ORIGINAL_ARTICLE
Cove Vol.5, No.3, October 2008
http://ijfs.usb.ac.ir/article_2901_670fd9d88f16069bbcbb60c0052e20bf.pdf
2008-10-29T11:23:20
2017-11-22T11:23:20
0
10.22111/ijfs.2008.2901
ORIGINAL_ARTICLE
OPTIMIZATION OF FUZZY CLUSTERING CRITERIA BY A HYBRID
PSO AND FUZZY C-MEANS CLUSTERING ALGORITHM
This paper presents an efficient hybrid method, namely fuzzy particleswarm optimization (FPSO) and fuzzy c-means (FCM) algorithms, to solve the fuzzyclustering problem, especially for large sizes. When the problem becomes large, theFCM algorithm may result in uneven distribution of data, making it difficult to findan optimal solution in reasonable amount of time. The PSO algorithm does find agood or near-optimal solution in reasonable time, but we show that its performancemay be improved by seeding the initial swarm with the result of the c-meansalgorithm. Various clustering simulations are experimentally compared with the FCMalgorithm in order to illustrate the efficiency and ability of the proposed algorithms.
http://ijfs.usb.ac.ir/article_339_3fd4baa8d09bbcf87e9f15a5e6ec363b.pdf
2008-10-08T11:23:20
2017-11-22T11:23:20
1
14
10.22111/ijfs.2008.339
Fuzzy clustering
Particle Swarm Optimization (PSO)
Fuzzy
c-means (FCM)
E.
MEHDIZADEH
mehdizadeh@qazviniau.ac.ir
true
1
DEPARTMENT OF INDUSTRIAL ENGINEERING, SCIENCE & RESEARCH BRANCH,
ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
DEPARTMENT OF INDUSTRIAL ENGINEERING, SCIENCE & RESEARCH BRANCH,
ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
DEPARTMENT OF INDUSTRIAL ENGINEERING, SCIENCE & RESEARCH BRANCH,
ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
LEAD_AUTHOR
S.
SADI-NEZHAD
sadinejad@hotmail.com
true
2
DEPARTMENT OF INDUSTRIAL ENGINEERING, SCIENCE & RESEARCH BRANCH,
ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
DEPARTMENT OF INDUSTRIAL ENGINEERING, SCIENCE & RESEARCH BRANCH,
ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
DEPARTMENT OF INDUSTRIAL ENGINEERING, SCIENCE & RESEARCH BRANCH,
ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
AUTHOR
R.
TAVAKKOLI-MOGHADDAM
tavakoli@ut.ac.ir
true
3
DEPARTMENT OF INDUSTRIAL ENGINEERING, COLLEGE OF
ENGINEERING, UNIVERSITY OF TEHRAN, TEHRAN, IRAN
DEPARTMENT OF INDUSTRIAL ENGINEERING, COLLEGE OF
ENGINEERING, UNIVERSITY OF TEHRAN, TEHRAN, IRAN
DEPARTMENT OF INDUSTRIAL ENGINEERING, COLLEGE OF
ENGINEERING, UNIVERSITY OF TEHRAN, TEHRAN, IRAN
AUTHOR
[1] J. C. Bezdek and R. J. Hathaway, Optimization of fuzzy clustering criteria using genetic algorithms,
1
Proceedings of the IEEE Conf. on Evolutionary Computation, Orlando, 2 (1994), 589-594.
2
[2] J. C. Bezdek, Cluster validity with fuzzy sets, Journal of Cybernetics, 3 (1974), 58-72.
3
[3] J. C. Bezdek, Pattern recognition with fuzzy objective function algorithms, New York, 1981.
4
[4] C. Y. Chen and F. Ye, Particle swarm optimization and its application to clustering analysis,
5
Proceedings of the Int. Conf. on Networking, Sensing and Control, Taipei: Taiwan, 2004, 789-794.
6
[5] M. Dorigo and V. Maniezzo, Ant system: Optimization by a colony of cooperating agents, IEEE
7
Transactions on Systems, Man, and Cybernetics B, 26 (1) (1996), 29-41.
8
[6] J. C. Dunn, Fuzzy relative of the ISODATA process and its use in detecting compact well-separated
9
clusters, Journal of Cybernetics, 3 (1974), 32-57.
10
[7] R.C. Eberhart and Y. H. Shi, Evolving artificial neural networks, Proceedings of the Int. Conf.
11
on Neural Networks and Brain, Beijing: P. R. China, Publishing House of Electronics Industry, PL5-
12
PL13, 1998.
13
[8] T. Gu and B. Ddubuissonb, Similarity of classes and fuzzy clustering, Fuzzy Sets and Systems, 34
14
(1990), 213-221.
