ORIGINAL_ARTICLE
Cover Vol.4, No.1 April 2007
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ORIGINAL_ARTICLE
DISTRIBUTED AND COLLABORATIVE FUZZY MODELING
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 rule-based systems. The paper elaborates on a number ofmechanisms of collaboration offering two general categories of so-calledhorizontal 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., type-2 fuzzy sets.
http://ijfs.usb.ac.ir/article_353_e16a2e92cedec4f2fbb09d7c81a6cb72.pdf
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10.22111/ijfs.2007.353
Computational Intelligence
C^{3} paradigm
Distributed processing
Fuzzy
clustering
Fuzzy models
WITOLD
PEDRYCZ
pedrycz@ee.ualberta.ca
true
1
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, UNIVERSITY OF ALBERTA,
EDMONTON T6R 2G7 CANADA AND SYSTEMS RESEARCH INSTITUTE OF THE POLISH ACADEMY OF SCIENCE,
WARSAW, POLAND
DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING, UNIVERSITY OF ALBERTA,
EDMONTON T6R 2G7 CANADA AND SYSTEMS RESEARCH INSTITUTE OF THE POLISH ACADEMY OF SCIENCE,
WARSAW, POLAND
AUTHOR
[1] R. Agarwal and R. Srikant, Privacy-preserving data mining., Proc. of the ACM SIGMOD
1
Conference on Management of Data, ACM Press, New York, May (2000), 439–450.
2
[2] A. M. Bensaid, L. O. Hall, J. C. Bezdek and L. P. Clarke. Partially supervised clustering
3
for image segmentation, Pattern Recognition, 29(5) (1996), 859-871.
4
[3] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press,
5
NY. (1981)
6
[4] C. Clifton and D. Marks, Security and privacy implications of data mining, Workshop on
7
Data Mining and Knowledge Discovery, Montreal, Canada, (1996), 15–19.
8
[5] J. C. Da Silva, C. Giannella, R. Bhargava, H. Kargupta and M. Klusch, Distributed data
9
mining and agents, Engineering Applications of Artificial Intelligence, 18 (7) (2005), 791-
10
[6] W. Du and Z. Zhan, Building decision tree classifier on private data, Clifton, C., Estivill-
11
Castro, V. (Eds.), IEEE ICDM Workshop on Privacy, Security and Data Mining,
12
Conferences in Research and Practice in Information Technology, Vol. 14, Maebashi
13
City, Japan, ACS, (2002), 1–8.
14
[7] T. Johnsten and V. V. Raghavan, A methodology for hiding knowledge in databases,
15
Clifton, C., Estivill-Castro, C. (Eds.), IEEE ICDM Workshop on Privacy, Security and
16
Data Mining, Conferences in Research and Practice in Information Technology, Vol.
17
14. Maebashi City, Japan, ACS, (2002), 9–17.
18
[8] H. Kargupta, L. Kun, S. Datta, J. Ryan and K. Sivakumar, Homeland security and
19
privacy sensitive data mining from multi-party distributed resources, Proc. 12th IEEE
20
International Conference on Fuzzy Systems, FUZZ '03, .Volume 2, May (2003), 25-28,
21
Vol. 2 (2003), 1257 – 1260.
22
[9] S. Merugu, and J. Ghosh, A privacy-sensitive approach to distributed clustering, Pattern
23
Recognition Letters, 26 (4) (2005), 399-410.
24
[10] B. Park and H. Kargupta, Distributed data mining: algorithms, systems, and applications, In:
25
Ye, N. (Ed.), The Handbook of Data Mining. Lawrence Erlbaum Associates, New
26
York, (2003), 341–358.
27
[11] W. Pedrycz, Algorithms of fuzzy clustering with partial supervision, Pattern Recognition
28
Letters, 3 (1985), 13 - 20.
29
[12] W. Pedrycz, and J. Waletzky, Fuzzy clustering with partial supervision, IEEE Trans. on
30
Systems, Man and Cybernetics, 5 (1997), 787-795.
31
[13] W. Pedrycz and J. Waletzky, Neural network front-ends in unsupervised learning, IEEE
32
Trans. on Neural Networks, 8 (1997), 390-401.
33
[14] W. Pedrycz, V. Loia and S. Senatore, P-FCM: A proximity-based clustering, Fuzzy Sets &
34
Systems, 148, (2004), 21-41.
