ORIGINAL_ARTICLE
Cover Vol.7, No.1, February 2010
http://ijfs.usb.ac.ir/article_2882_805c73a895fae89f104edbd1129a9be3.pdf
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10.22111/ijfs.2010.2882
ORIGINAL_ARTICLE
AN INTELLIGENT INFORMATION SYSTEM FOR FUZZY ADDITIVE MODELLING
(HYDROLOGICAL RISK APPLICATION)
In this paper we propose and construct Fuzzy Algebraic Additive Model, for the estimation of risk in various fields of human activities or nature’s behavior. Though the proposed model is useful in a wide range of scientific fields, it was designed for to torrential risk evaluation in the area of river Evros. Clearly the model’s performance improves when the number of parameters and the actual data increases. A Fuzzy Decision Support System was designed and implemented to incorporate the model’s risk estimation capacity and the risk estimation output of the system was compared with the output of other existing methods with very interesting results.
http://ijfs.usb.ac.ir/article_157_4505a193f72c5619791b6d85f1248951.pdf
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10.22111/ijfs.2010.157
Fuzzy additive models
fuzzy algebra
Decision support system
Torrential risk
L
Iliadis
liliadis@fmenr.duth.gr
true
1
Department of Forestry, Management of the Environment & Natural
Resources, Democritus University of Thrace, 193 Padazidou st., 68200, N. Orestiada,
Greece
Department of Forestry, Management of the Environment & Natural
Resources, Democritus University of Thrace, 193 Padazidou st., 68200, N. Orestiada,
Greece
Department of Forestry, Management of the Environment & Natural
Resources, Democritus University of Thrace, 193 Padazidou st., 68200, N. Orestiada,
Greece
LEAD_AUTHOR
S
Spartalis
sspart@pme.duth.gr
true
2
Department of Production Engineering & Management, School of Engineering,
Democritus University of Thrace, University Library Building, 67100Xanthi,
Greece
Department of Production Engineering & Management, School of Engineering,
Democritus University of Thrace, University Library Building, 67100Xanthi,
Greece
Department of Production Engineering & Management, School of Engineering,
Democritus University of Thrace, University Library Building, 67100Xanthi,
Greece
AUTHOR
[1] E. Cox, Fuzzy modeling and genetic algorithms for data mining and exploration, Elsevier
1
Morgan Kaufmann Publishers, USA, 2005.
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[2] C. J. Date, An introduction to database systems, Addison-Wesley, New York, 1990.
3
[3] J. De Vente and J. Poesen, Predicting soil erosion and sediment yield at the basin scale:
4
scale issues and semi-quantitative models , Earth Science Reviews, Elsevier Science, 71(1-2) (2005), 95-125.
5
[4] I. Douglas, Predicting road erosion rates in selectively logged tropical rain forests, Erosion
6
Prediction in Ungauged Basins: Integrating Methods and Techniques (Procecdinss of symposium
7
I-IS01 held during IUGG2003 at Sapporo. July 2003). IAHS Ptibl, 279 (2003).
8
[5] S. Gavrilovic, Engineering of torrents flows and erosion, Special edition, Belgrade, 1972.
9
[6] Z. Gavrilovic, The use of an empirical method (Erosion potential method for calculating
10
sediment production and transportation in unstudied or torrential streams) , International
11
Conference on River Regime: Wallingford, England, 1998.
12
[7] L. Iliadis, F. Maris and D. Marinos, A decision support system using fuzzy relations for the
13
estimation of long-term torrential risk of mountainous watersheds: the case of river evros
14
, Proceeding ICNAAM 2004 Conference, Chalkis, Greece, 2004.
15
[8] M. T. Jones,AI application programming, Thomson Delmar Learning, 2nd Edition, Boston,2005.
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[9] A. Kandel,Fuzzy expert systems, CRC Press Florida, USA, 1992.
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[10] V. Kecman,Learning and soft computing, MIT Press. London England, 2001.
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Man and Cybernetics – Part C: Applications and Reviews,28(3) (1998).
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[12] B. Kosko,Neural networks and fuzzy systems: a dynamical systems approach to machine
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learning intelligence, Englewood Cliff, NJ: Prentice-Hall, 1991.
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[13] D. Kotoulas,Management of torrents I, Publications of the University of Thessaloniki, 1997.
