Mathematics, Celal Bayar University, 45040 Manisa,
Turkey
Department of Mathematics, Celal Bayar University, 45040 Manisa,
Turkey
Department of Mathematics, Celal Bayar University, 45040 Manisa,
Turkey
AUTHOR
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1
B. Altay and F. Bad{s}ar, emph{Some new spaces of double sequences}, J. Math. Anal. Appl., textbf{309(1)} (2005), 70--90.
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H. Alt{i}nok, Y. Alt{i}n and M. Id{s}{i}k, emph{Statistical convergence and strong p-Ces'{a}ro summability of order $beta$ in sequences of fuzzy numbers}, Iranian Journal of Fuzzy
4
Systems, textbf{9(2)} (2012), 63--73.
5
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Fuzzy Sets and Systems, textbf{147} (2004), 385--403.
7
bibitem{cc-ba}
8
d{C}. CÇakan and B. Altay, emph{Statistically boundedness and statistical core
9
of double sequences}, J. Math. Anal. Appl., textbf{317} (2006), 690--697.
10
bibitem{das 1}
11
P. Das, P. Kostyrko, W. Wilczy'{n}ski and P. Malik, emph{I and
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$I^{*}$-convergence of double sequences}, Math. Slovaca, textbf{58(5)} (2008), 605--620.
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P. Das and P. Malik, emph{On extremal I-limit points of double
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sequences}, Tatra Mt. Math. Publ., textbf{40} (2008), 91--102.
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E. D"{u}ndar and B. Altay emph{$mathcal{I}_2$-uniform convergence of double
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J. A. Fridy, emph{On statistical convergence}, Analysis,
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J. A. Fridy and C. Orhan, emph{Statistical limit superior and inferior}, Proc. Amer. Math. Soc., textbf{125} (1997), 3625--3631.
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J. A. Fridy, emph{Statistical limit points}, Proc. Amer. Math. Soc.,
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P. Kostyrko, T. u{S}al'{a}t and W. Wilczy'{n}ski, emph{I-convergence},
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Real Anal. Exchange, textbf{26(2)} (2000), 669-686.
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P. Kostyrko, M. Mav{c}aj, T. u{S}al'{a}t and M. Sleziak, emph{I-convergence
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and extremal I-limit points}, Math. Slovaca, textbf{55} (2005), 443--464.
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V. Kumar, emph{On I and $I^{*}$-convergence of double sequences},
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Math. Commun., textbf {12} (2007), 171--181.
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V. Kumar and K. Kumar, emph{On the ideal convergence of sequences of fuzzy numbers}, Information Sciences, textbf{178} (2008), 4670--4678.
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M. Matloka, emph{Sequences of fuzzy numbers}, Busefal, textbf{28} (1986), 28--37.
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Mursaleen and O. H. H. Edely, emph{Statistical convergence of double
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S. Nanda, emph{On sequences of fuzzy numbers}, Fuzzy Sets and Systems, textbf{33} (1989), 123--126.
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A. Nabiev, S. Pehlivan and M. G"{u}rdal, emph{On I-Cauchy sequence},
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F. Nuray and W. H. Ruckle, emph{Generalized statistical convergence and convergence free spaces}, J. Math. Anal. Appl., textbf{245} (2000), 513--527.
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F. Nuray, emph{Lacunary statistical convergence of sequences of fuzzy numbers},
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Fuzzy Sets and Systems, textbf{99} (1998), 353--355.
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F. Nuray and E. Savad{s}, emph{Statistical convergence of sequences of fuzzy numbers}, Math. Slovaca, textbf{45(3)} (1995), 269--273.
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E. Savad{s}, emph{On statistical convergent sequences of fuzzy numbers},
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E. Savad{s} and Mursaleen, emph{On statistically convergent
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E. Savad{s}, emph{A note on double sequences of fuzzy numbers}, Turk. Jour. Math., textbf{20(20)} (1996), 175--178.
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E. Savad{s}, emph{$(A)_{Delta}$-double sequence spaces of fuzzy numbers via orlicz function}, Iranian Journal of Fuzzy
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related summability methods}, Amer. Math. Monthly, textbf {66}
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(1959), 361--375.