35
[15] W. Pedrycz, Collaborative fuzzy clustering, Pattern Recognition Letters, 23(14)(2002),
36
1675-1686.
37
[16] W. Pedrycz, Knowledge-Based Clustering: From Data to Information Granules, J. Wiley,
38
New York (2005).
39
[17] W. Pedrycz and F. Gomide, Fuzzy Systems Engineering: Toward Human-Centric
40
Computing, J. Wiley, NJ Hoboken, ( 2007).
41
[18] A. Strehl and J. Ghosh, Cluster ensembles—a knowledge reuse framework for combining
42
multiple partitions, Journal of Machine Learning Research, 3, (2002), 583–617.
43
[19] H. Timm, F. Klawonn and R. Kruse, An extension of partially supervised fuzzy cluster
44
analysis, Proc. Annual Meeting of the North American Fuzzy Information Processing
45
Society, NAFIPS, (2002), 63 –68.
46
[20] G. Tsoumakas, L. Angelis and I. Vlahavas, Clustering classifiers for knowledge discovery
47
from physically distributed databases, Data & Knowledge Engineering, 49(3) (2004), 223-
48
[21] V. S. Verykios, et al. State of the art in privacy preserving data mining, SIGMOID
49
Record, 33(1) (2004), 50-57.
50
[22] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU) – an outline, Information
51
Sciences, 172(1-2) (2005), 1-40.
52
ORIGINAL_ARTICLE
USING DISTRIBUTION OF DATA TO ENHANCE PERFORMANCE OF FUZZY CLASSIFICATION SYSTEMS
This paper considers the automatic design of fuzzy rule-basedclassification 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 well-known data sets show the effectiveness of ourapproach.
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10.22111/ijfs.2007.355
Fuzzy rule-based classification systems
Rule weight
EGHBAL G.
MANSOORI
mansoori@shirazu.ac.ir
true
1
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF
ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF
ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF
ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN
LEAD_AUTHOR
MANSOOR J.
ZOLGHADRI
zjahromi@shirazu.ac.ir
true
2
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF
ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF
ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF
ENGINEERING, SHIRAZ UNIVERSITY, SHIRAZ, IRAN
AUTHOR
SERAJ D.
KATEBI
katebi@shirazu.ac.ir
true
3
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF ENGINEERING,
SHIRAZ UNIVERSITY, SHIRAZ, IRAN
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF ENGINEERING,
SHIRAZ UNIVERSITY, SHIRAZ, IRAN
COMPUTER SCIENCE AND ENGINEERING DEPARTMENT, COLLEGE OF ENGINEERING,
SHIRAZ UNIVERSITY, SHIRAZ, IRAN
AUTHOR
[1] S. Abe and M. S. Lan, A method for fuzzy rules extraction directly from numerical data and
1
its application to pattern classification, IEEE Transaction on Fuzzy Systems, 3 (1) (1995),
2
[2] S. Abe and R. Thawonmas, A fuzzy classifier with ellipsoidal regions, IEEE Transaction
3
on Fuzzy Systems, 5 (3) (1997), 358-368.
4
[3] J. C. Bezdek, Pattern Analysis. In E. H. Ruspini, P. Bonissone and W. Pedrycz, Handbook
5
of Distributed representation of fuzzy rules and its application to pattern classification,
6
Handbook of Fuzzy Computation, Chapter F6, Institute of Physics Publishing, London,
7
[4] C. L. Blake and C. J. Merz, UCI Repository of machine learning databases, University of
8
California, Department of Information and Computer Science, Irvine, CA, 1998.
9
[5] H. Ishibuchi and T. Nakashima, Improving the performance of fuzzy classifier systems for
10
pattern classification problems with continuous attributes, IEEE Transaction on Industrial
11
Electronics, 46 (6) (1999), 157-168.
12
[6] H. Ishibuchi and T. Nakashima, Effect of rule weights in fuzzy rule-based classification
13
systems, IEEE Transaction on Fuzzy Systems, 9 (4) (2001), 506-515.
14
[7] H. Ishibuchi, T. Nakashima and T. Morisawa, Voting in fuzzy rule-based systems for pattern
15
classification problems, Fuzzy sets and systems, 103 (2) (1999), 223-238.