23
[14] E. G. Mansoori, M. J. Zolghadri, S. D. Katebi and H. Mohabatkar,Generating fuzzy rules
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for protein classification, Iranian Journal of Fuzzy Systems, 5(2) (2008).
25
[15] F. Maris and L. Iliadis,A computer system using two membership functions and T-norms
26
for the calculation of mountainous watersheds torrential risk: the case of lakes trixonida and
27
lisimaxia, Book Series: Developments in Plant and Soil Sciences, Book Title: Eco-and Ground
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Bio-Engineering: The Use of Vegetation to Improve Slope Stability, Springer Netherlands,103(2007), 247-254.
29
[16] M. Meidani, G. Habibaghai and S. Katebi,An aggregated fuzzy reliability index for slope
30
stability analysis, Iranian Journal of Fuzzy Systems, 1(1) (2004), 17.
31
[17] R. Satur , Z. Liu and M. Gahegan,Multi-layered FCM’s applied to context dependent learning,
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Proc. IEEE FUZZ-95,2 (1992), 561-568.
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[18] A. K. Shaymal and M. Pal,Triangular fuzzy matrices, Iranian Journal of Fuzzy Systems,4(1)(2007).
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[19] N. Skermer and D. Van Dine,Debris-flow hazards and related phenomena, Springer Berlin,
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(2005), 25-51.
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[20] P. Stefanidis,The torrent problems in mediterranean areas (example from greece), Proc.
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XXIUFRO Congress. Finland, 1995.
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and control, IEEE Trans. Syst. Man. Cybern., 15 (1985), 116-132.
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[23] A. Tazioli,Evaluation of erosion in equipped basins: preliminary results of a comparison
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between the gavrilovic model and direct measurements of sediment transport
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, Environmental Geology, Springer Berlin,56(5) (2009), 825-831.
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[24] R. R. Yager, S. Ovchinnikov, R. M. Tong and H. T. Nguyen,Fuzzy sets and applications:
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selected papers, Wiley New York, 1987.
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Part I: Inf. Sci., 8, 199, Part II: Inf. Sci., 8, 301; Part II: Inf. Sci., 9, 43, 1975.
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[27] H. J. Zimmermann, Fuzzy set theory and its applications, 2nd Edition. Boston: Kluwer, 1991.
51
ORIGINAL_ARTICLE
SUBCLASS FUZZY-SVM CLASSIFIER AS AN EFFICIENT
METHOD TO ENHANCE THE MASS DETECTION IN
MAMMOGRAMS
This paper is concerned with the development of a novel classifier
for automatic mass detection of mammograms, based on contourlet feature
extraction in conjunction with statistical and fuzzy classifiers. In this method,
mammograms are segmented into regions of interest (ROI) in order to extract
features including geometrical and contourlet coefficients. The extracted features
benefit from the superiority of the contourlet method to the state of the
art multi-scale techniques. A genetic algorithm is applied for feature weighting
with the objective of increasing classification accuracy. Although fuzzy classifiers
are interpretable, the majority are order sensitive and suffer from the
lack of generalization. In this study, a kernel SVM is integrated with a nerofuzzy
rule-based classifier to form a support vector based fuzzy neural network
( SVFNN). This classifier benefits from the superior classification power of
SVM in high dimensional data spaces and also from the efficient human-like
reasoning of fuzzy and neural networks in handling uncertainty information.
We use the Mammographic Image Analysis Society (MIAS) standard data
set and the features extracted of the digital mammograms are applied to the
fuzzy-SVM classifiers to assess the performance. Our experiments resulted in
95.6%,91.52%,89.02%, 85.31% classification accuracy for the subclass FSVM,
SVFNN, fuzzy rule based and kernel SVM classifiers respectively and we conclude
that the subclass fuzzy-SVM is superior to the other classifiers.