15
[9] J. Handl, J. Knowles and M. Dorigo, Strategies for the increased robustness of ant–based clustering,
16
in: Engineering self-organizing systems, Heidelberg, Germany: Springer-Verlag, LNCS, 2977 (2003),
17
[10] R. J. Hathaway and J. C. Bezdek, Recent convergence results for fuzzy c-means clustering algorithms,
18
Journal of Classification, 5 (1988), 237-247.
19
[11] M. A. Ismail, Soft clustering: Algorithms and validity of solutions, Fuzzy Computing Theory Hardware
20
and Applications, North Holland, 1988, 445-471.
21
[12] P. M. Kanade and L. O. Hall, Fuzzy ant clustering by centroids, Proceeding of the IEEE Conference on
22
Fuzzy Systems, Budapest: Hungary, 2004, 371-376.
23
[13] P. M. Kanade and L. O. Hall, Fuzzy ants as a clustering concept, The 22nd Int. Conf. of the North
24
American Fuzzy Information Processing Society (NAFIPS), Chicago, 2003, 227-232.
25
[14] L. Kaufman and P. Rousseeuw, Finding groups in Data: Introduction to cluster analysis, John Wily &
26
Sons Inc., New York, 1990.
27
[15] J. Kennedy and R. C. Eberhart, Particle swarm optimization, Proceedings of the IEEE International
28
Joint Conference on Neural Networks, 4 (1995), 1942-1948.
29
[16] J. Kennedy, R. C. Eberhart and Y. Shi, Swarm intelligence, San Mateo: Morgan Kaufmann, CA, 2001.
30
[17] F. Klawonn and A. Keller, Fuzzy clustering with evolutionary algorithms, Int. Journal of Intelligent
31
Systems, 13 (10-11) (1998), 975-991.
32
[18] J. G. Klir and B. Yuan, Fuzzy sets and fuzzy logic, theory and applications, Prentice-Hall Co., 2003.
33
[19] D. J. Newman, S. Hettich, C. L. Blake and C. J. Merz, UCI Repository of machine learning databases,
34
http://www.ics.uci.edu/~mlearn/MLRepository.html, Department of Information and Computer
35
Science, University of California, Irvine, CA, 1998.
36
[20] M. Omran, A. Salman and A. P. Engelbrecht, Image classification using particle swarm optimization,
37
Proceedings of the 4th Asia-Pacific Conference on Simulated Evolution and Learning, Singapore, 2002,
38
[21] M. Roubens, Pattern classification problems and fuzzy sets, Fuzzy Sets and Systems, 1 (1978), 239-253.
39
[22] M. Roubens, Fuzzy clustering algorithms and their cluster validity, European Journal of Operation
40
Research, 10 (1982), 294-301.
41
[23] T. A. Runkler and C. Katz, Fuzzy clustering by particle swarm optimization, IEEE Int. Conf. on Fuzzy
42
Systems, Vancouver: Canada, July 16-21, 2006, 601-608.
43
[24] T. A. Runkler, Ant colony optimization of clustering models, Int. Journal of Intelligent Systems, 20 (12)
44
(2005), 1233-1261.
45
[25] E. H. Ruspini, Numerical methods for fuzzy clustering, Information Sciences, 2 (1970), 319-50.
46
[26] J. Tillett, R. Rao, F. Sahin and T. M. Rao, Particle swarms optimization for the clustering of wireless
47
sensors, Proceedings of SPIE: Digital Wireless Communications V, 5100 (2003), 73-83.
48
[27] D. W. Van der Merwe and A. P. Engelbrecht, Data clustering using particle swarm optimization,
49
Proceedings of the IEEE Congress on Evolutionary Computation, Canberra: Australia, 2003, 215-220.
50
[28] R. T. Yen and S. Y. Bang, Fuzzy relations, fuzzy graphs and their applications to clustering analysis, in:
51
L. Zadeh et al. (Eds.), Fuzzy Sets and their Applications to Cognitive and Decision Processes, New
52
York: Academic Press, Inc., 1975, 125-150.
53
[29] N. Zahid, M. Limoun and A. Essaid, A new cluster-validity for fuzzy clustering, Pattern Recognition, 32
54
(1999), 1089-1097.
55
[30] C. J. Zhang, Y. Gao, S. P. Yuan and Z. Li, Particle swarm optimization for mobile and hoc networks
56
clustering, Proceeding of the Int. Conf. on Networking, Sensing and Control, Taipei: Taiwan, 2004,
57
[31] H. J. Zimmermann, Fuzzy set theory and its applications, Lower Academic Publishers, 1996.
