2007
4
1
1
0
Cover Vol.4, No.1 April 2007
2
2
1

0
0
DISTRIBUTED AND COLLABORATIVE FUZZY MODELING
DISTRIBUTED AND COLLABORATIVE FUZZY MODELING
2
2
In this study, we introduce and study a concept of distributed fuzzymodeling. Fuzzy modeling encountered so far is predominantly of a centralizednature by being focused on the use of a single data set. In contrast to this style ofmodeling, the proposed paradigm of distributed and collaborative modeling isconcerned with distributed models which are constructed in a highly collaborativefashion. In a nutshell, distributed models reconcile and aggregate findings of theindividual fuzzy models produced on a basis of local data sets. The individualmodels are formed in a highly synergistic, collaborative manner. Given the fact thatfuzzy models are inherently granular constructs that dwell upon collections ofinformation granules – fuzzy sets, this observation implies a certain generaldevelopment process. There are two fundamental design issues of this style ofmodeling, namely (a) a formation of information granules carried out on a basis oflocally available data and their collaborative refinement, and (b) construction oflocal models with the use of properly established collaborative linkages. We discussthe underlying general concepts and then elaborate on their detailed development.Information granulation is realized in terms of fuzzy clustering. Local modelsemerge in the form of rulebased systems. The paper elaborates on a number ofmechanisms of collaboration offering two general categories of socalledhorizontal and vertical clustering. The study also addresses an issue ofcollaboration in cases when such interaction involves information granules formedat different levels of specificity (granularity). It is shown how various algorithms ofcollaboration lead to the emergence of fuzzy models involving informationgranules of higher type such as e.g., type2 fuzzy sets.
1
In this study, we introduce and study a concept of distributed fuzzymodeling. Fuzzy modeling encountered so far is predominantly of a centralizednature by being focused on the use of a single data set. In contrast to this style ofmodeling, the proposed paradigm of distributed and collaborative modeling isconcerned with distributed models which are constructed in a highly collaborativefashion. In a nutshell, distributed models reconcile and aggregate findings of theindividual fuzzy models produced on a basis of local data sets. The individualmodels are formed in a highly synergistic, collaborative manner. Given the fact thatfuzzy models are inherently granular constructs that dwell upon collections ofinformation granules – fuzzy sets, this observation implies a certain generaldevelopment process. There are two fundamental design issues of this style ofmodeling, namely (a) a formation of information granules carried out on a basis oflocally available data and their collaborative refinement, and (b) construction oflocal models with the use of properly established collaborative linkages. We discussthe underlying general concepts and then elaborate on their detailed development.Information granulation is realized in terms of fuzzy clustering. Local modelsemerge in the form of rulebased systems. The paper elaborates on a number ofmechanisms of collaboration offering two general categories of socalledhorizontal and vertical clustering. The study also addresses an issue ofcollaboration in cases when such interaction involves information granules formedat different levels of specificity (granularity). It is shown how various algorithms ofcollaboration lead to the emergence of fuzzy models involving informationgranules of higher type such as e.g., type2 fuzzy sets.
1
19
WITOLD
PEDRYCZ
WITOLD
PEDRYCZ
DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING, UNIVERSITY OF ALBERTA,
EDMONTON T6R 2G7 CANADA AND SYSTEMS RESEARCH INSTITUTE OF THE POLISH ACADEMY OF SCIENCE,
WARSAW, POLAND
DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING,
Poland
pedrycz@ee.ualberta.ca
Computational Intelligence
C^{3} paradigm
Distributed processing
Fuzzy clustering
Fuzzy models