http://ijfs.usb.ac.ir/article_158_da31701004c02b62a0d1ce107e8ebbb2.pdf
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10.22111/ijfs.2010.158
Mammography
Support vector based fuzzy neural network
Fuzzy
support vector machine
Contourlet
Fatemeh
Moayedi
moayyedi,boostani,kazemi,katebi@cse.shirazu.ac.ir
true
1
Reza Boostani, Ali Reza Kazemi and Serajodin Katebi, Vision and
Image Processing Laboratory, School of Electrical and Computer Engineering, Shiraz
University, Shiraz, Iran
Reza Boostani, Ali Reza Kazemi and Serajodin Katebi, Vision and
Image Processing Laboratory, School of Electrical and Computer Engineering, Shiraz
University, Shiraz, Iran
Reza Boostani, Ali Reza Kazemi and Serajodin Katebi, Vision and
Image Processing Laboratory, School of Electrical and Computer Engineering, Shiraz
University, Shiraz, Iran
LEAD_AUTHOR
Ebrahim
Dashti
sayed.dashti@jia.ac.ir
true
2
Board of Science, Azad Universitiy Branch of Jahrom, Iran
Board of Science, Azad Universitiy Branch of Jahrom, Iran
Board of Science, Azad Universitiy Branch of Jahrom, Iran
AUTHOR
[1] R. A. Aliev, B. G. Guirimov and R. R. Aliev,A neuro-fuzzy object classifier with modified
1
distance measure estimator, Iranian Journal of Fuzzy Systems, 1(1) (2004), 5-15.
2
[2] K. Bovis, S. Singh, J. Fieldsend and C. Pinder,Identification of masses in digital mammograms
3
with MLP and RBF nets, IEEE Trans. on Image Processing, 1 (2005), 342-347.
4
[3] E. J. Candes and D. L. Donoho,Curvelets: a surprisingly effective non adaptive representation
5
for objects with edges, Saint-Malo Proceedings, Nashville, TN: Vanderbilt Univ, 2000.
6
[4] O. Cordon and M. J. del Jesus and F. Herrera,Genetic learning of fuzzy rule based classification
7
systems cooperating with fuzzy reasoning methods, Technical Report, DECSAI-970130,1997.
8
[5] M. N. Do and M. Vetterli,The contourlet transform: an efficient directional multi-resolution
9
image representation, IEEE Trans. on Image Processing, 14(12) (2005), 2091-2106.
10
[6] I. El-Naqa, Y. Yang, M. Wernick, N. Galatsanos and R. Nishikawa,A support vector machine
11
approach for detection of microcalcifications, IEEE Trans. on Medical Imaging, 21(12)(2002), 1552-1563.
12
[7] E. A. Fischer, J. Y. Lo and M. K. Markey,Bayesian networks of BI-RADS descriptors for
13
breast lesion classification, IEEE EMBS, San Francisco, 4 (2004), 3031-3034.
14
[8] O. J. Freixenet, A. Bosch, D. Raba and R. Zwiggelaar,Automatic classification of breast
15
tissue, Lecture Notes in Computer Science, Pattern Recognition and Image Analysis, (2000),431-438.
16
[9] W. H. Land, J. L. Wong Daniel, W. McKee, T. Masters and F. R Anderson,Breast cancer
17
computer aided diagnosis (CAD) using a recently developed SVM/GRNN oracle hybrid, IEEE
18
International Conference on Systems, Man and Cybernetics, 2003.
19
[10] C. T. Lin, C. M. Yeh, S. F. Liang, J. F. Chung and N. Kumar, Support-vector-based fuzzy
20
neural network for pattern classification, IEEE Trans. on Fuzzy Systems, 14(1) (2006), 31-41.
21
[11] A. O. Malagelada, Automatic mass segmentation in mammographic images, PhD Thesis,
22
Universitat de Girona, Spain, 2004.
23
[12] E. G. Mansoori, M. J. Zolghadri and S. D. Katebi,Using distribution of data to enhance
24
prformance of fuzzy classification systems, Iranian Journal of Fuzzy Systems, 4(1) (2007),21-36.
25
[13] E. G. Mansoori, M. J. Zolghadri, S. D. Katebi, H. Mohabatkar, R. Boostani and M. H.Sadreddini,
26
Generating fuzzy for protein classification, Iranian Journal of Fuzzy Systems,5(2)(2008), 21-33.
27
[14] F. Moayedi, Z. Azimifar, R. Boostani and S. Katebi,Contourlet based mammography mass
28
classification, Lecture Notes in Computer Science, Image Analysis and Recognition, 4633(2007), 923-934.
29
[15] F. Moayedi, R. Boostani, Z. Azimifar and S. Katebi,A support vector based fuzzy neural network
30
approach for mass classification in mammography, International Conference on Digital
31
Signal Processing, Britain, 2007.