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"{O}. Talo and F. Bad{s}ar, emph{Determination of the
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duals of classical sets of sequences of fuzzy numbers and related
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matrix transformations}, Comput. Math. Appl., textbf{58} (2009),
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B. Tripathy and B. C. Tripathy, emph{On I-convergent double
96
sequences}, Soochow J. Math., textbf {31} (2005), 549--560.
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B. C. Tripathy, emph{Statistically convergent double sequences}, Tamkang J. Math., textbf{34(3)} (2003), 231--237.
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B. C. Tripathy and B. Sarma, emph{Double sequence spaces of fuzzy numbers defined by Orlicz function}, Acta Math. Sci., textbf{31B(1)} (2011), 134--140.
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103
ORIGINAL_ARTICLE
ON APPROXIMATE CAUCHY EQUATION IN FELBIN'S TYPE
FUZZY NORMED LINEAR SPACES
n this paper we study the Hyers-Ulam-Rassias stability of Cauchyequation in Felbin's type fuzzy normed linear spaces. As a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. This shows how the category offuzzy normed linear spaces differs from the classical normed linearspaces in general.
http://ijfs.usb.ac.ir/article_862_96b9bdd60ae0f69019dd773c9ce92817.pdf
2013-06-01T11:23:20
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51
63
10.22111/ijfs.2013.862
Fuzzy real number
Fuzzy normed space
Hyers-Ulam-Rassias
stability
I.
Sadeqi
esadeqi@sut.ac.ir
true
1
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
LEAD_AUTHOR
F.
Moradlou
moradlou@sut.ac.ir
true
2
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
AUTHOR
M.
Salehi
mit-paydar@yahoo.com
true
3
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
AUTHOR
[1] T. Bag and S. K. Samanta, A comparative study of fuzzy norms on a linear space, Fuzzy
1
Sets and Systems, 159(6) (2008), 670{684.
2
[2] T. Bag and S. K. Samanta, Fixed point theorems in Felbin type fuzzy normed linear spaces,
3
The Journal of Fuzzy Mathematics, to appear.
4
[3] C. Borelli and G. L. Forti, On a general Hyers{Ulam stability result, Internat. J. Math. Math.
5
Sci., 18 (1995), 229{236.
6
[4] S. Czerwik, The stability of the quadratic functional equation, in: Th. M. Rassias, J. Tabor,
7
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75
ORIGINAL_ARTICLE
ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND
ATTACHMENTS
The paper continues the study of the authors on relationships between \emph{topological systems} of S.~Vickers and \emph{attachments} of C.~Guido. We extend topological systems to \emph{algebraically-topological systems}. A particular instance of the latter, called \emph{attachment system}, incorporates the notion of attachment, thus, making it categorically redundant in mathematics. We show that attachment systems are equipped with an internal topology, which is similar to the topology induced by locales. In particular, we provide an attachment system analogue of the well-known categorical equivalence between sober topological spaces and spatial locales.
http://ijfs.usb.ac.ir/article_863_f7926f99d233d0b927339f4338ddbc5c.pdf
2013-06-01T11:23:20
2018-12-16T11:23:20
65
102
10.22111/ijfs.2013.863
Algebraically-topological system
Attachment system
Categorically-algebraic topology
Dual attachment pair
Localic algebra
Localification of systems
(Variety-based) pointless topology
Spatialization of systems
Topological theory morphism
Variety
Anna
Frascella
frascella anna@libero.it
true
1
Department of Mathematics \E. De Giorgi", University of Salento,
P. O. Box 193, 73100 Lecce, Italy
Department of Mathematics \E. De Giorgi", University of Salento,
P. O. Box 193, 73100 Lecce, Italy
Department of Mathematics \E. De Giorgi", University of Salento,
P. O. Box 193, 73100 Lecce, Italy
AUTHOR
Cosimo
Guido
cosimo.guido@unisalento.it
true
2
Department of Mathematics \E. De Giorgi", University of Salento,
P. O. Box 193, 73100 Lecce, Italy
Department of Mathematics \E. De Giorgi", University of Salento,
P. O. Box 193, 73100 Lecce, Italy
Department of Mathematics \E. De Giorgi", University of Salento,
P. O. Box 193, 73100 Lecce, Italy
AUTHOR
Sergey A.