16
[8] H. Ishibuchi, K. Nozaki and H. Tanaka, Distributed representation of fuzzy rules and its
17
application to pattern classification, Fuzzy sets and systems, 52 (1) (1992), 21-32.
18
[9] H. Ishibuchi and T. Yamamoto, Comparison of heuristic criteria for fuzzy rule selection in
19
classification problems, Fuzzy Optimization and Decision Making, 3 (2) (2004), 119-139.
20
[10] H. Ishibuchi and T. Yamamoto, Rule Weight Specification in Fuzzy Rule-Based
21
Classification Systems, IEEE Trans. on Fuzzy Systems, 13 (4) (2005), 428-435.
22
[11] H. Ishibuchi, T. Yamamoto and T. Nakashima, Fuzzy data mining: Effect of fuzzy
23
discretization, Proceeding of 1st IEEE International Conference on Data Mining, (2001),
24
[12] L. I. Kuncheva, Fuzzy Classifier Design, Physica-Verlag, Heidelberg, 2000.
25
[13] L.I.Kuncheva and J. C. Bezdek, A fuzzy generalized nearest prototype classifier, Proceeding
26
of 7th IFSA World Congress, Prague, 3 (1997), 217-222.
27
[14] S. Mitra and Y. Hayashi, Neuro-fuzzy rule generation: Survey in soft computing framework,
28
IEEE Transaction on Neural Networks, 11 (3) (2000), 748-768.
29
[15] D. Nauck and R. Kruse, How the learning of rule weights affects the interpretability of fuzzy
30
systems, Proceeding of 7th IEEE International Conference on Fuzzy Systems,
31
Anchorage, (1998), 1235-1240.
32
[16] D. Nauk and R. Kruse, Obtaining interpretable fuzzy classification rules from medical data,
33
Artificial Intelligence in Medicine, 16 (1999), 149-169.
34
[17] K. Nozaki, H. Ishibuchi and H. Tanaka, Adaptive Fuzzy Rule-Based Classification Systems,
35
IEEE Trans. on Fuzzy Systems, 4 (3) (1996), 238-250.
36
[18] J. A. Roubos, M. Setnes and J. Abonyi, Learning fuzzy classification rules from labeled data,
37
IEEE Transaction on Fuzzy Systems, 8 (5) (2001), 509-522.
38
[19] D. Setiono, Generating concise and accurate classification rules for breast cancer diagnosis,
39
Artificial Intelligence in Medicine, 18 (1999), 205-219.
40
[20] M. Setnes and R. Babuska, Rule-Based Modeling: Precision and Transparency, IEEE
41
Transaction on Systems, Man, and Cybernetics-Part C: Applications and reviews, 28 (1)
42
(1998), 165-169.
43
[21] M. Setnes and R. Babuska, Fuzzy relational classifier trained by fuzzy clustering, IEEE
44
Transaction on Systems, Man, and Cybernetics-Part B: Cybernetics, 29 (1999), 619-625.
45
[22] M. Setnes and J. A. Roubos, GA-fuzzy modeling and classification: complexity and
46
performance, IEEE Transaction on Fuzzy Systems, 8 (5) (2000), 509-522.
47
[23] J. Valente de Oliveira, Semantic constraints for membership function optimization, IEEE
48
Transaction on Fuzzy Systems, 19 (1) (1999), 128-138.
49
[24] J. Van den Berg, U. Kaymak and W. M. Van den Berg, Fuzzy classification using
50
probability based rule weighting, proceeding of 11th IEEE International Conference on
51
Fuzzy Systems, (2002), 991-996.
52
[25] L. Wang and Jerry M. Mendel, Generating fuzzy rules by learning from examples, IEEE
53
Transaction on Systems, Man, and Cybernetics, 22 (6) (1992), 1414-1427.
54
[26] S. M. Weiss and C. A. Kulikowski, Computer Systems that Learn, Morgan Kaufmann, San
55
Mateo, 1991.
56
ORIGINAL_ARTICLE
FUZZY BASED FAULT DETECTION AND CONTROL FOR 6/4 SWITCHED RELUCTANCE MOTOR
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.
http://ijfs.usb.ac.ir/article_356_9057931d5fc7d9338fab8be76e173fb2.pdf
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10.22111/ijfs.2007.356
Fault Diagnosis
Fuzzy logic
Switched Reluctance Motor
Fuzzy
Inference Systems
N.
