2008
5
3
3
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Cove Vol.5, No.3, October 2008
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OPTIMIZATION OF FUZZY CLUSTERING CRITERIA BY A HYBRID
PSO AND FUZZY CMEANS CLUSTERING ALGORITHM
OPTIMIZATION OF FUZZY CLUSTERING CRITERIA BY A HYBRID
PSO AND FUZZY CMEANS CLUSTERING ALGORITHM
2
2
This paper presents an efficient hybrid method, namely fuzzy particleswarm optimization (FPSO) and fuzzy cmeans (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 nearoptimal solution in reasonable time, but we show that its performancemay be improved by seeding the initial swarm with the result of the cmeansalgorithm. Various clustering simulations are experimentally compared with the FCMalgorithm in order to illustrate the efficiency and ability of the proposed algorithms.
1
This paper presents an efficient hybrid method, namely fuzzy particleswarm optimization (FPSO) and fuzzy cmeans (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 nearoptimal solution in reasonable time, but we show that its performancemay be improved by seeding the initial swarm with the result of the cmeansalgorithm. Various clustering simulations are experimentally compared with the FCMalgorithm in order to illustrate the efficiency and ability of the proposed algorithms.
1
14
E.
MEHDIZADEH
E.
MEHDIZADEH
DEPARTMENT OF INDUSTRIAL ENGINEERING, SCIENCE & RESEARCH BRANCH,
ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
DEPARTMENT OF INDUSTRIAL ENGINEERING, SCIENCE
Iran
mehdizadeh@qazviniau.ac.ir
S.
SADINEZHAD
S.
SADINEZHAD
DEPARTMENT OF INDUSTRIAL ENGINEERING, SCIENCE & RESEARCH BRANCH,
ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
DEPARTMENT OF INDUSTRIAL ENGINEERING, SCIENCE
Iran
sadinejad@hotmail.com
R.
TAVAKKOLIMOGHADDAM
R.
TAVAKKOLIMOGHADDAM
DEPARTMENT OF INDUSTRIAL ENGINEERING, COLLEGE OF
ENGINEERING, UNIVERSITY OF TEHRAN, TEHRAN, IRAN
DEPARTMENT OF INDUSTRIAL ENGINEERING, COLLEGE
Iran
tavakoli@ut.ac.ir
Fuzzy clustering
Particle Swarm Optimization (PSO)
Fuzzy cmeans (FCM)
[[1] J. C. Bezdek and R. J. Hathaway, Optimization of fuzzy clustering criteria using genetic algorithms,##Proceedings of the IEEE Conf. on Evolutionary Computation, Orlando, 2 (1994), 589594.##[2] J. C. Bezdek, Cluster validity with fuzzy sets, Journal of Cybernetics, 3 (1974), 5872.##[3] J. C. Bezdek, Pattern recognition with fuzzy objective function algorithms, New York, 1981.##[4] C. Y. Chen and F. Ye, Particle swarm optimization and its application to clustering analysis,##Proceedings of the Int. Conf. on Networking, Sensing and Control, Taipei: Taiwan, 2004, 789794.##[5] M. Dorigo and V. Maniezzo, Ant system: Optimization by a colony of cooperating agents, IEEE##Transactions on Systems, Man, and Cybernetics B, 26 (1) (1996), 2941.##[6] J. C. Dunn, Fuzzy relative of the ISODATA process and its use in detecting compact wellseparated##clusters, Journal of Cybernetics, 3 (1974), 3257.##[7] R.C. Eberhart and Y. H. Shi, Evolving artificial neural networks, Proceedings of the Int. Conf.##on Neural Networks and Brain, Beijing: P. R. China, Publishing House of Electronics Industry, PL5##PL13, 1998.##[8] T. Gu and B. Ddubuissonb, Similarity of classes and fuzzy clustering, Fuzzy Sets and Systems, 34##(1990), 213221.##[9] J. Handl, J. Knowles and M. Dorigo, Strategies for the increased robustness of ant–based clustering,##in: Engineering selforganizing systems, Heidelberg, Germany: SpringerVerlag, LNCS, 2977 (2003),##[10] R. J. Hathaway and J. C. Bezdek, Recent convergence results for fuzzy cmeans clustering algorithms,##Journal of Classification, 5 (1988), 237247. ##[11] M. A. Ismail, Soft clustering: Algorithms and validity of solutions, Fuzzy Computing Theory Hardware##and Applications, North Holland, 1988, 445471.