[[1] R. Agarwal and R. Srikant, Privacypreserving data mining., Proc. of the ACM SIGMOD##Conference on Management of Data, ACM Press, New York, May (2000), 439–450.##[2] A. M. Bensaid, L. O. Hall, J. C. Bezdek and L. P. Clarke. Partially supervised clustering##for image segmentation, Pattern Recognition, 29(5) (1996), 859871.##[3] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press,##NY. (1981)##[4] C. Clifton and D. Marks, Security and privacy implications of data mining, Workshop on##Data Mining and Knowledge Discovery, Montreal, Canada, (1996), 15–19.##[5] J. C. Da Silva, C. Giannella, R. Bhargava, H. Kargupta and M. Klusch, Distributed data##mining and agents, Engineering Applications of Artificial Intelligence, 18 (7) (2005), 791##[6] W. Du and Z. Zhan, Building decision tree classifier on private data, Clifton, C., Estivill##Castro, V. (Eds.), IEEE ICDM Workshop on Privacy, Security and Data Mining, ##Conferences in Research and Practice in Information Technology, Vol. 14, Maebashi##City, Japan, ACS, (2002), 1–8.##[7] T. Johnsten and V. V. Raghavan, A methodology for hiding knowledge in databases,##Clifton, C., EstivillCastro, C. (Eds.), IEEE ICDM Workshop on Privacy, Security and##Data Mining, Conferences in Research and Practice in Information Technology, Vol.##14. Maebashi City, Japan, ACS, (2002), 9–17.##[8] H. Kargupta, L. Kun, S. Datta, J. Ryan and K. Sivakumar, Homeland security and##privacy sensitive data mining from multiparty distributed resources, Proc. 12th IEEE##International Conference on Fuzzy Systems, FUZZ '03, .Volume 2, May (2003), 2528,##Vol. 2 (2003), 1257 – 1260.##[9] S. Merugu, and J. Ghosh, A privacysensitive approach to distributed clustering, Pattern##Recognition Letters, 26 (4) (2005), 399410.##[10] B. Park and H. Kargupta, Distributed data mining: algorithms, systems, and applications, In:##Ye, N. (Ed.), The Handbook of Data Mining. Lawrence Erlbaum Associates, New##York, (2003), 341–358.##[11] W. Pedrycz, Algorithms of fuzzy clustering with partial supervision, Pattern Recognition##Letters, 3 (1985), 13  20.##[12] W. Pedrycz, and J. Waletzky, Fuzzy clustering with partial supervision, IEEE Trans. on##Systems, Man and Cybernetics, 5 (1997), 787795.##[13] W. Pedrycz and J. Waletzky, Neural network frontends in unsupervised learning, IEEE##Trans. on Neural Networks, 8 (1997), 390401.##[14] W. Pedrycz, V. Loia and S. Senatore, PFCM: A proximitybased clustering, Fuzzy Sets &##Systems, 148, (2004), 2141.##[15] W. Pedrycz, Collaborative fuzzy clustering, Pattern Recognition Letters, 23(14)(2002),##16751686.##[16] W. Pedrycz, KnowledgeBased Clustering: From Data to Information Granules, J. Wiley,##New York (2005).##[17] W. Pedrycz and F. Gomide, Fuzzy Systems Engineering: Toward HumanCentric##Computing, J. Wiley, NJ Hoboken, ( 2007).##[18] A. Strehl and J. Ghosh, Cluster ensembles—a knowledge reuse framework for combining##multiple partitions, Journal of Machine Learning Research, 3, (2002), 583–617.##[19] H. Timm, F. Klawonn and R. Kruse, An extension of partially supervised fuzzy cluster##analysis, Proc. Annual Meeting of the North American Fuzzy Information Processing##Society, NAFIPS, (2002), 63 –68.##[20] G. Tsoumakas, L. Angelis and I. Vlahavas, Clustering classifiers for knowledge discovery##from physically distributed databases, Data & Knowledge Engineering, 49(3) (2004), 223##[21] V. S. Verykios, et al. State of the art in privacy preserving data mining, SIGMOID##Record, 33(1) (2004), 5057.##[22] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU) – an outline, Information##Sciences, 172(12) (2005), 140.##]
USING DISTRIBUTION OF DATA TO ENHANCE PERFORMANCE OF FUZZY CLASSIFICATION SYSTEMS
USING DISTRIBUTION OF DATA TO ENHANCE PERFORMANCE OF FUZZY CLASSIFICATION SYSTEMS
2
2
This paper considers the automatic design of fuzzy rulebasedclassification systems based on labeled data. The classification performance andinterpretability are of major importance in these systems. In this paper, weutilize the distribution of training patterns in decision subspace of each fuzzyrule to improve its initially assigned certainty grade (i.e. rule weight). Ourapproach uses a punishment algorithm to reduce the decision subspace of a ruleby reducing its weight, such that its performance is enhanced. Obviously, thisreduction will cause the decision subspace of adjacent overlapping rules to beincreased and consequently rewarding these rules. The results of computersimulations on some wellknown data sets show the effectiveness of ourapproach.
1
This paper considers the automatic design of fuzzy rulebasedclassification systems based on labeled data. The classification performance andinterpretability are of major importance in these systems. In this paper, weutilize the distribution of training patterns in decision subspace of each fuzzyrule to improve its initially assigned certainty grade (i.e. rule weight). Ourapproach uses a punishment algorithm to reduce the decision subspace of a ruleby reducing its weight, such that its performance is enhanced. Obviously, thisreduction will cause the decision subspace of adjacent overlapping rules to beincreased and consequently rewarding these rules. The results of computersimulations on some wellknown data sets show the effectiveness of ourapproach.
21
36
EGHBAL G.
MANSOORI
EGHBAL G.