SELVAGANESAN
n_selvag@rediffmail.com
true
1
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING, PONDICHERRY
ENGINEERING COLLEGE, PONDICHERRY-605014, INDIA
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING, PONDICHERRY
ENGINEERING COLLEGE, PONDICHERRY-605014, INDIA
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING, PONDICHERRY
ENGINEERING COLLEGE, PONDICHERRY-605014, INDIA
LEAD_AUTHOR
D.
RAJA
true
2
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING, PONDICHERRY ENGINEERING
COLLEGE, PONDICHERRY-605014, INDIA
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING, PONDICHERRY ENGINEERING
COLLEGE, PONDICHERRY-605014, INDIA
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING, PONDICHERRY ENGINEERING
COLLEGE, PONDICHERRY-605014, INDIA
AUTHOR
S.
SRINIVASAN
srini@mitindia.edu
true
3
DEPARTMENT OF INSTRUMENTATION ENGINEERING, MIT CAMPUS, ANNA UNIVERSITY,
CHROMEPET, CHENNAI-600044, INDIA
DEPARTMENT OF INSTRUMENTATION ENGINEERING, MIT CAMPUS, ANNA UNIVERSITY,
CHROMEPET, CHENNAI-600044, INDIA
DEPARTMENT OF INSTRUMENTATION ENGINEERING, MIT CAMPUS, ANNA UNIVERSITY,
CHROMEPET, CHENNAI-600044, INDIA
AUTHOR
[1] A. A. Arkadan and B. W. Kielgas, Switched reluctance motor drive systems dynamic
1
performance prediction under internal and external fault conditions, IEEE Trans. on
2
Energy Conversion, 9 (1994), 45-52.
3
[2] I. Husain and M. N. Anwa, Fault analysis of switched reluctance motor drives, IEEE
4
Conference, (1999), 41-43.
5
[3] C. C. Lee, Fuzzy logic control systems: fuzzy logic controller–Part I, IEEE Transaction on
6
systems, man and Cybernetics, 20, 404-418.
7
[4] J. M. Mendel, Fuzzy logic systems for engineering: tutorial, Proceedings of IEEE, 83
8
[5] T. J. E. Miller, Switched reluctance motors and their control, Hillsboro, OH: Magna
9
Physics, (1993).
10
[6] S. Mir, M. E. Elbuluk and I. Husain, Torque-ripple minimization in switched reluctance
11
motor, IEEE Transactions on Industry Applications, 35 (1999).
12
[7] S. Mir, I. Husain and M. E. Elbuluk, Switched reluctance motor modeling with on-line
13
parameter identification, IEEE Transactions on Industry Applications, 34 (1998).
14
[8] R. Muthu and E. El Kanzi, Fuzzy logic control of A pH neutralization process, IEEE -
15
ICECS-(2003), 1066-1069.
16
[9] A.V. Radun, Design Considerations for the switched reluctance motor, IEEE Trans. on
17
Industry Applications, 31 (1995), 1079-1087.
18
[10] M. G. Rodrigues, W. I. Suemitsu, P. Branco, J. A. Dente and L. G. B. Rolim, Fuzzy logic
19
control of a switched reluctance motor, Coppe/UFRJ-Federal University of Rio de
20
[11] K. Russa, I. Husain and M. E. Elbuluk, A Self-tuning controller for switched reluctance
21
motors, IEEE Transactions on Power Electronics, 15 (2000).
22
[12] F. Soares and P. J. Costa Branco, Simulation of a 6/4 switched reluctance motor based on
23
matlab/simulink environment, IEEE Transactions on Aero Space and Electronic Systems,
24
37 (2001).
25
[13] C. M. Stephens, Fault detectionand managementSystem for fault tolerant switched reluctance
26
motor, IEEE-Industry Applications Society Conf. Rec., (1989), 574-578.