##[12] P. M. Kanade and L. O. Hall, Fuzzy ant clustering by centroids, Proceeding of the IEEE Conference on##Fuzzy Systems, Budapest: Hungary, 2004, 371376.##[13] P. M. Kanade and L. O. Hall, Fuzzy ants as a clustering concept, The 22nd Int. Conf. of the North##American Fuzzy Information Processing Society (NAFIPS), Chicago, 2003, 227232.##[14] L. Kaufman and P. Rousseeuw, Finding groups in Data: Introduction to cluster analysis, John Wily &##Sons Inc., New York, 1990.##[15] J. Kennedy and R. C. Eberhart, Particle swarm optimization, Proceedings of the IEEE International##Joint Conference on Neural Networks, 4 (1995), 19421948.##[16] J. Kennedy, R. C. Eberhart and Y. Shi, Swarm intelligence, San Mateo: Morgan Kaufmann, CA, 2001.##[17] F. Klawonn and A. Keller, Fuzzy clustering with evolutionary algorithms, Int. Journal of Intelligent##Systems, 13 (1011) (1998), 975991.##[18] J. G. Klir and B. Yuan, Fuzzy sets and fuzzy logic, theory and applications, PrenticeHall Co., 2003.##[19] D. J. Newman, S. Hettich, C. L. Blake and C. J. Merz, UCI Repository of machine learning databases,##http://www.ics.uci.edu/~mlearn/MLRepository.html, Department of Information and Computer##Science, University of California, Irvine, CA, 1998.##[20] M. Omran, A. Salman and A. P. Engelbrecht, Image classification using particle swarm optimization,##Proceedings of the 4th AsiaPacific Conference on Simulated Evolution and Learning, Singapore, 2002,##[21] M. Roubens, Pattern classification problems and fuzzy sets, Fuzzy Sets and Systems, 1 (1978), 239253.##[22] M. Roubens, Fuzzy clustering algorithms and their cluster validity, European Journal of Operation##Research, 10 (1982), 294301.##[23] T. A. Runkler and C. Katz, Fuzzy clustering by particle swarm optimization, IEEE Int. Conf. on Fuzzy##Systems, Vancouver: Canada, July 1621, 2006, 601608.##[24] T. A. Runkler, Ant colony optimization of clustering models, Int. Journal of Intelligent Systems, 20 (12)##(2005), 12331261.##[25] E. H. Ruspini, Numerical methods for fuzzy clustering, Information Sciences, 2 (1970), 31950.##[26] J. Tillett, R. Rao, F. Sahin and T. M. Rao, Particle swarms optimization for the clustering of wireless##sensors, Proceedings of SPIE: Digital Wireless Communications V, 5100 (2003), 7383.##[27] D. W. Van der Merwe and A. P. Engelbrecht, Data clustering using particle swarm optimization,##Proceedings of the IEEE Congress on Evolutionary Computation, Canberra: Australia, 2003, 215220.##[28] R. T. Yen and S. Y. Bang, Fuzzy relations, fuzzy graphs and their applications to clustering analysis, in:##L. Zadeh et al. (Eds.), Fuzzy Sets and their Applications to Cognitive and Decision Processes, New##York: Academic Press, Inc., 1975, 125150.##[29] N. Zahid, M. Limoun and A. Essaid, A new clustervalidity for fuzzy clustering, Pattern Recognition, 32##(1999), 10891097.##[30] C. J. Zhang, Y. Gao, S. P. Yuan and Z. Li, Particle swarm optimization for mobile and hoc networks##clustering, Proceeding of the Int. Conf. on Networking, Sensing and Control, Taipei: Taiwan, 2004,##[31] H. J. Zimmermann, Fuzzy set theory and its applications, Lower Academic Publishers, 1996.##]
SOLVING FUZZY LINEAR SYSTEMS BY USING THE SCHUR
COMPLEMENT WHEN COEFFICIENT MATRIX IS AN
MMATRIX
SOLVING FUZZY LINEAR SYSTEMS BY USING THE SCHUR
COMPLEMENT WHEN COEFFICIENT MATRIX IS AN
MMATRIX
2
2
This paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp Mmatrix. 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}.