MANSOORI
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF
ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT,
Iran
mansoori@shirazu.ac.ir
MANSOOR J.
ZOLGHADRI
MANSOOR J.
ZOLGHADRI
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF
ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT,
Iran
zjahromi@shirazu.ac.ir
SERAJ D.
KATEBI
SERAJ D.
KATEBI
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF ENGINEERING,
SHIRAZ UNIVERSITY, SHIRAZ, IRAN
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT,
Iran
katebi@shirazu.ac.ir
Fuzzy rulebased classification systems
Rule weight
[[1] S. Abe and M. S. Lan, A method for fuzzy rules extraction directly from numerical data and##its application to pattern classification, IEEE Transaction on Fuzzy Systems, 3 (1) (1995),##[2] S. Abe and R. Thawonmas, A fuzzy classifier with ellipsoidal regions, IEEE Transaction##on Fuzzy Systems, 5 (3) (1997), 358368. ##[3] J. C. Bezdek, Pattern Analysis. In E. H. Ruspini, P. Bonissone and W. Pedrycz, Handbook##of Distributed representation of fuzzy rules and its application to pattern classification,##Handbook of Fuzzy Computation, Chapter F6, Institute of Physics Publishing, London,##[4] C. L. Blake and C. J. Merz, UCI Repository of machine learning databases, University of##California, Department of Information and Computer Science, Irvine, CA, 1998.##[5] H. Ishibuchi and T. Nakashima, Improving the performance of fuzzy classifier systems for##pattern classification problems with continuous attributes, IEEE Transaction on Industrial##Electronics, 46 (6) (1999), 157168.##[6] H. Ishibuchi and T. Nakashima, Effect of rule weights in fuzzy rulebased classification##systems, IEEE Transaction on Fuzzy Systems, 9 (4) (2001), 506515.##[7] H. Ishibuchi, T. Nakashima and T. Morisawa, Voting in fuzzy rulebased systems for pattern##classification problems, Fuzzy sets and systems, 103 (2) (1999), 223238.##[8] H. Ishibuchi, K. Nozaki and H. Tanaka, Distributed representation of fuzzy rules and its##application to pattern classification, Fuzzy sets and systems, 52 (1) (1992), 2132.##[9] H. Ishibuchi and T. Yamamoto, Comparison of heuristic criteria for fuzzy rule selection in##classification problems, Fuzzy Optimization and Decision Making, 3 (2) (2004), 119139.##[10] H. Ishibuchi and T. Yamamoto, Rule Weight Specification in Fuzzy RuleBased##Classification Systems, IEEE Trans. on Fuzzy Systems, 13 (4) (2005), 428435.##[11] H. Ishibuchi, T. Yamamoto and T. Nakashima, Fuzzy data mining: Effect of fuzzy##discretization, Proceeding of 1st IEEE International Conference on Data Mining, (2001),##[12] L. I. Kuncheva, Fuzzy Classifier Design, PhysicaVerlag, Heidelberg, 2000.##[13] L.I.Kuncheva and J. C. Bezdek, A fuzzy generalized nearest prototype classifier, Proceeding##of 7th IFSA World Congress, Prague, 3 (1997), 217222.##[14] S. Mitra and Y. Hayashi, Neurofuzzy rule generation: Survey in soft computing framework,##IEEE Transaction on Neural Networks, 11 (3) (2000), 748768.##[15] D. Nauck and R. Kruse, How the learning of rule weights affects the interpretability of fuzzy##systems, Proceeding of 7th IEEE International Conference on Fuzzy Systems,##Anchorage, (1998), 12351240.##[16] D. Nauk and R. Kruse, Obtaining interpretable fuzzy classification rules from medical data,##Artificial Intelligence in Medicine, 16 (1999), 149169.##[17] K. Nozaki, H. Ishibuchi and H. Tanaka, Adaptive Fuzzy RuleBased Classification Systems,##IEEE Trans. on Fuzzy Systems, 4 (3) (1996), 238250.##[18] J. A. Roubos, M. Setnes and J. Abonyi, Learning fuzzy classification rules from labeled data,##IEEE Transaction on Fuzzy Systems, 8 (5) (2001), 509522.##[19] D. Setiono, Generating concise and accurate classification rules for breast cancer diagnosis,##Artificial Intelligence in Medicine, 18 (1999), 205219.##[20] M. Setnes and R. Babuska, RuleBased Modeling: Precision and Transparency, IEEE##Transaction on Systems, Man, and CyberneticsPart C: Applications and reviews, 28 (1)##(1998), 165169.##[21] M. Setnes and R. Babuska, Fuzzy relational classifier trained by fuzzy clustering, IEEE##Transaction on Systems, Man, and CyberneticsPart B: Cybernetics, 29 (1999), 619625.##[22] M. Setnes and J. A. Roubos, GAfuzzy modeling and classification: complexity and##performance, IEEE Transaction on Fuzzy Systems, 8 (5) (2000), 509522.##[23] J. Valente de Oliveira, Semantic constraints for membership function optimization, IEEE##Transaction on Fuzzy Systems, 19 (1) (1999), 128138. ##[24] J. Van den Berg, U. Kaymak and W. M. Van den Berg, Fuzzy classification using##probability based rule weighting, proceeding of 11th IEEE International Conference on##Fuzzy Systems, (2002), 991996.##[25] L. Wang and Jerry M. Mendel, Generating fuzzy rules by learning from examples, IEEE##Transaction on Systems, Man, and Cybernetics, 22 (6) (1992), 14141427.##[26] S. M. Weiss and C. A. Kulikowski, Computer Systems that Learn, Morgan Kaufmann, San##Mateo, 1991.##]