Solovyov
solovjovs@fme.vutbr.cz
true
3
Department of Mathematics, University of Latvia, Zellu iela 8,
LV-1002 Riga, Latvia and Institute of Mathematics and Computer Science, University
of Latvia, Raina bulvaris 29, LV-1459 Riga, Latvia
Department of Mathematics, University of Latvia, Zellu iela 8,
LV-1002 Riga, Latvia and Institute of Mathematics and Computer Science, University
of Latvia, Raina bulvaris 29, LV-1459 Riga, Latvia
Department of Mathematics, University of Latvia, Zellu iela 8,
LV-1002 Riga, Latvia and Institute of Mathematics and Computer Science, University
of Latvia, Raina bulvaris 29, LV-1459 Riga, Latvia
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Linz Seminar on Fuzzy Set Theory, Johannes Kepler Universitat, Linz, 2009.
19
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20
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Linz Seminar on Fuzzy Set Theory, Johannes Kepler Universitat, Linz, 2010.
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23
valued topological systems, Fuzzy Sets and Systems, 192 (2012), 58{103.
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and topological systems, Quaest. Math., 32(2) (2009), 139{186.
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ORIGINAL_ARTICLE
Preservation theorems in {\L}ukasiewicz \\model theory
We present some model theoretic results for {\L}ukasiewiczpredicate logic by using the methods of continuous model theorydeveloped by Chang and Keisler.We prove compactness theorem with respect to the class of allstructures taking values in the {\L}ukasiewicz $\texttt{BL}$-algebra.We also prove some appropriate preservation theorems concerning universal and inductive theories.Finally, Skolemization and Morleyization in this framework are discussed andsome natural examples of fuzzy theories are presented.
http://ijfs.usb.ac.ir/article_864_4dc824201c1a83e208595fdce2760b02.pdf
2013-06-01T11:23:20
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103
113
10.22111/ijfs.2013.864
Continuous model theory
{L}ukasiewicz logic
Preservation theorems
Seyed-Mohammad
Bagheri
bagheri@modares.ac.ir
true
1
Department of Pure Mathematics, Faculty of Mathemat-
ical Sciences, Tarbiat Modares University, P.O. Box 14115-134, and Institute for Re-
search in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
Department of Pure Mathematics, Faculty of Mathemat-
ical Sciences, Tarbiat Modares University, P.O. Box 14115-134, and Institute for Re-
search in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
Department of Pure Mathematics, Faculty of Mathemat-
ical Sciences, Tarbiat Modares University, P.O. Box 14115-134, and Institute for Re-
search in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
AUTHOR
Morteza
Moniri
m-moniri@sbu.ac.ir, ezmoniri@gmail.com
true
2
Department of Mathematics, Shahid Beheshti University, G. C.,
Evin, Tehran, Iran
Department of Mathematics, Shahid Beheshti University, G. C.,
Evin, Tehran, Iran
Department of Mathematics, Shahid Beheshti University, G. C.,
Evin, Tehran, Iran
LEAD_AUTHOR
bibitem{Barwise} J. Barwise (editor), {it Handbook of mathematical logic}, North-Holland, 1977.
1
bibitem{CK} Chang and Keisler, {it Continuous Model Theory}, Annals of Mathematical Studies, Princeton University Press, {bf58} (1966).
2
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3
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5
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6
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7
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8
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9
Kluwer Academic Publishers, Dordercht, {bf4} (1998).
10
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11
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12
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13
Archive for Mathematical Logic, {bf44} (2005), 97-114.
14
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15
first-order logic}, Journal of Symbolic Logic, {bf75} (2010), 168-190.
16
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17
{it Model theory for metric structures}, In Model Theory with Applications to Algebra and Analysis,
18
Vol. II, eds. Z. Chatzidakis, D. Macpherson, A. Pillay, and A.Wilkie, Lecture Notes series
19
of the London Mathematical Society, No. 350, Cambridge University Press, (2008), 315-427.