1

15
29
M. S.
Hashemi
M. S.
Hashemi
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, TabrizIran
Department of Applied Mathematics,
Faculty
Iran
hashemi math396@yahoo.com
M. K.
Mirnia
M. K.
Mirnia
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, TabrizIran
Department of Applied Mathematics,
Faculty
Iran
mirniakam@tabrizu.ac.ir
S.
Shahmorad
S.
Shahmorad
Department of Applied Mathematics,
Faculty of Mathematical Science, University of Tabriz, TabrizIran
Department of Applied Mathematics,
Faculty
Iran
shahmorad@tabrizu.ac.ir
Fuzzy linear system
Schur complement
Mmatrix
Hmatrix
[1. T. Allahviranloo, The adomain decomposition method for fuzzy system of linear equation,##Applied Mathematics and Computation, 163 (2005), 553563.##2. O. Axelson, Iterative solution methods, Cambridge University Press, 1994.##3. J. J. Buckley and Y. Qu, Solving systems of linear fuzzy equations, Fuzzy Sets and Systems##43 (1991), 3343.##4. B. N. Datta, Numerical linear algebra and applications, Brooks/Cole Publishing Company,##5. M. Dehgan and B. Hashemi, Iterative solution of fuzzy linear systems, Applied Mathematics##and Computation, 175 (2006), 645674.##6. D. Dubois and H. Prade, Fuzzy Sets and systems: Theory and Applications, Academic Press,##New York, 1980.##7. M. Friedman, M. Ming and A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96##(1998), 201209.##8. C. R. Johnson, Inverse Mmatrices, Linear Algebra and its Application, 47 (1982), 195216.##9. M. Ma, M. Friedman and A. Kandel, Duality in fuzzy linear systems, Fuzzy Sets and Systems,##109 (2000), 5558.##10. M. Otadi, S.Abbasbandy and A. Jafarian, Minimal solution of a fuzzy linear system, 6th##Iranian Conference on Fuzzy Systems and 1st Islamic World Conference on Fuzzy Systemms,##2006, pp.125.##11. X. Wang, Z. Zhong and M. Ha, Iteration algorithms for solving a system of fuzzy linear##equations, Fuzzy Sets and Systems, 119 (2001), 121128.##12. B. Zheng and K.Wang, General fuzzy linear systems, Applied Mathematics and Computation,##]
ALMOST S^{*}COMPACTNESS IN LTOPOLOGICAL SPACES
ALMOST S^{*}COMPACTNESS IN LTOPOLOGICAL SPACES
2
2
In this paper, the notion of almost S^{*}compactness in Ltopologicalspaces 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.
1
In this paper, the notion of almost S^{*}compactness in Ltopologicalspaces 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.