32
[16] R. Mousa, Q. Munib and A. Mousa,Breast cancer diagnosis system based on wavelet analysis
33
and fuzzy-neural netwrok, IEEE Trans. on Image Processing, 28(4) (2005), 713-723.
34
[17] D. Y. Po and N. Do, Directional multiscale modeling of images using the contourlet transform,
35
IEEE Trans. on Image Processing, (2006), 1-11.
36
[18] D. Raba, A. Oliver, J. Marti, M. Peracaula and J. Espunya, Breast segmentation with pectoral
37
muscle suppression on digital mammograms, Springer-Verlag: Medical Imaging: Pattern
38
Recognition and Image Analysis, 3523 (2005), 471-478.
39
[19] M. Roffilli, Advanced machine learning techniques for digital mammography, Technical Report,
40
Department of Computer Science University of Bologna, Italy, 2006.
41
[20] M. S. B. Sehgal, I. Gondal and L. Dooley, Support vector machine and generalized regression
42
neural network based classification fusion models for cancer diagnosis, proceedings in Fourth
43
IEEE International Conference on Hybrid Intelligent System, Computer Society, 2004.
44
[21] L. Semler and L. Dettori, A comparison of wavelet-based and ridgelet-based texture classification
45
of tissues in computed tomography, International Conference on Computer Vision
46
Theory and Applications, 2006.
47
[22] L. Semler, L. Dettori and J. Furst, Wavelet-based texture classification of tissues in computed
48
tomography, IEEE International Symposium on Computer-Based Medical Systems, 2005.
49
[23] J. L. Starck, E. J. Candes and D. L. Donoho, The curvelet transform for image denoising,
50
IEEE Trans. on Image Processing, 11(6) (2002), 670-684.
51
[24] C. Varelaa, P. G. Tahocesb, A. J. Mndezc, M. Soutoa and J. J. Vidala, Computerized detection
52
of breast masses in digitized mammograms, Computers in Biology and Medicine, 37(2)(2007), 214-226.
53
[25] W. Xiaodan and W. Chongming, Using membership function to improve multi-class SVM
54
classification, ICSP Proceeding, China, 2004.
55
[26] Z. Yu and C. Bajaj, A fast and adaptive for image contrast enhancement, IEEE International
56
Conference on Image Processing, 2004.
57
[27] M. Zhu and A. M. Martinez, Subclass discriminant analysis, IEEE Trans. on Pattern Analysis
58
and Machine Intelligence, 28(8) (2006), 1247-1286.
59
ORIGINAL_ARTICLE
THE URYSOHN AXIOM AND THE COMPLETELY HAUSDORFF
AXIOM IN L-TOPOLOGICAL SPACES
In this paper, the Urysohn and completely Hausdorff axioms in general topology are generalized to L-topological spaces so as to be compatible with pointwise metrics. Some properties and characterizations are also derived
http://ijfs.usb.ac.ir/article_159_a392d427a40e4380b76776825363be68.pdf
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10.22111/ijfs.2010.159
Fu-Gui
Shi
fuguishi@bit.edu.cn or f.g.shi@263.net
true
1
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing, 100081, P. R. China
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing, 100081, P. R. China
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing, 100081, P. R. China
LEAD_AUTHOR
Peng
Chen
chenpengbeijing@sina.com
true
2
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing, 100081, P. R. China
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing, 100081, P. R. China
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing, 100081, P. R. China
AUTHOR
[1] S. L. Chen,Fuzzy Urysohn spaces and $alpha$-stratified fuzzy Urysohn spaces, Proceedings of the
1
Fifth IFSA World Congress I, Korea, (1993), 453-456.
2
[2] S. L. Chen and Z. X.Wu,Urysohn separation property in topological molecular lattices, Fuzzy
3
Sets and Systems,123(2) (2001), 177-184.
4
[3] Z. Deng,Fuzzy pseudo-metric space, J. Math. Anal. Appl., 86 (1982), 74-95.
5
[4] P. Dwinger,Characterizations of the complete homomorphic images of a completely distributive
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complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403-414.
7
[5] M. A. Erceg,Metric space in fuzzy set theory, J. Math. Anal. Appl., 69 (1979), 205-230.