FUZZY BASED FAULT DETECTION AND CONTROL FOR 6/4 SWITCHED RELUCTANCE MOTOR
FUZZY BASED FAULT DETECTION AND CONTROL FOR 6/4 SWITCHED RELUCTANCE MOTOR
2
2
Prompt detection and diagnosis of faults in industrial systems areessential to minimize the production losses, increase the safety of the operatorand the equipment. Several techniques are available in the literature to achievethese objectives. This paper presents fuzzy based control and fault detection for a6/4 switched reluctance motor. The fuzzy logic control performs like a classicalproportional plus integral control, giving the current reference variation based onspeed error and its change. Also, the fuzzy inference system is created and rulebase are evaluated relating the parameters to the type of the faults. These rules arefired for specific changes in system parameters and the faults are diagnosed. Thefeasibility of fuzzy based fault diagnosis and control scheme is demonstrated byapplying it to a simulated system.
1
Prompt detection and diagnosis of faults in industrial systems areessential to minimize the production losses, increase the safety of the operatorand the equipment. Several techniques are available in the literature to achievethese objectives. This paper presents fuzzy based control and fault detection for a6/4 switched reluctance motor. The fuzzy logic control performs like a classicalproportional plus integral control, giving the current reference variation based onspeed error and its change. Also, the fuzzy inference system is created and rulebase are evaluated relating the parameters to the type of the faults. These rules arefired for specific changes in system parameters and the faults are diagnosed. Thefeasibility of fuzzy based fault diagnosis and control scheme is demonstrated byapplying it to a simulated system.
37
51
N.
SELVAGANESAN
N.
SELVAGANESAN
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING, PONDICHERRY
ENGINEERING COLLEGE, PONDICHERRY605014, INDIA
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING
India
n_selvag@rediffmail.com
D.
RAJA
D.
RAJA
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING, PONDICHERRY ENGINEERING
COLLEGE, PONDICHERRY605014, INDIA
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING
India
S.
SRINIVASAN
S.
SRINIVASAN
DEPARTMENT OF INSTRUMENTATION ENGINEERING, MIT CAMPUS, ANNA UNIVERSITY,
CHROMEPET, CHENNAI600044, INDIA
DEPARTMENT OF INSTRUMENTATION ENGINEERING,
India
srini@mitindia.edu
Fault Diagnosis
Fuzzy logic
Switched Reluctance Motor
Fuzzy Inference Systems
[[1] A. A. Arkadan and B. W. Kielgas, Switched reluctance motor drive systems dynamic##performance prediction under internal and external fault conditions, IEEE Trans. on##Energy Conversion, 9 (1994), 4552.##[2] I. Husain and M. N. Anwa, Fault analysis of switched reluctance motor drives, IEEE##Conference, (1999), 4143. ##[3] C. C. Lee, Fuzzy logic control systems: fuzzy logic controller–Part I, IEEE Transaction on##systems, man and Cybernetics, 20, 404418.##[4] J. M. Mendel, Fuzzy logic systems for engineering: tutorial, Proceedings of IEEE, 83##[5] T. J. E. Miller, Switched reluctance motors and their control, Hillsboro, OH: Magna##Physics, (1993).##[6] S. Mir, M. E. Elbuluk and I. Husain, Torqueripple minimization in switched reluctance##motor, IEEE Transactions on Industry Applications, 35 (1999).##[7] S. Mir, I. Husain and M. E. Elbuluk, Switched reluctance motor modeling with online##parameter identification, IEEE Transactions on Industry Applications, 34 (1998).##[8] R. Muthu and E. El Kanzi, Fuzzy logic control of A pH neutralization process, IEEE ##ICECS(2003), 10661069.##[9] A.V. Radun, Design Considerations for the switched reluctance motor, IEEE Trans. on##Industry Applications, 31 (1995), 10791087.##[10] M. G. Rodrigues, W. I. Suemitsu, P. Branco, J. A. Dente and L. G. B. Rolim, Fuzzy logic##control of a switched reluctance motor, Coppe/UFRJFederal University of Rio de##[11] K. Russa, I. Husain and M. E. Elbuluk, A Selftuning controller for switched reluctance##motors, IEEE Transactions on Power Electronics, 15 (2000).##[12] F. Soares and P. J. Costa Branco, Simulation of a 6/4 switched reluctance motor based on##matlab/simulink environment, IEEE Transactions on Aero Space and Electronic Systems,##37 (2001).##[13] C. M. Stephens, Fault detectionand managementSystem for fault tolerant switched reluctance##motor, IEEEIndustry Applications Society Conf. Rec., (1989), 574578.##]
SOME RESULTS ON INTUITIONISTIC FUZZY SPACES
SOME RESULTS ON INTUITIONISTIC FUZZY SPACES
2
2
In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of approximation theory in intuitionistic fuzzymetric spaces.