58
ORIGINAL_ARTICLE
SOLVING FUZZY LINEAR SYSTEMS BY USING THE SCHUR
COMPLEMENT WHEN COEFFICIENT MATRIX IS AN
M-MATRIX
This paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp M-matrix. Thefuzzy linear system (FLS) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. However, solving this crisp system isdifficult for large n because of dimensionality problems . It is shown that thisdifficulty may be avoided by computing the inverse of an n×n matrix insteadof Z^{−1}.
http://ijfs.usb.ac.ir/article_340_45018795472748406c9f0737e0cd837f.pdf
2008-10-08T11:23:20
2017-11-22T11:23:20
15
29
10.22111/ijfs.2008.340
Fuzzy linear system
Schur complement
M-matrix
H-matrix
M. S.
Hashemi
hashemi math396@yahoo.com
true
1
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, Tabriz-Iran
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, Tabriz-Iran
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, Tabriz-Iran
AUTHOR
M. K.
Mirnia
mirnia-kam@tabrizu.ac.ir
true
2
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, Tabriz-Iran
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, Tabriz-Iran
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, Tabriz-Iran
AUTHOR
S.
Shahmorad
shahmorad@tabrizu.ac.ir
true
3
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, Tabriz-Iran
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, Tabriz-Iran
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, Tabriz-Iran
LEAD_AUTHOR
1. T. Allahviranloo, The adomain decomposition method for fuzzy system of linear equation,
1
Applied Mathematics and Computation, 163 (2005), 553-563.
2
2. O. Axelson, Iterative solution methods, Cambridge University Press, 1994.
3
3. J. J. Buckley and Y. Qu, Solving systems of linear fuzzy equations, Fuzzy Sets and Systems
4
43 (1991), 33-43.
5
4. B. N. Datta, Numerical linear algebra and applications, Brooks/Cole Publishing Company,
6
5. M. Dehgan and B. Hashemi, Iterative solution of fuzzy linear systems, Applied Mathematics
7
and Computation, 175 (2006), 645-674.
8
6. D. Dubois and H. Prade, Fuzzy Sets and systems: Theory and Applications, Academic Press,
9
New York, 1980.
10
7. M. Friedman, M. Ming and A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96
11
(1998), 201-209.
12
8. C. R. Johnson, Inverse M-matrices, Linear Algebra and its Application, 47 (1982), 195-216.
13
9. M. Ma, M. Friedman and A. Kandel, Duality in fuzzy linear systems, Fuzzy Sets and Systems,
14
109 (2000), 55-58.
15
10. M. Otadi, S.Abbasbandy and A. Jafarian, Minimal solution of a fuzzy linear system, 6th
16
Iranian Conference on Fuzzy Systems and 1st Islamic World Conference on Fuzzy Systemms,
17
2006, pp.125.
18
11. X. Wang, Z. Zhong and M. Ha, Iteration algorithms for solving a system of fuzzy linear
19
equations, Fuzzy Sets and Systems, 119 (2001), 121-128.
20
12. B. Zheng and K.Wang, General fuzzy linear systems, Applied Mathematics and Computation,
21
ORIGINAL_ARTICLE
ALMOST S^{*}-COMPACTNESS IN L-TOPOLOGICAL SPACES
In this paper, the notion of almost S^{*}-compactness in L-topologicalspaces is introduced following Shi’s definition of S^{*}-compactness. The propertiesof this notion are studied and the relationship between it and otherdefinitions of almost compactness are discussed. Several characterizations ofalmost S^{*}-compactness are also presented.
http://ijfs.usb.ac.ir/article_344_38806068a065c4d5b10248627da60caa.pdf
2008-10-09T11:23:20
2017-11-22T11:23:20
31
44
10.22111/ijfs.2008.344
L-topology
$beta$_{a}-cover
Q_{a} -cover
S^{*}-compactness
Almost S^{*}-compactness
Guo-Feng
Wen
wenguofeng@sdibt.edu.cn
true
1
School of Management Science and Engineering, Shandong Institute
of Business and Technology, Yantai 264005, P. R. China
School of Management Science and Engineering, Shandong Institute
of Business and Technology, Yantai 264005, P. R. China
School of Management Science and Engineering, Shandong Institute
of Business and Technology, Yantai 264005, P. R. China
AUTHOR
Fu-Gui
Shi
fuguishi@bit.edu.cn
true
2
Department of Mathematics, Beijing Institute of Technology, Beijing,100081,
P. R. China
Department of Mathematics, Beijing Institute of Technology, Beijing,100081,
P. R. China
Department of Mathematics, Beijing Institute of Technology, Beijing,100081,
P. R. China
AUTHOR
Hong-Yan
Li
lihongyan@sdibt.edu.cn
true
3
School of Mathematics and Information Science, Shandong Institute
of Business and Technology, Yantai 264005, P. R. China
School of Mathematics and Information Science, Shandong Institute
of Business and Technology, Yantai 264005, P. R. China
School of Mathematics and Information Science, Shandong Institute
of Business and Technology, Yantai 264005, P. R. China
LEAD_AUTHOR
[1] P. Alexandroff and P. Urysohn,Zur theorie der topologischen r¨aiume, Math. Ann., 92 (1924),
1
[2] S. P. Arya and R. Gupta, On strongly continuous functions, Kyungpook Math. J., 14 (1974),
2
131–141.