31
44
GuoFeng
Wen
GuoFeng
Wen
School of Management Science and Engineering, Shandong Institute
of Business and Technology, Yantai 264005, P. R. China
School of Management Science and Engineering,
China
wenguofeng@sdibt.edu.cn
FuGui
Shi
FuGui
Shi
Department of Mathematics, Beijing Institute of Technology, Beijing,100081,
P. R. China
Department of Mathematics, Beijing Institute
China
fuguishi@bit.edu.cn
HongYan
Li
HongYan
Li
School of Mathematics and Information Science, Shandong Institute
of Business and Technology, Yantai 264005, P. R. China
School of Mathematics and Information Science,
China
lihongyan@sdibt.edu.cn
Ltopology
$beta$_{a}cover
Q_{a} cover
S^{*}compactness
Almost S^{*}compactness
[[1] P. Alexandroff and P. Urysohn,Zur theorie der topologischen r¨aiume, Math. Ann., 92 (1924),##[2] S. P. Arya and R. Gupta, On strongly continuous functions, Kyungpook Math. J., 14 (1974),##131–141.##[3] K. K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity,##J. Math. Anal. Appl., 82 (1981), 14–32.##[4] A. B¨ulb¨ul and M.W. Warner, Some good dilutions of fuzzy compactness, Fuzzy Sets and##Systems, 51 (1992), 111–115.##[5] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182–190.##[6] S. L. Chen, Almost Fcompactness in Lfuzzy topological spaces, J. Northeastern Math., 7(4)##(1991), 428–432.##[7] S. L. Chen, The nearly nice compactness in Lfuzzy topological spaces, Chinese Journal of##Mathematics, 16 (1996), 67–71.##[8] A. D. Concilio and G. Gerla, Almost compactness in fuzzy topological spaces, Fuzzy Sets and##Systems, 13 (1984), 187–192.##[9] P. Dwinger,Characterizations of the complete homomorphic images of a completely distributive##complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403–414. ##[10] A. H. Es, Almost compactness and near compactness in fuzzy topological spaces, Fuzzy Sets##and System, 22 (1987), 289–295.##[11] T. E. Gantner, R. C. Steinlage and R. H. Warren, Compactness in fuzzy topological spaces,##J. Math. Anal. Appl., 62 (1978), 547562.##[12] G. Gierz and et al., A compendium of continuous lattices, Springer Verlag, Berlin, 1980.##[13] R. Goguen, The fuzzy tychnoff theorem, J. Math. Anal. Appl., 43 (1973), 734–742.##[14] T. Kubi´ak, The topological modification of the Lfuzzy unit interval, Chapter 11, In applications##of category theory to fuzzy subsets, S. E. Rodabaugh, E. P. Klement, U. H¨ohle, eds.,##1992, Kluwer Academic Publishers, 275–305.##[15] S. R. T. Kudri and M. W. Warner, Some good Lfuzzy compactnessrelated concepts and their##properties I, Fuzzy Sets and Systems, 76 (1995), 141–155.##[16] Y. M. Liu, Compactness and Tychnoff theorem in fuzzy topological spaces, Acta Mathematica##Sinica, 24 (1981), 260268.##[17] Y. M. Liu and M.K. Luo, Fuzzy topology, World Scientific, Singapore, 1997.##[18] R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl., 56 (1976),##621–633.##[19] R. Lowen, A comparision of different compactness notions in fuzzy topological spaces, J.##Math. Anal. Appl., 64 (1978), 446–454.##[20] H. W. Martin, Weakly induced fuzzy topological spaces, J. Math. Anal. Appl., 78 (1980),##634–639.##[21] A. S. Mashhour, M. H. Ghanim and M. A. F. Alla, On fuzzy noncontinuous mappings, Bull.##Calcutta Math.Soc., 78 (1986), 57–69.##[22] H. Meng and G. W. Meng, Almost Ncompact sets in Lfuzzy topological spaces, Fuzzy Sets##and Systems, 91 (1997), 115–122.##[23] M. N. Mukherjee, On fuzzy almost compact spaces, Fuzzy Sets and Systems, 98 (1998),##207–210.##[24] F. G. Shi, A new notion of fuzzy compactness in Ltopological spaces, Information Sciences,##173 (2005), 35–48.##[25] F. G. Shi, C. Y. Zheng, Oconvergence of fuzzy nets and its applications, Fuzzy Sets and##Systems, 140 (2003), 499–507.##[26] F. G. Shi, A new definition of fuzzy compactness, Fuzzy Sets and Systems, 158 (2007),##1486–1495.##[27] F. G. Shi, Theory of L−nested sets and L−nested sets and its applications, Fuzzy Systems##and Mathematics, Chinese, 4 (1995), 6572.##[28] G. J. Wang, A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl., 94 (1983),##1–23.##[29] G. J. Wang, Theory of Lfuzzy topological space, Shanxi Normal University Press, Chinese,##[30] D. S. Zhao, The Ncompactness in Lfuzzy topological spaces, J. Math. Anal. Appl., 128##(1987), 64–70.##]
FUZZY ROUGH NARY SUBHYPERGROUPS
FUZZY ROUGH NARY SUBHYPERGROUPS
2
2
Fuzzy rough nary subhypergroups are introduced and characterized.