27
ORIGINAL_ARTICLE
SOME RESULTS ON INTUITIONISTIC FUZZY SPACES
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.
http://ijfs.usb.ac.ir/article_357_3141e238301eb28b17f345772521dbda.pdf
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10.22111/ijfs.2007.357
Intuitionistic fuzzy metric (normed) spaces
Completeness
Compactness
Finite dimensional
Weak convergence
Quotient spaces
Approximation theory
S. B.
Hosseini
true
1
Islamic Azad University-Nour Branch, Nour, Iran
Islamic Azad University-Nour Branch, Nour, Iran
Islamic Azad University-Nour Branch, Nour, Iran
AUTHOR
Donal
O’Regan
donal.oregan@nuigalway.ie
true
2
Department of Mathematics, National University of Ireland, Galway,
Ireland
Department of Mathematics, National University of Ireland, Galway,
Ireland
Department of Mathematics, National University of Ireland, Galway,
Ireland
AUTHOR
Reza
Saadati
rsaadati@eml.cc
true
3
Department of Mathematics, Islamic Azad University-Ayatollah Amoly
Branch, Amol, Iran and Institute for Studies in Applied Mathematics 1, Fajr 4, Amol
46176-54553, Iran
Department of Mathematics, Islamic Azad University-Ayatollah Amoly
Branch, Amol, Iran and Institute for Studies in Applied Mathematics 1, Fajr 4, Amol
46176-54553, Iran
Department of Mathematics, Islamic Azad University-Ayatollah Amoly
Branch, Amol, Iran and Institute for Studies in Applied Mathematics 1, Fajr 4, Amol
46176-54553, Iran
LEAD_AUTHOR
[1] M. Amini and R. Saadati, Topics in fuzzy metric space, Journal of Fuzzy Math., 4 (2003),
1
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87–96.
2
[3] C. Cornelis, G. Deschrijver and E. E. Kerre, Classification of intuitionistic fuzzy implicators:
3
an algebraic approach, In H. J. Caulfield, S. Chen, H. Chen, R. Duro, V. Honaver, E. E.
4
Kerre, M. Lu, M. G. Romay, T. K. Shih, D. Ventura, P. P. Wang and Y. Yang, editors,
5
Proceedings of the 6th Joint Conference on Information Sciences, (2002), 105-108.
6
[4] C. Cornelis, G. Deschrijver and E. E. Kerre, Intuitionistic fuzzy connectives revisited, Proceedings
7
of the 9th International Conference on Information Processing and Management of
8
Uncertainty in Knowledge-Based Systems, (2002), 1839-1844.
9
[5] G. Deschrijver, C. Cornelis and E. E. Kerre, On the representation of intuitionistic fuzzy
10
tnorms and t-conorms, IEEE Transactions on Fuzzy Systems, 12 (2004), 45–61.
11
[6] G. Deschrijver and E. E. Kerre, On the relationship between some extensions of fuzzy set
12
theory, Fuzzy Sets and Systems, 23 (2003), 227-235.
13
[7] M. S. Elnaschie, On the uncertainty of Cantorian geometry and two-slit expriment, Chaos,
14
Soliton and Fractals, 9 (1998), 517–529.
15
[8] M. S. Elnaschie, On a fuzzy Kahler-like manifold which is consistent with two-slit expriment,
16
Int. Journal of Nonlinear Science and Numerical Simulation, 6 (2005), 95–98.
17
[9] M. S. Elnaschie, A review of E infinity theory and the mass spectrum of high energy particle
18
physics, Chaos, Soliton and Fractals, 19 (2004), 209–236.
19
[10] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and System,
20
64 (1994), 395–399.
21
[11] A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets
22
and Systems, 90 (1997), 365–368.
23
[12] S. B. Hosseini , J. H. Park and R. Saadati , Intuitionistic fuzzy invariant metric spaces, Int.
24
Journal of Pure Appl. Math. Sci., 2(2005).
25
[13] C. M. Hu , C-structure of FTS. V. fuzzy metric spaces, Journal of Fuzzy Math., 3(1995)
26
711–721.
27
[14] P. C. Kainen , Replacing points by compacta in neural network approximation, Journal of
28
Franklin Inst., 341 (2004), 391–399.
29
[15] E. Kreyszig, Introductory functional analysis with applications, John Wiley and Sons, New
30
York, 1978.
31
[16] R. Lowen, Fuzzy set theory, Kluwer Academic Publishers, Dordrecht, 1996.
32
[17] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004) 1039-
33
[18] R. Saadati and S. M. Vaezpour, Some results on fuzzy Banach spaces, Journal of Appl. Math.
34
Comput., 17 (2005), 475–484.
35
[19] R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons and
36
Fractals, 27 (2006), 331–344.
37
[20] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific Journal of Math., 10 (1960),
38
314–334.