1
In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of approximation theory in intuitionistic fuzzymetric spaces.
53
64
S. B.
Hosseini
S. B.
Hosseini
Islamic Azad UniversityNour Branch, Nour, Iran
Islamic Azad UniversityNour Branch, Nour,
Iran
Donal
O’Regan
Donal
O’Regan
Department of Mathematics, National University of Ireland, Galway,
Ireland
Department of Mathematics, National University
Ireland
donal.oregan@nuigalway.ie
Reza
Saadati
Reza
Saadati
Department of Mathematics, Islamic Azad UniversityAyatollah Amoly
Branch, Amol, Iran and Institute for Studies in Applied Mathematics 1, Fajr 4, Amol
4617654553, Iran
Department of Mathematics, Islamic Azad University
Ireland
rsaadati@eml.cc
Intuitionistic fuzzy metric (normed) spaces
Completeness
Compactness
Finite dimensional
Weak convergence
Quotient spaces
Approximation theory
[[1] M. Amini and R. Saadati, Topics in fuzzy metric space, Journal of Fuzzy Math., 4 (2003),##[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87–96.##[3] C. Cornelis, G. Deschrijver and E. E. Kerre, Classification of intuitionistic fuzzy implicators:##an algebraic approach, In H. J. Caulfield, S. Chen, H. Chen, R. Duro, V. Honaver, E. E.##Kerre, M. Lu, M. G. Romay, T. K. Shih, D. Ventura, P. P. Wang and Y. Yang, editors,##Proceedings of the 6th Joint Conference on Information Sciences, (2002), 105108.##[4] C. Cornelis, G. Deschrijver and E. E. Kerre, Intuitionistic fuzzy connectives revisited, Proceedings##of the 9th International Conference on Information Processing and Management of##Uncertainty in KnowledgeBased Systems, (2002), 18391844.##[5] G. Deschrijver, C. Cornelis and E. E. Kerre, On the representation of intuitionistic fuzzy##tnorms and tconorms, IEEE Transactions on Fuzzy Systems, 12 (2004), 45–61.##[6] G. Deschrijver and E. E. Kerre, On the relationship between some extensions of fuzzy set##theory, Fuzzy Sets and Systems, 23 (2003), 227235.##[7] M. S. Elnaschie, On the uncertainty of Cantorian geometry and twoslit expriment, Chaos,##Soliton and Fractals, 9 (1998), 517–529.##[8] M. S. Elnaschie, On a fuzzy Kahlerlike manifold which is consistent with twoslit expriment,##Int. Journal of Nonlinear Science and Numerical Simulation, 6 (2005), 95–98.##[9] M. S. Elnaschie, A review of E infinity theory and the mass spectrum of high energy particle##physics, Chaos, Soliton and Fractals, 19 (2004), 209–236. ##[10] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and System,##64 (1994), 395–399.##[11] A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets##and Systems, 90 (1997), 365–368.##[12] S. B. Hosseini , J. H. Park and R. Saadati , Intuitionistic fuzzy invariant metric spaces, Int.##Journal of Pure Appl. Math. Sci., 2(2005).##[13] C. M. Hu , Cstructure of FTS. V. fuzzy metric spaces, Journal of Fuzzy Math., 3(1995)##711–721.##[14] P. C. Kainen , Replacing points by compacta in neural network approximation, Journal of##Franklin Inst., 341 (2004), 391–399.##[15] E. Kreyszig, Introductory functional analysis with applications, John Wiley and Sons, New##York, 1978.##[16] R. Lowen, Fuzzy set theory, Kluwer Academic Publishers, Dordrecht, 1996.##[17] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004) 1039##[18] R. Saadati and S. M. Vaezpour, Some results on fuzzy Banach spaces, Journal of Appl. Math.##Comput., 17 (2005), 475–484.##[19] R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons and##Fractals, 27 (2006), 331–344.##[20] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific Journal of Math., 10 (1960),##314–334.##[21] Y. Tanaka, Y. Mizno and T. Kado, Chaotic dynamics in Friedmann equation, chaos, soliton##and fractals, 24 (2005), 407–422.##[22] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338–353.##]
LFUZZY BILINEAR OPERATOR AND ITS CONTINUITY
LFUZZY BILINEAR OPERATOR AND ITS CONTINUITY
2
2
The purpose of this paper is to introduce the concept of Lfuzzybilinear operators. We obtain a decomposition theorem for Lfuzzy bilinearoperators and then prove that a Lfuzzy bilinear operator is the same as apowerset operator for the variablebasis introduced by S.E.Rodabaugh (1991).Finally we discuss the continuity of Lfuzzy bilinear operators.