1
Fuzzy rough nary subhypergroups are introduced and characterized.
45
56
Violeta Leoreanu
Fotea
Violeta Leoreanu
Fotea
Faculty of Mathematics, ”Al.I. Cuza” University, Street
Carol I, n.11, Iasi, Romania
Faculty of Mathematics, ”Al.I. Cuza” University,
Romania
leoreanu2002@yahoo.com
Fuzzy rough nary subhypergroup
Fuzzy set
Rough set
nary subhypergroup
[[1] W. Cheng, Z. W. Mo and J. Wang, Notes on the lower and upper approximations in a fuzzy##group and rough ideals in semigroups, Information Sciences, 177(22) (2007), 51345140.##[2] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publishers,##Advances in Mathematics, 5 (2003).##[3] B. Davvaz, Roughness based on fuzzy ideals, Information Sciences, 176(16) (2006), 2417##[4] B. Davvaz, Roughness in rings, Information Sciences , 164(14) (2004), 147163.##[5] B. Davvaz, A new view of the approximations in Hvgroups, Soft Computing, 10 (2006),##10431046.##[6] B. Davvaz, Fuzzy Hvgroups, Fuzzy Sets and Systems, 101 (1999), 191195.##[7] B. Davvaz and P. Corsini, Generalized fuzzy subhyperquasigroups of hyper quasigroups, Soft##Computing, 10(11) (2006), 11091114.##[8] B. Davvaz and P. Corsini, Fuzzy nary hypergroups, J. of Intelligent and Fuzzy Systems,##18(4) (2007), 377382.##[9] B. Davvaz and T. Vougiouklis, nary hypergroups, Iranian Journal of Science and Technology,##Transaction A, 30 (2006).##[10] W. D¨ornte, Untersuchungen auber einen verallgemeinerten gruppenbegri, Math. Z., 29##(1928), 1–19.##[11] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, Int. J. General Systems,##17(23) (1990), 191209.##[12] V. G. Kaburlasos and V. V. Petridis, Fuzzy lattice neurocomputing (FLN) Models, Neural##Networks, 13 (2000), 11451170.##[13] N. Kuroki, Rough ideals in semigroups, Information Science , 100 (1997), 139163.##[14] N. Kuroki and J. N. Mordeson, Structure of rough sets and rough groups, J. Fuzzy Math.,##5(1) (1997), 183191.##[15] V. Leoreanu Fotea, The upper and lower approximations in a hypergroup, Information Sciences,##178 (2008), 36053615.##[16] V. Leoreanu Fotea, Several types of nary subhypergroup, Italian J. of Pure and Applied##Math., 23 (2008), 261274.##[17] V. Leoreanu Fotea and B. Davvaz, Roughness in nary hypergroups, Information Sciences,##doi: 10.1016/j.ins.2008.06.019, 2008. ##[18] V. Leoreanu Fotea and B. Davvaz, Join nspaces and lattices, Multiple Valued Logic and Soft##Computing, accepted for publication in 15 (2008).##[19] V. Leoreanu Fotea and B. Davvaz, nhypergroups and binary relations, European Journal of##Combinatorics, 29(5) (2008), 12071218.##[20] F. Marty, Sur une g´en´eralisation de la notion de group, 4th Congress Math. Scandinaves,##Stockholm (1934), 4549.##[21] J. N. Mordeson and M. S. Malik, Fuzzy commutative algebra, Word Publ., 1998.##[22] S. Nanda and S. Majumdar, Fuzzy rough sets, Fuzzy Sets and Systems, 45 (1992), 157160.##[23] Z. Pawlak, Rough Sets, Int. J. Comp. Inf. Sci., 11 (1982), 341356.##[24] Z. Pawlak and A. Skowron, Rudiments of rough sets, Information Sciences, 177(1) (2007),##[25] Z. Pawlak and A. Skowron, Rough sets: Some extensions, Information Sciences, 177(1)##(2007), 2840.##[26] V. Petridis and V. G. Kaburlasos, Fuzzy lattice neural network (FLNN), A Hybrid Model for##Learning IEEE Transactions on Neural Networks, 9 (1998), 877890.