39
[21] Y. Tanaka, Y. Mizno and T. Kado, Chaotic dynamics in Friedmann equation, chaos, soliton
40
and fractals, 24 (2005), 407–422.
41
[22] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338–353.
42
ORIGINAL_ARTICLE
L-FUZZY BILINEAR OPERATOR AND ITS CONTINUITY
The purpose of this paper is to introduce the concept of L-fuzzybilinear operators. We obtain a decomposition theorem for L-fuzzy bilinearoperators and then prove that a L-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by S.E.Rodabaugh (1991).Finally we discuss the continuity of L-fuzzy bilinear operators.
http://ijfs.usb.ac.ir/article_358_af8602c55b74198bfce9a442e63cec84.pdf
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10.22111/ijfs.2007.358
Order-homomorphism
Powerset operator
L-bilinear operator
Molecule
net
Cong-hua
Yan
chyan@njnu.edu.cn
true
1
Department of Mathematics, Nanjing Normal University, Nanjing
Jiangsu, 210097, P.R.China
Department of Mathematics, Nanjing Normal University, Nanjing
Jiangsu, 210097, P.R.China
Department of Mathematics, Nanjing Normal University, Nanjing
Jiangsu, 210097, P.R.China
LEAD_AUTHOR
Jin-xuan
Fang
jxfang@njnu.edu.cn
true
2
Department of Mathematics, Nanjing Normal University, Nanjing
Jiangsu, 210097, P.R.China
Department of Mathematics, Nanjing Normal University, Nanjing
Jiangsu, 210097, P.R.China
Department of Mathematics, Nanjing Normal University, Nanjing
Jiangsu, 210097, P.R.China
AUTHOR
[1] Jin-xuan Fang, Fuzzy linear order-homomorphism and its structures, The Journal of Fuzzy
1
Mathematics, 4(1)(1996), 93–102.
2
[2] Jin-xuan Fang, The continuity of fuzzy linear order-homomorphisms, The Journal of Fuzzy
3
Mathematics, 5(4)(1997), 829–838.
4
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(Dordrecht).
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297–347.
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[12] Cong-hua Yan, Projective limit of L-fuzzy locally convex topological vector spaces, The Journal
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of Fuzzy Mathematics, 7(1999), 765–772.
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spaces, Fuzzy Sets and Systems, 136(2003), 121–126.
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31
ORIGINAL_ARTICLE
TRIANGULAR FUZZY MATRICES
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 skew-symmetric, singular, semi-singular, constant)are defined and a number of properties of these TFMs are presented.
http://ijfs.usb.ac.ir/article_359_0038d4fb0f550de224041cbbbd77caf6.pdf
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75
87
10.22111/ijfs.2007.359
Triangular fuzzy numbers
Triangular fuzzy number arithmetic
Triangular
fuzzy matrices
Triangular fuzzy determinant
Amiya Kumar l
Shyama
true
1
Department of Applied Mathematics
with Oceanology and Computer Programming, Vidyasagar University, Midnapore -
721102, West Bengal, India
Department of Applied Mathematics
with Oceanology and Computer Programming, Vidyasagar University, Midnapore -
721102, West Bengal, India
Department of Applied Mathematics
with Oceanology and Computer Programming, Vidyasagar University, Midnapore -
721102, West Bengal, India
AUTHOR
Madhumangal
Pal
madhumangal@lycos.com
true
2
Department of Applied Mathematics
with Oceanology and Computer Programming, Vidyasagar University, Midnapore -
721102, West Bengal, India
Department of Applied Mathematics
with Oceanology and Computer Programming, Vidyasagar University, Midnapore -
721102, West Bengal, India
Department of Applied Mathematics
with Oceanology and Computer Programming, Vidyasagar University, Midnapore -
721102, West Bengal, India
LEAD_AUTHOR
[1] D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press
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London, 1980.
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[2] H. Hashimoto, Convergence of powers of a fuzzy transitive matrix, Fuzzy Sets and Systems,
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9 (1983), 153-160.
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[3] H. Hashimoto, Canonical form of a transitive fuzzy matrix, Fuzzy Sets and Systems, 11
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(1983), 157-162.
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(1988), 273-276.
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[9] M. Pal, Intuitionistic fuzzy determinant, V.U.J.Physical Sciences, 7 (2001), 87-93.
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Fuzzy Sets, 8(2) (2002), 51-62.