3
[3] K. K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity,
4
J. Math. Anal. Appl., 82 (1981), 14–32.
5
[4] A. B¨ulb¨ul and M.W. Warner, Some good dilutions of fuzzy compactness, Fuzzy Sets and
6
Systems, 51 (1992), 111–115.
7
[5] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182–190.
8
[6] S. L. Chen, Almost F-compactness in L-fuzzy topological spaces, J. Northeastern Math., 7(4)
9
(1991), 428–432.
10
[7] S. L. Chen, The nearly nice compactness in L-fuzzy topological spaces, Chinese Journal of
11
Mathematics, 16 (1996), 67–71.
12
[8] A. D. Concilio and G. Gerla, Almost compactness in fuzzy topological spaces, Fuzzy Sets and
13
Systems, 13 (1984), 187–192.
14
[9] P. Dwinger,Characterizations of the complete homomorphic images of a completely distributive
15
complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403–414.
16
[10] A. H. Es, Almost compactness and near compactness in fuzzy topological spaces, Fuzzy Sets
17
and System, 22 (1987), 289–295.
18
[11] T. E. Gantner, R. C. Steinlage and R. H. Warren, Compactness in fuzzy topological spaces,
19
J. Math. Anal. Appl., 62 (1978), 547-562.
20
[12] G. Gierz and et al., A compendium of continuous lattices, Springer Verlag, Berlin, 1980.
21
[13] R. Goguen, The fuzzy tychnoff theorem, J. Math. Anal. Appl., 43 (1973), 734–742.
22
[14] T. Kubi´ak, The topological modification of the L-fuzzy unit interval, Chapter 11, In applications
23
of category theory to fuzzy subsets, S. E. Rodabaugh, E. P. Klement, U. H¨ohle, eds.,
24
1992, Kluwer Academic Publishers, 275–305.
25
[15] S. R. T. Kudri and M. W. Warner, Some good L-fuzzy compactness-related concepts and their
26
properties I, Fuzzy Sets and Systems, 76 (1995), 141–155.
27
[16] Y. M. Liu, Compactness and Tychnoff theorem in fuzzy topological spaces, Acta Mathematica
28
Sinica, 24 (1981), 260-268.
29
[17] Y. M. Liu and M.K. Luo, Fuzzy topology, World Scientific, Singapore, 1997.
30
[18] R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl., 56 (1976),
31
621–633.
32
[19] R. Lowen, A comparision of different compactness notions in fuzzy topological spaces, J.
33
Math. Anal. Appl., 64 (1978), 446–454.
34
[20] H. W. Martin, Weakly induced fuzzy topological spaces, J. Math. Anal. Appl., 78 (1980),
35
634–639.
36
[21] A. S. Mashhour, M. H. Ghanim and M. A. F. Alla, On fuzzy noncontinuous mappings, Bull.
37
Calcutta Math.Soc., 78 (1986), 57–69.
38
[22] H. Meng and G. W. Meng, Almost N-compact sets in L-fuzzy topological spaces, Fuzzy Sets
39
and Systems, 91 (1997), 115–122.
40
[23] M. N. Mukherjee, On fuzzy almost compact spaces, Fuzzy Sets and Systems, 98 (1998),
41
207–210.
42
[24] F. G. Shi, A new notion of fuzzy compactness in L-topological spaces, Information Sciences,
43
173 (2005), 35–48.
44
[25] F. G. Shi, C. Y. Zheng, O-convergence of fuzzy nets and its applications, Fuzzy Sets and
45
Systems, 140 (2003), 499–507.
46
[26] F. G. Shi, A new definition of fuzzy compactness, Fuzzy Sets and Systems, 158 (2007),
47
1486–1495.
48
[27] F. G. Shi, Theory of L−nested sets and L−nested sets and its applications, Fuzzy Systems
49
and Mathematics, Chinese, 4 (1995), 65-72.
50
[28] G. J. Wang, A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl., 94 (1983),
51
1–23.
52
[29] G. J. Wang, Theory of L-fuzzy topological space, Shanxi Normal University Press, Chinese,
53
[30] D. S. Zhao, The N-compactness in L-fuzzy topological spaces, J. Math. Anal. Appl., 128
54
(1987), 64–70.