20
ORIGINAL_ARTICLE
NEW RESULTS ON THE EXISTING FUZZY DISTANCE
MEASURES
In this paper, we investigate the properties of some recently pro-posed fuzzy distance measures. We find out some shortcomings for these dis-tances and then the obtained results are illustrated by solving several examplesand compared with the other fuzzy distances.
http://ijfs.usb.ac.ir/article_865_f126130d163cdce4954709acbe123b64.pdf
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124
10.22111/ijfs.2013.865
Fuzzy distance measure
Metric properties
Fuzzy numbers
Saeid
Abbasbandy
abbasbandy@yahoo.com
true
1
Department of Mathematics, Imam Khomeini International Uni-
versity, Ghazvin, 34149-16818, Iran
Department of Mathematics, Imam Khomeini International Uni-
versity, Ghazvin, 34149-16818, Iran
Department of Mathematics, Imam Khomeini International Uni-
versity, Ghazvin, 34149-16818, Iran
LEAD_AUTHOR
Soheil
Salahshour
soheilsalahshour@yahoo.com
true
2
Young Researchers and Elite Club, Mobarakeh Branch, Islamic
Azad University, Mobarakeh, Iran
Young Researchers and Elite Club, Mobarakeh Branch, Islamic
Azad University, Mobarakeh, Iran
Young Researchers and Elite Club, Mobarakeh Branch, Islamic
Azad University, Mobarakeh, Iran
AUTHOR
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1
fuzzy number, Internat. J. Approx. Reason., 170 (2006), 166-178.
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3
fuzzy number, Comput. Math. Appl., 59 (2010), 3066-3077.
4
[3] A. I. Ban, On the nearest parametric approximation of a fuzzy number-revisited, Fuzzy Sets
5
and Systems, 160 (2009), 3027-3047.
6
[4] A. I. Ban, Triangular and parametric approximations of fuzzy numbers-inadvertences and
7
corrections, Fuzzy Sets and Systems, 160 (2009), 3048-3058.
8
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Approx. Reason., 50 (2009), 485-493.
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for fuzzy numbers, Math. Compu. Modelling, 43 (2006), 254-261.
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measure between two generalized fuzzy numbers, Appl. Soft Comput., 10 (2010), 90-99.
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(2009), 49-59.
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Iranian Journal of Fuzzy Systems, 6(1) (2009), 27-44.
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[13] R. O. Rodrguez, F. Esteva, P. Garcia and L. Godo, On implicative closure operators in
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approximate reasoning, Int. J. Approximate Reasoning, 33 (2003), 159{184.
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[14] L. Tran and L. Duckstein, Comparison of fuzzy numbers using a fuzzy distance measure,
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Fuzzy Sets and Systems, 130 (2002), 331-341.
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ternat. J. Approx. Reason., 50 (2009), 529-540.
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Systems, 119 (2001), 215-223.
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Systems, Man and Cybernetics Part B, 27 (1997), 1-13.
34
ORIGINAL_ARTICLE
representation theorems of $L-$subsets and $L-$families on complete residuated lattice
In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete residuated lattice is obtained. Secondly, weintroduce the concepts of $L-$family and the system of $L-$subsets,then with the tool of the system of $L-$subsets, we obtain therepresentation theorem of intersection-preserving $L-$families oncomplete residuated lattice.
http://ijfs.usb.ac.ir/article_866_34e66093d052f7fc3dc927be495d286b.pdf
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125
136
10.22111/ijfs.2013.866
Complete residuated lattices
$L-$subsets
$L-$nested systems
$L-$families
Level $L-$subsets
Representation theorems
Hui
Han
hanhui200801@163.com
true
1
Department of Mathematics, Ocean University of China, 266100 Qingdao,
P.R. China
Department of Mathematics, Ocean University of China, 266100 Qingdao,
P.R. China
Department of Mathematics, Ocean University of China, 266100 Qingdao,
P.R. China
LEAD_AUTHOR
Jinming
Fang
jinming-fang@163.com
true
2
Department of Mathematics, Ocean University of China, 266100 Qing-
dao, P.R. China
Department of Mathematics, Ocean University of China, 266100 Qing-
dao, P.R. China
Department of Mathematics, Ocean University of China, 266100 Qing-
dao, P.R. China
AUTHOR
[1] R. Belohlavek, Fuzzy relational systems: foundations and principles, Kluwer Academic/
1
Plenum Press, New York, 2002.
2
[2] J. M. Fang and Y. L. Han, A new representation theorem of L-Sets, Periodical of Ocean
3
University of China (Natural Science), 38(6) (2008), 1025-1028.
4
[3] M. Gorjanac-Ranitovic and A. Tepavcevic, General form of lattice-valued fuzzy sets under
5
the cutworthy approach, Fuzzy Sets and Systems, 158(11) (2007), 1213-1216.