1
The purpose of this paper is to introduce the concept of Lfuzzybilinear operators. We obtain a decomposition theorem for Lfuzzy bilinearoperators and then prove that a Lfuzzy bilinear operator is the same as apowerset operator for the variablebasis introduced by S.E.Rodabaugh (1991).Finally we discuss the continuity of Lfuzzy bilinear operators.
65
73
Conghua
Yan
Conghua
Yan
Department of Mathematics, Nanjing Normal University, Nanjing
Jiangsu, 210097, P.R.China
Department of Mathematics, Nanjing Normal
China
chyan@njnu.edu.cn
Jinxuan
Fang
Jinxuan
Fang
Department of Mathematics, Nanjing Normal University, Nanjing
Jiangsu, 210097, P.R.China
Department of Mathematics, Nanjing Normal
China
jxfang@njnu.edu.cn
Orderhomomorphism
Powerset operator
Lbilinear operator
Molecule net
[[1] Jinxuan Fang, Fuzzy linear orderhomomorphism and its structures, The Journal of Fuzzy##Mathematics, 4(1)(1996), 93–102.##[2] Jinxuan Fang, The continuity of fuzzy linear orderhomomorphisms, The Journal of Fuzzy##Mathematics, 5(4)(1997), 829–838.##[3] Jinxuan Fang and Conghua Yan, Lfuzzy topological vector spaces, The Journal of Fuzzy##Mathematics, 5(1)(1997), 133–144.##[4] He Ming, Biinduced mapping on Lfuzzy sets, KeXue TongBao 31(1986) 475(in Chinese).##[5] U. H¨ohle and S. E. Rodabaugh, eds., Mathematics of fuzzy sets: logic, topology and measure##theory, The handbooks of Fuzzy Sets Series, Vol. 3(1999), Kluwer Academic Publishers##(Dordrecht).##[6] Yingming Liu and Maokang Luo, Fuzzy topology, World Scientific Publishing, Singapore,##[7] S. E. Rodabaugh, Pointset latticetheoretic topology, Fuzzy Sets and Systems, 40(1991),##297–347.##[8] S.E.Rodabaugh, Powerset operator foundations for pointset latticetheoretic(Poslat) fuzzy##set theories and topologies, Questions Mathematicae, 20(1997), 463–530.##[9] Guojun Wang, Orderhomomorphism of fuzzes, Fuzzy Sets and Systems, 12(1984), 281–288.##[10] Guojun Wang, Theory of Lfuzzy topological spaces, Shanxi Normal University Publishing##House, 1988 (in Chineses).##[11] Conghua Yan, Initial Lfuzzy topologies determined by the family of Lfuzzy linear orderhomomorphims,##Fuzzy Sets and Systems, 116(2000), 409–413.##[12] Conghua Yan, Projective limit of Lfuzzy locally convex topological vector spaces, The Journal##of Fuzzy Mathematics, 9(2001), 8996.##[13] Conghua Yan, Generalization of inductive topologies to Ltopological vector spaces, Fuzzy##Sets and Systems, 131(3)(2002), 347–352.##[14] Conghua Yan and Jinxuan Fang, Lfuzzy locally convex topological vector spaces, The Journal##of Fuzzy Mathematics, 7(1999), 765–772.##[15] Conghua Yan and Jinxuan Fang, The uniform boundedness principle in Ltopological vector##spaces, Fuzzy Sets and Systems, 136(2003), 121–126.##[16] Conghua Yan and Congxin Wu, Fuzzy Lbornological spaces, Information Sciences,##173(2005), 1–10.##[17] L.A. Zadeh, Fuzzy sets, Information and Control, 8(1965), 338–353.##]
TRIANGULAR FUZZY MATRICES
TRIANGULAR FUZZY MATRICES
2
2
In this paper, some elementary operations on triangular fuzzynumbers (TFNs) are defined. We also define some operations on triangularfuzzy matrices (TFMs) such as trace and triangular fuzzy determinant(TFD). Using elementary operations, some important properties of TFMs arepresented. The concept of adjoints on TFM is discussed and some of theirproperties are. Some special types of TFMs (e.g. pure and fuzzy triangular,symmetric, pure and fuzzy skewsymmetric, singular, semisingular, constant)are defined and a number of properties of these TFMs are presented.