55
ORIGINAL_ARTICLE
FUZZY ROUGH N-ARY SUBHYPERGROUPS
Fuzzy rough n-ary subhypergroups are introduced and characterized.
http://ijfs.usb.ac.ir/article_345_9c9774448c11be68582d02c4034ba721.pdf
2008-10-09T11:23:20
2017-11-22T11:23:20
45
56
10.22111/ijfs.2008.345
Fuzzy rough n-ary subhypergroup
Fuzzy set
Rough set
n-ary subhypergroup
Violeta Leoreanu
Fotea
leoreanu2002@yahoo.com
true
1
Faculty of Mathematics, ”Al.I. Cuza” University, Street
Carol I, n.11, Iasi, Romania
Faculty of Mathematics, ”Al.I. Cuza” University, Street
Carol I, n.11, Iasi, Romania
Faculty of Mathematics, ”Al.I. Cuza” University, Street
Carol I, n.11, Iasi, Romania
AUTHOR
[1] W. Cheng, Z. W. Mo and J. Wang, Notes on the lower and upper approximations in a fuzzy
1
group and rough ideals in semigroups, Information Sciences, 177(22) (2007), 5134-5140.
2
[2] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publishers,
3
Advances in Mathematics, 5 (2003).
4
[3] B. Davvaz, Roughness based on fuzzy ideals, Information Sciences, 176(16) (2006), 2417-
5
[4] B. Davvaz, Roughness in rings, Information Sciences , 164(1-4) (2004), 147-163.
6
[5] B. Davvaz, A new view of the approximations in Hv-groups, Soft Computing, 10 (2006),
7
1043-1046.
8
[6] B. Davvaz, Fuzzy Hv-groups, Fuzzy Sets and Systems, 101 (1999), 191-195.
9
[7] B. Davvaz and P. Corsini, Generalized fuzzy sub-hyperquasigroups of hyper- quasigroups, Soft
10
Computing, 10(11) (2006), 1109-1114.
11
[8] B. Davvaz and P. Corsini, Fuzzy n-ary hypergroups, J. of Intelligent and Fuzzy Systems,
12
18(4) (2007), 377-382.
13
[9] B. Davvaz and T. Vougiouklis, n-ary hypergroups, Iranian Journal of Science and Technology,
14
Transaction A, 30 (2006).
15
[10] W. D¨ornte, Untersuchungen auber einen verallgemeinerten gruppenbegri, Math. Z., 29
16
(1928), 1–19.
17
[11] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, Int. J. General Systems,
18
17(2-3) (1990), 191-209.
19
[12] V. G. Kaburlasos and V. V. Petridis, Fuzzy lattice neurocomputing (FLN) Models, Neural
20
Networks, 13 (2000), 1145-1170.
21
[13] N. Kuroki, Rough ideals in semigroups, Information Science , 100 (1997), 139-163.
22
[14] N. Kuroki and J. N. Mordeson, Structure of rough sets and rough groups, J. Fuzzy Math.,
23
5(1) (1997), 183-191.
24
[15] V. Leoreanu Fotea, The upper and lower approximations in a hypergroup, Information Sciences,
25
178 (2008), 3605-3615.
26
[16] V. Leoreanu Fotea, Several types of n-ary subhypergroup, Italian J. of Pure and Applied
27
Math., 23 (2008), 261-274.
28
[17] V. Leoreanu Fotea and B. Davvaz, Roughness in n-ary hypergroups, Information Sciences,
29
doi: 10.1016/j.ins.2008.06.019, 2008.
30
[18] V. Leoreanu Fotea and B. Davvaz, Join n-spaces and lattices, Multiple Valued Logic and Soft
31
Computing, accepted for publication in 15 (2008).
32
[19] V. Leoreanu Fotea and B. Davvaz, n-hypergroups and binary relations, European Journal of
33
Combinatorics, 29(5) (2008), 1207-1218.
34
[20] F. Marty, Sur une g´en´eralisation de la notion de group, 4th Congress Math. Scandinaves,
35
Stockholm (1934), 45-49.
36
[21] J. N. Mordeson and M. S. Malik, Fuzzy commutative algebra, Word Publ., 1998.
37
[22] S. Nanda and S. Majumdar, Fuzzy rough sets, Fuzzy Sets and Systems, 45 (1992), 157-160.
38
[23] Z. Pawlak, Rough Sets, Int. J. Comp. Inf. Sci., 11 (1982), 341-356.
39
[24] Z. Pawlak and A. Skowron, Rudiments of rough sets, Information Sciences, 177(1) (2007),
40
[25] Z. Pawlak and A. Skowron, Rough sets: Some extensions, Information Sciences, 177(1)
41
(2007), 28-40.
42
[26] V. Petridis and V. G. Kaburlasos, Fuzzy lattice neural network (FLNN), A Hybrid Model for
43
Learning IEEE Transactions on Neural Networks, 9 (1998), 877-890.