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and Physical Sciences, 19(1)(2005), 39-58.
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[16] A. K. Shyamal and M. Pal, Distances between intuitionistics fuzzy matrices, V. U. J. Physical
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(1994), 83-88.
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[20] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338-353.
34
ORIGINAL_ARTICLE
INTUITIONISTIC FUZZY BOUNDED LINEAR OPERATORS
The object of this paper is to introduce the notion of intuitionisticfuzzy continuous mappings and intuitionistic fuzzy bounded linear operatorsfrom one intuitionistic fuzzy n-normed linear space to another. Relation betweenintuitionistic fuzzy continuity and intuitionistic fuzzy bounded linearoperators are studied and some interesting results are obtained.
http://ijfs.usb.ac.ir/article_361_9c78a3a61bf8f44f026f0d019b06cef9.pdf
2007-04-09T11:23:20
2017-09-20T11:23:20
89
101
10.22111/ijfs.2007.361
fuzzy n-norm
intuitionistic fuzzy n-norm
intuitionistic fuzzy continuous
mapping
intuitionistic fuzzy bounded linear operator
S.
Vijayabalaji
balaji−nandini@rediffmail.com
true
1
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
LEAD_AUTHOR
N.
Thillaigovindan
thillai−n@sify.com
true
2
Department of Mathematics Section, Faculty of Engineering and
Technology, Annamalai University, Annamalainagar-608002, Tamilnadu, India
Department of Mathematics Section, Faculty of Engineering and
Technology, Annamalai University, Annamalainagar-608002, Tamilnadu, India
Department of Mathematics Section, Faculty of Engineering and
Technology, Annamalai University, Annamalainagar-608002, Tamilnadu, India
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Fuzzy Mathematics, 11(3)(2003), 687-705.
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[5] T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems,
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151(2005), 513-547.
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Cal. Math. Soc., 86(1994), 429-436.
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[7] G. Deschrijver and E. Kerre , On the Cartesian product of the intuitionistic fuzzy sets, The
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Journal of Fuzzy Mathematics, 11 (3)(2003), 537-547.
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[8] MS. Elnaschie, On the uncertainty of Cantorian geometry and two-slit experiment, Chaos,
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Soliton and Fractals, 9 (3)(1998), 517-529.
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[9] MS. Elnaschie, On the verications of heterotic strings theory and 1 theory, Chaos, Soliton
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and Fractals,11 (2) (2000), 2397-2407.
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[10] C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems, 48 (1992),
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[11] C. Felbin, The Completion of fuzzy normed linear space, Journal of Mathematical Analysis
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and Applications, 174 (2)(1993), 428-440.
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(1969), 165-189.
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[15] H. Gunawan and M. Mashadi, on n-Normed spaces, International J. Math. & Math. Sci., 27
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(10)(2001), 631-639.
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[16] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), 143-
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[17] S. S. Kim and Y. J. Cho, Strict convexity in linear n-normed spaces, Demonstratio Math.,
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29 (4) (1996), 739-744.
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[18] S. V. Krishna and K. K. M. Sharma, Separation of fuzzy normed linear spaces, Fuzzy Sets
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and Systems, 63 (1994), 207-217.
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[19] R. Malceski, Strong n-convex n-normed spaces, Mat. Bilten, 21 (1997), 81-102.
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31
[21] AL. Narayanan and S. Vijayabalaji, Fuzzy n-normed linear space, 24(2005), 3963-3977.
32
[22] J. H. Park, Intuitionistic fuzzy metric space, Chaos, Solitons and Fractals, 22(2004), 1039-
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[23] G. S. Rhie, B. M. Choi and S. K. Dong, On the completeness of fuzzy normed linear spaces,
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Math. Japonica, 45 (1) (1997), 33-37.
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[24] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math., 10(1960), 314-334.
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[25] S. Vijayabalaji, N. Thillaigovindan and Y. B. Jun, Intuitionistic fuzzy n-normed linear space,
37
Submitted to Bulletin of Korean Mathematical Society, Korea.
38
ORIGINAL_ARTICLE
Persian-translation Vol.4, No.1 April 2007
http://ijfs.usb.ac.ir/article_2911_64fd55c1f871dba2e12a5205e4b5b3d1.pdf
2007-04-30T11:23:20
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105
111
10.22111/ijfs.2007.2911