6
[4] G. Jager, Level spaces for lattice-valued uniform convergence spaces, Quaest. Math, 31
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(2008), 255-277.
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[5] C. Z. Luo, Fuzzy sets and nested systems, Fuzzy Mathematics, 3(4) (1983), 113-126.
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(1975), 169-174.
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[7] B. Seselja and A. Tepavcevic, A note on a natural equivalence relation on fuzzy power set,
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Fuzzy Sets and Systems, 148(2) (2004), 201-210.
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[8] B. Seselja and A. Tepavcevic, Representing ordered structures by fuzzy sets: an overview,
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Fuzzy Sets and Systems, 136(1) (2003), 21-39.
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[9] B. Seselja and A. Tepavcevic, Completion of ordered structures by cuts of fuzzy sets: an
16
overview, Fuzzy Sets and Systems, 136(1) (2003), 1-19.
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[10] F. G. Shi, Theory of L-nested sets and L-nested sets and applications, Fuzzy Systems
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and Mathematics, 9(4) (1995), 65-72.
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[11] M. Voskoglou, Measuring students modeling capacities: a fuzzy approach, Iranian Journal of
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Fuzzy Systems, 8(3) (2011), 23-33.
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[12] F. L. Xiong, The representation theorems on complete lattice and their application, Periodical
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of Ocean University of Qingdao, 28(2) (1998), 339-344.
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[13] W. X. Zhang, Fuzzy mathematic basis, Xi'an: Xi'an Jiao Tong University Press, 1984.
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[14] Q. Y. Zhang, Algebraic generations of some fuzzy powerset operators, Iranian Journal of
25
Fuzzy Systems, 8(5) (2011), 31-58.
26
ORIGINAL_ARTICLE
Existence of Extremal Solutions for Impulsive Delay Fuzzy
Integrodifferential Equations in $n$-dimensional Fuzzy Vector Space
In this paper, we study the existence of extremal solutions forimpulsive delay fuzzy integrodifferential equations in$n$-dimensional fuzzy vector space, by using monotone method. Weshow that obtained result is an extension of the result ofRodr'{i}guez-L'{o}pez cite{rod2} to impulsive delay fuzzyintegrodifferential equations in $n$-dimensional fuzzy vector space.
http://ijfs.usb.ac.ir/article_867_92344978ee7caa723a34d804983d83c0.pdf
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137
157
10.22111/ijfs.2013.867
Extremal solution
Impulsive delay fuzzy
integrodifferential equation
$n$-dimensional fuzzy vector space
Monotone method
Young
Chel Kwun
yckwun@dau.ac.kr
true
1
Department of Mathematics, Dong-A University, Busan 604-714,
Republic of Korea
Department of Mathematics, Dong-A University, Busan 604-714,
Republic of Korea
Department of Mathematics, Dong-A University, Busan 604-714,
Republic of Korea
AUTHOR
Jeong Soon
Kim
jeskim@donga.ac.kr
true
2
Department of Math. Education, Daegu-University, Gyeongsan 712-
714, Republic of Korea
Department of Math. Education, Daegu-University, Gyeongsan 712-
714, Republic of Korea
Department of Math. Education, Daegu-University, Gyeongsan 712-
714, Republic of Korea
AUTHOR
Jin Han
Park
jihpark@pknu.ac.kr
true
3
Department of Applied Mathematics, Pukyong National University,
Buan 608-737, Republic of Korea
Department of Applied Mathematics, Pukyong National University,
Buan 608-737, Republic of Korea
Department of Applied Mathematics, Pukyong National University,
Buan 608-737, Republic of Korea
LEAD_AUTHOR
[1] P. Balasubramaniam and S. Muralisankar, Existence and uniqueness of fuzzy solution for
1
semilinear fuzzy integrodierential equations with nonlocal conditions, Computer & Mathe-
2
matics with Applications, 47 (2004), 1115{1122.
3
[2] P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, World Scientic, 1994.
4
[3] Y. C. Kwun, J. S. Kim, M. J. Park and J. H. Park, Nonlocal controllability for the semilinear
5
fuzzy integrodierential equations in n-dimensional fuzzy vector space, Advances in Dierence
6
Equations, Article ID734090, 2009 (2009).
7
[4] Y. C. Kwun, J. S. Kim, M. J. Park and J. H. Park, Controllability for the impulsive semilinear
8
nonlocal fuzzy integrodierential equations in n-dimensional fuzzy vector space , Advances
9
in Dierence Equations, Article ID983483, 2010(2010).