44
[27] V. Petridis and V. G. Kaburlasos, Learning in the framework of fuzzy lattices, IEEE Transactions
45
on Fuzzy Systems, 7 (1999), 422-440.
46
[28] L. Polkowski and A. Skowron, Eds., Rough sets in knowledge discovery. 1. methodology and
47
applications. studies in fuzziness and soft computing, Physical-Verlag, Heidelberg, 18 (1998).
48
[29] L. Polkowski and A. Skowron, Eds., Rough sets in knowledge discovery. 2. applications.
49
studies in fuzziness and soft Computing, Physical-Verlag, Heidelberg, 19 (1998).
50
[30] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
51
[31] M. M. Zahedi, M. Bolurian and A. Hasankhani, On polygroups and fuzzy subpolygroups, J.
52
Fuzzy Math., 3 (1995), 115.
53
ORIGINAL_ARTICLE
BEST APPROXIMATION SETS IN -n-NORMED SPACE
CORRESPONDING TO INTUITIONISTIC FUZZY n-NORMED
LINEAR SPACE
The aim of this paper is to present the new and interesting notionof ascending family of $alpha $−n-norms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an $alpha $−n-normedspace corresponding to an intuitionistic fuzzy n-normed linear space is alsodefined and several related results are obtained.
http://ijfs.usb.ac.ir/article_346_6ab0231a438fcfe753f8e98b207a377c.pdf
2008-10-09T11:23:20
2017-11-22T11:23:20
57
69
10.22111/ijfs.2008.346
Fuzzy n-normed linear space
intuitionistic fuzzy n-norm
Best approximation
sets
S.
Vijayabalaji
balaji−nandini@rediffmail.com
true
1
Department of Mathematics, Anna University, Tiruchirappallli,
Panruti Campus, Tamilnadu, India
Department of Mathematics, Anna University, Tiruchirappallli,
Panruti Campus, Tamilnadu, India
Department of Mathematics, Anna University, Tiruchirappallli,
Panruti Campus, Tamilnadu, India
LEAD_AUTHOR
N.
Thillaigovindan
thillai−n@sify.com
true
2
Department of Mathematics, Annamalai university, Annamalainagar-
608002, Tamilnadu, India
Department of Mathematics, Annamalai university, Annamalainagar-
608002, Tamilnadu, India
Department of Mathematics, Annamalai university, Annamalainagar-
608002, Tamilnadu, India
AUTHOR
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.
1
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Physica-Verlag Heidelberg, Newyork, 1999.
2
[3] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, The Journal of
3
Fuzzy Mathematics, 11(3) (2003), 687-705.
4
[4] S. C. Chang and J. N. Mordesen, Fuzzy linear operators and fuzzy normed linear spaces,
5
Bull. Cal. Math. Soc., 86 (1994), 429-436.
6
[5] C. Felbin, The completion of fuzzy normed linear space, Journal of Mathematical Analysis
7
and Applications, 174(2) (1993), 428-440.
8
[6] C. Felbin, Finite dimensional fuzzy normed linear spaces II, Journal of Analysis, 7 (1999),
9
[7] S. G¨ahler, Lineare 2-normierte R¨aume, Math. Nachr., 28 (1965), 1-43.
10
[8] S. G¨ahler, Unter Suchungen ¨U ber Veralla gemeinerte m-metrische R¨aume I, Math. Nachr.,
11
1969, 165-189.
12
[9] H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27(10) (2001),
13
[10] S. S. Kim and Y. J. Cho, Strict convexity in linear n-normed spaces, Demonstratio Math.,
14
29(4) (1996), 739-744.
15
[11] S. V. Krishna and K. K. M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and
16
Systems, 63 (1994), 207-217.
17
[12] R. Malceski, Strong n-convex n-normed spaces, Mat. Bilten, 21 (1997), 81-102.
18
[13] A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299-319.
19
[14] A. Narayanan and S. Vijayabalaji, Fuzzy n-normed linear space, Int. J. Math. Math. Sci.,
20
24 (2005), 3963-3977.
21
[15] A. Narayanan, S. Vijayabalaji and N. Thillaigovindan, Intuitionistic fuzzy bounded linear
22
operators, Iranian Journal of Fuzzy Systems, 4(1) (2007), 89-101.