##[27] V. Petridis and V. G. Kaburlasos, Learning in the framework of fuzzy lattices, IEEE Transactions##on Fuzzy Systems, 7 (1999), 422440.##[28] L. Polkowski and A. Skowron, Eds., Rough sets in knowledge discovery. 1. methodology and##applications. studies in fuzziness and soft computing, PhysicalVerlag, Heidelberg, 18 (1998).##[29] L. Polkowski and A. Skowron, Eds., Rough sets in knowledge discovery. 2. applications.##studies in fuzziness and soft Computing, PhysicalVerlag, Heidelberg, 19 (1998).##[30] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512517.##[31] M. M. Zahedi, M. Bolurian and A. Hasankhani, On polygroups and fuzzy subpolygroups, J.##Fuzzy Math., 3 (1995), 115.##]
BEST APPROXIMATION SETS IN nNORMED SPACE
CORRESPONDING TO INTUITIONISTIC FUZZY nNORMED
LINEAR SPACE
BEST APPROXIMATION SETS IN $alpha $nNORMED SPACE CORRESPONDING TO INTUITIONISTIC FUZZY nNORMED LINEAR SPACE
2
2
The aim of this paper is to present the new and interesting notionof ascending family of $alpha $−nnorms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an $alpha $−nnormedspace corresponding to an intuitionistic fuzzy nnormed linear space is alsodefined and several related results are obtained.
1
The aim of this paper is to present the new and interesting notionof ascending family of $alpha $−nnorms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an $alpha $−nnormedspace corresponding to an intuitionistic fuzzy nnormed linear space is alsodefined and several related results are obtained.
57
69
S.
Vijayabalaji
S.
Vijayabalaji
Department of Mathematics, Anna University, Tiruchirappallli,
Panruti Campus, Tamilnadu, India
Department of Mathematics, Anna University,
India
balaji−nandini@rediffmail.com
N.
Thillaigovindan
N.
Thillaigovindan
Department of Mathematics, Annamalai university, Annamalainagar
608002, Tamilnadu, India
Department of Mathematics, Annamalai university,
India
thillai−n@sify.com
Fuzzy nnormed linear space
intuitionistic fuzzy nnorm
Best approximation sets
[[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 8796.##[2] K. T. Atanassov, Intuitionistic fuzzy sets, PhysicaVerlag Heidelberg, Newyork, 1999.##[3] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, The Journal of##Fuzzy Mathematics, 11(3) (2003), 687705.##[4] S. C. Chang and J. N. Mordesen, Fuzzy linear operators and fuzzy normed linear spaces,##Bull. Cal. Math. Soc., 86 (1994), 429436.##[5] C. Felbin, The completion of fuzzy normed linear space, Journal of Mathematical Analysis##and Applications, 174(2) (1993), 428440.##[6] C. Felbin, Finite dimensional fuzzy normed linear spaces II, Journal of Analysis, 7 (1999),##[7] S. G¨ahler, Lineare 2normierte R¨aume, Math. Nachr., 28 (1965), 143.##[8] S. G¨ahler, Unter Suchungen ¨U ber Veralla gemeinerte mmetrische R¨aume I, Math. Nachr.,##1969, 165189.##[9] H. Gunawan and M. Mashadi, On nnormed spaces, Int. J. Math. Math. Sci., 27(10) (2001),##[10] S. S. Kim and Y. J. Cho, Strict convexity in linear nnormed spaces, Demonstratio Math.,##29(4) (1996), 739744.##[11] S. V. Krishna and K. K. M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and##Systems, 63 (1994), 207217.##[12] R. Malceski, Strong nconvex nnormed spaces, Mat. Bilten, 21 (1997), 81102.##[13] A. Misiak, ninner product spaces, Math. Nachr., 140 (1989), 299319.##[14] A. Narayanan and S. Vijayabalaji, Fuzzy nnormed linear space, Int. J. Math. Math. Sci.,##24 (2005), 39633977.##[15] A. Narayanan, S. Vijayabalaji and N. Thillaigovindan, Intuitionistic fuzzy bounded linear##operators, Iranian Journal of Fuzzy Systems, 4(1) (2007), 89101.##]