10
[5] Y. C. Kwun, J. S. Kim and J. H. Park, Existence of extremal solutions for impulsive fuzzy dif-
11
ferential equations with periodic boundary value in n-dimensional fuzzy vector space, Journal
12
of Computational Analysis and Applications, 13 (2011), 1157{1170.
13
[6] J. J. Nieto and R. Rodrguez-Lopez, Existence of extrmal solutions for quadratic fuzzy equa-
14
tions, Fixed Point Theory Appl., 3 (2005), 321{342.
15
[7] R. Rodrguez-Lopez, Periodic boundary value problems for impulsive fuzzy dierential equa-
16
tions Fuzzy Sets and Systems, 159 (2008), 1384{1409.
17
[8] R. Rodrguez-Lopez, Monotone method for fuzzy dierential equations Fuzzy Sets and Sys-
18
tems, 159 (2008), 2047{2076.
19
[9] S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 (1987), 319{330
20
[10] O. Solaymani Fard and A. Vahidian Kamyad, Modied k-step method for solving fuzzy initial
21
value problems, Iranian Journal of Fuzzy Systems, 8 (2011), 49{63.
22
[11] G. Wang, Y. Li and C. Wen, On fuzzy n-cell number and n-dimension fuzzy vectors, Fuzzy
23
Sets and Systems, 158 (2007), 71{84.
24
[12] G. Wang and C. Wu, Fuzzy n-cell number and the dierential of fuzzy n-cell number value
25
mappings, Fuzzy Sets and Systems, 130 (2002), 367{381.
26
ORIGINAL_ARTICLE
On fuzzy convex lattice-ordered subgroups
In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore, the Fundamental Homomorphism Theorem is established. Finally, it is proved that the class of all fuzzy convex lattice-ordered subgroups of a lattice-ordered group $G$ forms a complete Heyting sublattice of the lattice of fuzzy subgroups of $G$.
http://ijfs.usb.ac.ir/article_868_d0885d1f664c56b3166342279f5a2d45.pdf
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159
172
10.22111/ijfs.2013.868
Lattice-ordered group
Convex subgroup
Fuzzy convex subgroup
Mahmood
Bakhshi
bakhshi@ub.ac.ir
true
1
Department of Mathematics, Bojnord University, Bojnord, Iran
Department of Mathematics, Bojnord University, Bojnord, Iran
Department of Mathematics, Bojnord University, Bojnord, Iran
LEAD_AUTHOR
[1] N. Ajmal and K. V. Thomas, Fuzzy lattices, Information Sciences, 79 (1994), 271{291.
1
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[3] J. M. Anthony and H. Sherwood, A characterization of fuzzy subgroups, Fuzzy Sets and
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Systems, 7 (1982), 297{305.
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[4] T. S. Blyth, Lattices and ordered algebraic structures, Springer-Verlag, London, 2005.
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[5] Y. Bo and W. Wangming, Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems, 35
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(1990), 231{240.
7
[6] P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84 (1981), 264{269.
8
[7] D. S. Malik, J. N. Mordeson and P. S. Nair, Fuzzy generators and fuzzy direct sums of abelian
9
groups, Fuzzy Sets and Systems, 50 (1992), 193{199.
10
[8] J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, Fuzzy group theory, Springer-Verlag,
11
Netherlands, 2005.
12
[9] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512{517.
13
[10] G. S. V. Satya Saibaba, Fuzzy lattice ordered groups, Southeast Asian Bull. Math., 32 (2008),
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[11] U. M. Swamy and D. Viswanadha Raju, Fuzzy ideals and congruences of lattices, Fuzzy Sets
15
and Systems, 95 (1998), 249{253.
16
[12] Y. Yin, Y. B. Jun and Z. Yang, More general forms (; )-fuzzy ideals of ordered semigroups,
17
Iranian Journal of Fuzzy Systems, 9(4) (2012), 99-113.
18
[13] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.
19
ORIGINAL_ARTICLE
Persian-translation vol. 10, no. 3, June 2013
http://ijfs.usb.ac.ir/article_2705_a25aa8054af994783d70a20f9b71cfe4.pdf
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175
184
10.22111/ijfs.2013.2705