1
In this paper, some elementary operations on triangular fuzzynumbers (TFNs) are defined. We also define some operations on triangularfuzzy matrices (TFMs) such as trace and triangular fuzzy determinant(TFD). Using elementary operations, some important properties of TFMs arepresented. The concept of adjoints on TFM is discussed and some of theirproperties are. Some special types of TFMs (e.g. pure and fuzzy triangular,symmetric, pure and fuzzy skewsymmetric, singular, semisingular, constant)are defined and a number of properties of these TFMs are presented.
75
87
Amiya Kumar
Shyamal
Amiya Kumar l
Shyama
Department of Applied Mathematics
with Oceanology and Computer Programming, Vidyasagar University, Midnapore 
721102, West Bengal, India
Department of Applied Mathematics
with Oceanology
India
Madhumangal
Pal
Madhumangal
Pal
Department of Applied Mathematics
with Oceanology and Computer Programming, Vidyasagar University, Midnapore 
721102, West Bengal, India
Department of Applied Mathematics
with Oceanology
India
madhumangal@lycos.com
Triangular fuzzy numbers
Triangular fuzzy number arithmetic
Triangular fuzzy matrices
Triangular fuzzy determinant
[[1] D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press##London, 1980.##[2] H. Hashimoto, Convergence of powers of a fuzzy transitive matrix, Fuzzy Sets and Systems,##9 (1983), 153160.##[3] H. Hashimoto, Canonical form of a transitive fuzzy matrix, Fuzzy Sets and Systems, 11##(1983), 157162.##[4] A. Kandel, Fuzzy mathematical Techniques with Applications, AddisonWesley, Tokyo, 1996.##[5] K. H. Kim and F. W. Roush, Generalised fuzzy matrices, Fuzzy Sets and Systems, 4 (1980),##[6] J. B. Kim, Determinant theory for fuzzy and boolean matrices, Congressus Numerantium,##(1988), 273276.##[7] W. Kolodziejczyk, Canonical form of a strongly transitive fuzzy matrix, Fuzzy Sets and##Systems, 22 (1987), 292302.##[8] W. Kolodziejczyk, Convergence of powers of stransitive fuzzy matrices, Fuzzy Sets and##Systems, 26 (1988), 127130. ##[9] M. Pal, Intuitionistic fuzzy determinant, V.U.J.Physical Sciences, 7 (2001), 8793.##[10] M. Pal, S. K. Khan and A. K. Shyamal, Intuitionistic fuzzy matrices, Notes on Intuitionistic##Fuzzy Sets, 8(2) (2002), 5162.##[11] M. Z. Ragab and E. G. Emam, The determinant and adjoint of a square fuzzy matrix, Fuzzy##Sets and Systems, 61 (1994), 297307.##[12] M. Z. Ragab and E. G. Emam, On the minmax composition of fuzzy matrices, Fuzzy Sets##and Systems, 75 (1995), 8392.##[13] A. K. Shyamal and M. Pal, Two new operators on fuzzy matrices, J. Applied Mathematics##and Computing, 15 (2004), 91107.##[14] A. K. Shyamal and M. Pal, Distance between fuzzy matrices and its applications, Acta Siencia##Indica, XXXI.M (1) (2005), 199204.##[15] A. K. Shyamal and M. Pal, Distance between fuzzy matrices and its applicationsI, J. Natural##and Physical Sciences, 19(1)(2005), 3958.##[16] A. K. Shyamal and M. Pal, Distances between intuitionistics fuzzy matrices, V. U. J. Physical##Sciences, 8 (2002), 8191.##[17] M. G. Thomason,Convergence of powers of a fuzzy matrix, J. Math Anal. Appl., 57 (1977),##[18] L. J. Xin,Controllable fuzzy matrices, Fuzzy Sets and Systems, 45 (1992), 313319.##[19] L. J. Xin,Convergence of powers of controllable fuzzy matrices, Fuzzy Sets and Systems, 62##(1994), 8388.##[20] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338353.##]
INTUITIONISTIC FUZZY BOUNDED LINEAR OPERATORS
INTUITIONISTIC FUZZY BOUNDED LINEAR OPERATORS
2
2
The object of this paper is to introduce the notion of intuitionisticfuzzy continuous mappings and intuitionistic fuzzy bounded linear operatorsfrom one intuitionistic fuzzy nnormed linear space to another. Relation betweenintuitionistic fuzzy continuity and intuitionistic fuzzy bounded linearoperators are studied and some interesting results are obtained.