METACOMPACTNESS IN LTOPOLOGICAL SPACES
METACOMPACTNESS IN LTOPOLOGICAL SPACES
2
2
In this paper the concept of metacompactness in Ltopologicalspaces is introduced by means of point finite families of Lfuzzy sets. Thisfuzzy metacompactness is a natural generalization of Lowen fuzzy compactness.Further a characterization of fuzzy metacompactness in the weakly inducedLtopological spaces is also obtained.
1
In this paper the concept of metacompactness in Ltopologicalspaces is introduced by means of point finite families of Lfuzzy sets. Thisfuzzy metacompactness is a natural generalization of Lowen fuzzy compactness.Further a characterization of fuzzy metacompactness in the weakly inducedLtopological spaces is also obtained.
71
79
Sunil
Jacob John
Sunil
Jacob John
Department of Mathematics, National Institute of Technology
Calicut, Calicut673601, Kerala, India
Department of Mathematics, National Institute
India
sunil@nitc.ac.in
T.
Baiju
T.
Baiju
Department of Mathematics, National Institute of Technology Calicut,
Calicut673601, Kerala, India
Department of Mathematics, National Institute
India
bethelbai@yahoo.co.in
Ltopology
Fuzzy metacompactness
[[1] K. D. Burke, Covering properties, in K.Kunen, J.E Vaughan(Eds.), Hand Book of Set Theoretic##Topology, Elsevier Science Publishers, 1984, 349–422.##[2] J. L. Fan, Paracompactness and strong paracompactness in Lfuzzy topological spaces, Fuzzy##Systems and Mathematics, 4 (1990), 88–94.##[3] u. Hoehle and S. E. Rodabaugh (Eds.), Mathematics of fuzzy sets: logic, topology and measure##theory, The Hand Book of Fuzzy Set Series 3, Kluwer Academic Pub., 1999.##[4] T. Kubiak, The topological modification of the Lfuzzy unit interval, in: S. E. Rodabaugh,##E. P. Klement, U. Hoehle (Eds.), Applications of Category Theory to Fuzzy Subsets, Kluwer##Academic Publishers, Dordrecht, 1992, 275 – 305.##[5] Y. M. Liu and M. K. Luo, Fuzzy topology, Advances in Fuzzy Systems — Applications and##Theory , World Scientific, 9 (1997).##[6] M. K. Luo, Pracompactness in fuzzy topological spaces, J. Math. Anal. Appl., 130 (1988),##88–94.##[7] F. G. Shi, et al., Fuzzy countable compactness in Lfuzzy topological Spaces , J. Harbin Sci.##Technol. Univ., 3 (1992), 63–67.##[8] F. G. Shi and C. Y. Zheng, Pracompactness in Ltopological Spaces, Fuzzy Sets and Systems,##129 (2002), 29−37.##[9] G. J. Wang, On the structure of fuzzy lattices, Acta Math. Sinica, 29 (1986), 539–543.##[10] G. J. Wang, Theory of Lfuzzy topological spaces, Shaanxi Normal University Pub., Xian,##]
INTUITIONISTIC FUZZY QUASIMETRIC AND PSEUDOMETRIC SPACES
INTUITIONISTIC FUZZY QUASIMETRIC AND PSEUDOMETRIC SPACES
2
2
In this paper, we propose a new definition of intuitionistic fuzzyquasimetric and pseudometric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi metric and pseudometricspaces, and show that every intuitionistic fuzzy pseudometric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy normal. These are the intuitionistic fuzzy generalization ofthe corresponding properties of fuzzy quasimetric and pseudo metric spaces.