23
ORIGINAL_ARTICLE
METACOMPACTNESS IN L-TOPOLOGICAL SPACES
In this paper the concept of metacompactness in L-topologicalspaces is introduced by means of point finite families of L-fuzzy sets. Thisfuzzy metacompactness is a natural generalization of Lowen fuzzy compactness.Further a characterization of fuzzy metacompactness in the weakly inducedL-topological spaces is also obtained.
http://ijfs.usb.ac.ir/article_348_6213cfdd88862a790fbc012919f842d6.pdf
2008-10-09T11:23:20
2017-11-22T11:23:20
71
79
10.22111/ijfs.2008.348
L-topology
Fuzzy metacompactness
Sunil
Jacob John
sunil@nitc.ac.in
true
1
Department of Mathematics, National Institute of Technology
Calicut, Calicut-673601, Kerala, India
Department of Mathematics, National Institute of Technology
Calicut, Calicut-673601, Kerala, India
Department of Mathematics, National Institute of Technology
Calicut, Calicut-673601, Kerala, India
LEAD_AUTHOR
T.
Baiju
bethelbai@yahoo.co.in
true
2
Department of Mathematics, National Institute of Technology Calicut,
Calicut-673601, Kerala, India
Department of Mathematics, National Institute of Technology Calicut,
Calicut-673601, Kerala, India
Department of Mathematics, National Institute of Technology Calicut,
Calicut-673601, Kerala, India
AUTHOR
[1] K. D. Burke, Covering properties, in K.Kunen, J.E Vaughan(Eds.), Hand Book of Set Theoretic
1
Topology, Elsevier Science Publishers, 1984, 349–422.
2
[2] J. L. Fan, Paracompactness and strong paracompactness in L-fuzzy topological spaces, Fuzzy
3
Systems and Mathematics, 4 (1990), 88–94.
4
[3] u. Hoehle and S. E. Rodabaugh (Eds.), Mathematics of fuzzy sets: logic, topology and measure
5
theory, The Hand Book of Fuzzy Set Series 3, Kluwer Academic Pub., 1999.
6
[4] T. Kubiak, The topological modification of the L-fuzzy unit interval, in: S. E. Rodabaugh,
7
E. P. Klement, U. Hoehle (Eds.), Applications of Category Theory to Fuzzy Subsets, Kluwer
8
Academic Publishers, Dordrecht, 1992, 275 – 305.
9
[5] Y. M. Liu and M. K. Luo, Fuzzy topology, Advances in Fuzzy Systems — Applications and
10
Theory , World Scientific, 9 (1997).
11
[6] M. K. Luo, Pracompactness in fuzzy topological spaces, J. Math. Anal. Appl., 130 (1988),
12
88–94.
13
[7] F. G. Shi, et al., Fuzzy countable compactness in L-fuzzy topological Spaces , J. Harbin Sci.
14
Technol. Univ., 3 (1992), 63–67.
15
[8] F. G. Shi and C. Y. Zheng, Pracompactness in L-topological Spaces, Fuzzy Sets and Systems,
16
129 (2002), 29−37.
17
[9] G. J. Wang, On the structure of fuzzy lattices, Acta Math. Sinica, 29 (1986), 539–543.
18
[10] G. J. Wang, Theory of L-fuzzy topological spaces, Shaanxi Normal University Pub., Xian,
19
ORIGINAL_ARTICLE
INTUITIONISTIC FUZZY QUASI-METRIC AND PSEUDO-METRIC SPACES
In this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy normal. These are the intuitionistic fuzzy generalization ofthe corresponding properties of fuzzy quasi-metric and pseudo- metric spaces.
http://ijfs.usb.ac.ir/article_349_e462bdee3462b5203d0b7af5bdba624c.pdf
2008-10-09T11:23:20
2017-11-22T11:23:20
81
88
10.22111/ijfs.2008.349
Intuitionistic fuzzy quasi-metric spaces
Intuitionistic fuzzy pseudometric
spaces
Yongfa
Hong
hzycfl@ 126.com
true
1
College of Information Science and Engineering, Shandong University
of Science and Technology, Qingdao, Shandong, 266510, P. R. China
College of Information Science and Engineering, Shandong University
of Science and Technology, Qingdao, Shandong, 266510, P. R. China
College of Information Science and Engineering, Shandong University
of Science and Technology, Qingdao, Shandong, 266510, P. R. China
LEAD_AUTHOR
Xianwen
Fang
true
2
Department of Mathematics and Physics, Anhui University of Science
and Technology, Huainan,Anhui, 232001, P. R. China
Department of Mathematics and Physics, Anhui University of Science
and Technology, Huainan,Anhui, 232001, P. R. China
Department of Mathematics and Physics, Anhui University of Science
and Technology, Huainan,Anhui, 232001, P. R. China
AUTHOR
Binguo
Wang
true
3
College of Information Science and Engineering, Shandong University
of Science and Technology, Qingdao, Shandong, 266510, P. R. China
College of Information Science and Engineering, Shandong University
of Science and Technology, Qingdao, Shandong, 266510, P. R. China
College of Information Science and Engineering, Shandong University
of Science and Technology, Qingdao, Shandong, 266510, P. R. China
AUTHOR
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Central Tech. Library, Bulgarian Academy Science,
1
Sofia, Bulgaria, Rep. No. 1697/84, 1983.