1
The object of this paper is to introduce the notion of intuitionisticfuzzy continuous mappings and intuitionistic fuzzy bounded linear operatorsfrom one intuitionistic fuzzy nnormed linear space to another. Relation betweenintuitionistic fuzzy continuity and intuitionistic fuzzy bounded linearoperators are studied and some interesting results are obtained.
89
101
S.
Vijayabalaji
S.
Vijayabalaji
Department of Mathematics, Annamalai University, Annamalainagar
608002, Tamilnadu, India
Department of Mathematics, Annamalai University,
India
balaji−nandini@rediffmail.com
N.
Thillaigovindan
N.
Thillaigovindan
Department of Mathematics Section, Faculty of Engineering and
Technology, Annamalai University, Annamalainagar608002, Tamilnadu, India
Department of Mathematics Section, Faculty
India
thillai−n@sify.com
fuzzy nnorm
intuitionistic fuzzy nnorm
intuitionistic fuzzy continuous mapping
intuitionistic fuzzy bounded linear operator
[[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1)(1986), 8796.##[2] K. T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33(1989), 3746. ##[3] K. T. Atanassov, Intuitionistic fuzzy sets, PhysicaVerlag Heidelberg, Newyork, 1999.##[4] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, The Journal of##Fuzzy Mathematics, 11(3)(2003), 687705.##[5] T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems,##151(2005), 513547.##[6] S. C. Chang and J. N. Mordesen, Fuzzy linear operators and fuzzy normed linear spaces, Bull.##Cal. Math. Soc., 86(1994), 429436.##[7] G. Deschrijver and E. Kerre , On the Cartesian product of the intuitionistic fuzzy sets, The##Journal of Fuzzy Mathematics, 11 (3)(2003), 537547.##[8] MS. Elnaschie, On the uncertainty of Cantorian geometry and twoslit experiment, Chaos,##Soliton and Fractals, 9 (3)(1998), 517529.##[9] MS. Elnaschie, On the verications of heterotic strings theory and 1 theory, Chaos, Soliton##and Fractals,11 (2) (2000), 23972407.##[10] C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems, 48 (1992),##[11] C. Felbin, The Completion of fuzzy normed linear space, Journal of Mathematical Analysis##and Applications, 174 (2)(1993), 428440.##[12] C. Felbin, Finite dimensional fuzzy normed linear spaces II, Journal of Analysis, 7 (1999),##[13] S. G¨ahler, Lineare 2Normierte R¨aume, Math. Nachr., 28 (1965), 143.##[14] S. G¨ahler, Unter Suchungen ¨U ber Veralla gemeinerte mmetrische R¨aume I, Math. Nachr.,##(1969), 165189.##[15] H. Gunawan and M. Mashadi, on nNormed spaces, International J. Math. & Math. Sci., 27##(10)(2001), 631639.##[16] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), 143##[17] S. S. Kim and Y. J. Cho, Strict convexity in linear nnormed spaces, Demonstratio Math.,##29 (4) (1996), 739744.##[18] S. V. Krishna and K. K. M. Sharma, Separation of fuzzy normed linear spaces, Fuzzy Sets##and Systems, 63 (1994), 207217.##[19] R. Malceski, Strong nconvex nnormed spaces, Mat. Bilten, 21 (1997), 81102.##[20] A. Misiak, ninner product spaces, Math. Nachr., 140 (1989), 299319.##[21] AL. Narayanan and S. Vijayabalaji, Fuzzy nnormed linear space, 24(2005), 39633977.##[22] J. H. Park, Intuitionistic fuzzy metric space, Chaos, Solitons and Fractals, 22(2004), 1039##[23] G. S. Rhie, B. M. Choi and S. K. Dong, On the completeness of fuzzy normed linear spaces,##Math. Japonica, 45 (1) (1997), 3337.##[24] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math., 10(1960), 314334.##[25] S. Vijayabalaji, N. Thillaigovindan and Y. B. Jun, Intuitionistic fuzzy nnormed linear space,##Submitted to Bulletin of Korean Mathematical Society, Korea.##]
Persiantranslation Vol.4, No.1 April 2007
2
2
1

105
111