1
In this paper, we propose a new definition of intuitionistic fuzzyquasimetric and pseudometric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi metric and pseudometricspaces, and show that every intuitionistic fuzzy pseudometric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy normal. These are the intuitionistic fuzzy generalization ofthe corresponding properties of fuzzy quasimetric and pseudo metric spaces.
81
88
Yongfa
Hong
Yongfa
Hong
College of Information Science and Engineering, Shandong University
of Science and Technology, Qingdao, Shandong, 266510, P. R. China
College of Information Science and Engineering,
China
hzycfl@ 126.com
Xianwen
Fang
Xianwen
Fang
Department of Mathematics and Physics, Anhui University of Science
and Technology, Huainan,Anhui, 232001, P. R. China
Department of Mathematics and Physics, Anhui
China
Binguo
Wang
Binguo
Wang
College of Information Science and Engineering, Shandong University
of Science and Technology, Qingdao, Shandong, 266510, P. R. China
College of Information Science and Engineering,
China
Intuitionistic fuzzy quasimetric spaces
Intuitionistic fuzzy pseudometric spaces
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THE DIRECT AND THE INVERSE LIMIT OF HYPERSTRUCTURES ASSOCIATED WITH FUZZY SETS OF TYPE 2
THE DIRECT AND THE INVERSE LIMIT OF HYPERSTRUCTURES ASSOCIATED WITH FUZZY SETS OF TYPE 2
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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.
1
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.
89
94
Violeta Leoreanu
Fotea
Violeta Leoreanu
Fotea
Faculty of Mathematics, ”Al.I.Cuza” University, 6600 Iasi,
Romania
Faculty of Mathematics, ”Al.I.Cuza” University,
Romania
leoreanu2002@yahoo.com
Hyperstructure
Hypergroup
Fuzzy set of type 2
Direct limit
Inverse limit
[[1] J. Adamek, H. Herrlich and G. Strecker, Abstract and concrete categories, Wiley Interscience,##[2] P. Corsini, Fuzzy sets of type 2 and hyperstructures, Proceedings of the 8th Int. Congress of##Algebraic Hyperstructures and Applications, 2002, Samothraki, Hadronic Press, 2003.##[3] P. Corsini and V. Leoreanu, Applications of hyperstruycture theory, Kluwer Academic Publishers,##Boston/ Dordrecht/ London, 2003.##[4] M. M. Ebrahimi, A. Karimi and M. Mahmoudi, Limits and colimits in universal hyperalgebra,##Algebras Groups and Geometries, 22 (2005), 169–182.##[5] G. Gr¨atzer, Universal algebra, Second Edition, Springer–Verlag, New York, Inc., 1979. ##[6] V. Leoreanu Fotea, Direct limit and inverse limit of join spaces associated with fuzzy sets,##PU. M. A., 11 (2000).##[7] F. Marty, Sur une g´en´eralization de la notion de groupe, IV Congr`es des Math´ematiciens##Scandinaves, Stockholm, 1934.##[8] C. Pelea, On the direct limit of a direct system of complete multialgebras, Stud. Univ. Babes##Bolyai, Math., 49(1) (2004), 63–68.##[9] G. Romeo, Limite diretto di semi–ipergruppi e ipergruppi di associativit`a, Riv. Mat. Univ.##Parma, 1982.##[10] D. Rutkovska and Y. Hayashi, Fuzzy inferenceneural networks with fuzzy parameters, Task##Quarterly, 1 (2003).##[11] L. A. Zadeh, The concept of a linguistic variable and its application to approximate##reasoning, Inform. Sci., I.8 (1975).##]
Persiantranslation Vol.5, No.3, October 2008
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