2
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Heidelberg, Germany: Physica-Verlag, 1999.
3
[3] D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems,
4
88(1) (1997), 81 -89.
5
[4] J. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18 (1967), 145-74.
6
[5] V. Gregori, S. Romaguera and P. Veeramani, A note on intuitionistic fuzzy metric spaces,
7
Chaos, Solitons & Fractals, 28(4) (2006), 902-905.
8
[6] F. G. Lupia˜nez, Nets and filters in intuitionistic fuzzy topological spaces, Information Sciences
9
176(16) (2006), 2396-2404.
10
[7] N. Palaniappan, Fuzzy topology, CRC Press, 2002.
11
[8] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22(5) (2004),
12
[9] R. Saadati, A. Razani and H. Adibi, A common fixed point theorem in L-fuzzy metric spaces,
13
Chaos, Solitons & Fractals, 33(2) (2007), 358-363.
14
[10] R. Saadati, Notes to the paper ”Fixed points in intuitionistic fuzzy metric spaces” and its
15
generalization to L- fuzzy metric spaces, Chaos, Solitons & Fractals, 35(1) (2008), 176-180.
16
[11] R. Saadati, On the L-fuzzy topological spaces, Chaos, Solitons & Fractals, In Press, 37(5)
17
(2008), 1419-1426.
18
[12] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338-353.
19
ORIGINAL_ARTICLE
THE DIRECT AND THE INVERSE LIMIT OF HYPERSTRUCTURES ASSOCIATED WITH FUZZY SETS OF TYPE 2
In this paper we study two important concepts, i.e. the direct andthe inverse limit of hyperstructures associated with fuzzy sets of type 2, andshow that the direct and the inverse limit of hyperstructures associated withfuzzy sets of type 2 are also hyperstructures associated with fuzzy sets of type 2.
http://ijfs.usb.ac.ir/article_350_9c19173a4d46068588b174898d965fc8.pdf
2008-10-09T11:23:20
2017-11-22T11:23:20
89
94
10.22111/ijfs.2008.350
Hyperstructure
Hypergroup
Fuzzy set of type 2
Direct limit
Inverse
limit
Violeta Leoreanu
Fotea
leoreanu2002@yahoo.com
true
1
Faculty of Mathematics, ”Al.I.Cuza” University, 6600 Iasi,
Romania
Faculty of Mathematics, ”Al.I.Cuza” University, 6600 Iasi,
Romania
Faculty of Mathematics, ”Al.I.Cuza” University, 6600 Iasi,
Romania
AUTHOR
[1] J. Adamek, H. Herrlich and G. Strecker, Abstract and concrete categories, Wiley Interscience,
1
[2] P. Corsini, Fuzzy sets of type 2 and hyperstructures, Proceedings of the 8th Int. Congress of
2
Algebraic Hyperstructures and Applications, 2002, Samothraki, Hadronic Press, 2003.
3
[3] P. Corsini and V. Leoreanu, Applications of hyperstruycture theory, Kluwer Academic Publishers,
4
Boston/ Dordrecht/ London, 2003.
5
[4] M. M. Ebrahimi, A. Karimi and M. Mahmoudi, Limits and colimits in universal hyperalgebra,
6
Algebras Groups and Geometries, 22 (2005), 169–182.
7
[5] G. Gr¨atzer, Universal algebra, Second Edition, Springer–Verlag, New York, Inc., 1979.
8
[6] V. Leoreanu Fotea, Direct limit and inverse limit of join spaces associated with fuzzy sets,
9
PU. M. A., 11 (2000).
10
[7] F. Marty, Sur une g´en´eralization de la notion de groupe, IV Congr`es des Math´ematiciens
11
Scandinaves, Stockholm, 1934.
12
[8] C. Pelea, On the direct limit of a direct system of complete multialgebras, Stud. Univ. Babes-
13
Bolyai, Math., 49(1) (2004), 63–68.
14
[9] G. Romeo, Limite diretto di semi–ipergruppi e ipergruppi di associativit`a, Riv. Mat. Univ.
15
Parma, 1982.
16
[10] D. Rutkovska and Y. Hayashi, Fuzzy inferenceneural networks with fuzzy parameters, Task
17
Quarterly, 1 (2003).
18
[11] L. A. Zadeh, The concept of a linguistic variable and its application to approximate
19
reasoning, Inform. Sci., I.8 (1975).
20
ORIGINAL_ARTICLE
Persian-translation Vol.5, No.3, October 2008
http://ijfs.usb.ac.ir/article_2902_081e1c7c112e536df36567ef09aa9840.pdf
2008-10-30T11:23:20
2017-11-22T11:23:20
97
104
10.22111/ijfs.2008.2902