8
[6] J. Fang,H()-completely Hausdorff axiom on L-topological spaces, Fuzzy Sets and Systems,
9
140(3)(2003), 475-469.
10
[7] J. Fang and Y. Yue,Urysohn closedness on completely distributive lattices, Fuzzy Sets and
11
Systems,144(3) (2004), 367-381.
12
[8] M. H. Ghanim, O. A. Tantawy and F. M. Selim,On lower separation axioms, Fuzzy Sets
13
and Systems,85(3) (1997), 385-389.
14
[9] G. Gierz and et al.,A compendium of continuous lattices, Springer Verlag, Berlin, 1980.
15
[10] U. H¨ohle, S. E. Rodabaugh and eds,Mathematics of fuzzy sets: logic, topology and
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measure theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers
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(Boston/Dordrecht/London),3 (1999).
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[11] C. Hu,Fuzzy topological space, J. Math. Anal. Appl., 110 (1985), 141-178.
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[12] B. Hutton,Uniformities on fuzzy topological spaces, J. Math. Anal. Appl., 58 (1977), 559-571.
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[13] B. Hutton,Normality in fuzzy topological spaces, J. Math.Anal.Appl., 50 (1975), 74-79.
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[14] B. Hutton and I. Reilly,Separation axioms in fuzzy topological spaces, Fuzzy Sets and Systems,
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3(1)(1980), 93-104.
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[15] O. Kaleva and S. Seikkala,On fuzzy metric spaces, Fuzzy Sets and Systems, 12(3) (1984),
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[16] I. Kramosil and J. Michalek,Fuzzy metric and statistical metric spaces, Kybernetica, 11(1975), 326-334.
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[17] W. Kotz´e,Lifting of sobriety concepts with particular reference to (L,M)-topological spaces,
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in S. E. Rodabaugh, E. P. Klement and eds., Topological and Algebraic Structures in Fuzzy
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Sets, Kluwer Academic, Publishers (Boston/Dordrecht/London), 2003.
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[18] T. Kubiak,On L-Tychonoff spaces, Fuzzy Sets and Systems, 73(1) (1995), 25-53.
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[19] S. G. Li,H($lambda$)-completely regular L-fuzzy sets and their applications, Fuzzy Sets and Systems,
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95(2)(1998), 223-231
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[20] S. G. Li,Separation axioms in L-fuzzy topological spaces (I): T0 and T1, Fuzzy Sets and
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Systems,116(3) (2000), 377-383.
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[21] Y. M. Liu and M. K. Luo,Pointwise characterizations of complete regularity and embedding
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theorem in fuzzy topological spaces, Science in China Ser. A, 26 (1983), 138-147.
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[22] Y. M. Liu and M. K. Luo,Fuzzy topology, World Scientific Publishing, Singapore, 1997.
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[23] R. Lowen and A. K. Srivastava,Sierpinski objects in subcategories of FTS, Quaestiones
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[24] R. Lowen and A. K. Srivastava,FTS0: the epireflective hull of the Sierpinski object in FTS,
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Fuzzy Sets and Systems,29(2) (1989), 171-176.
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[25] P. M. Pu and Y. M. Liu,Fuzzy topology I, neighborhood structure of a fuzzy point and
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Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599.
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[26] A. Pultr and S. E. Rodabaugh,Lattice- valued frames, functor categories and classes of sober
43
spaces, in S. E. Rodabaugh, E. P. Klement and eds., Topological and Algebraic Structures in
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Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends
45
in Logic, Kluwer Academic Publishers (Boston/Dordrecht/London),20 (2003), 153-187.
46
[27] A. Pultr and S. E. Rodabaugh,Examples for different sobrieties in fixed-basis topology, in S.
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E. Rodabaugh, E. P. Klement and eds., Topological and Algebraic Structures in Fuzzy Sets:
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A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic,
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Kluwer Academic Publishers (Boston/Dordrecht/London),20 (2003), 427-440.
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[28] S. E. Rodabaugh,The Hausdorff separation axiom for fuzzy topological spaces, Topology and
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its Applications,11 (1980), 319-334.
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11(2)(1983), 163-183.
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[30] S. E. Rodabaugh,A point-set lattice-theoretic framework T for topology which contains LOC
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as a subcategory of singleton subspaces and in which there are general classes of stone representation
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and compactification theorems, First Printing February 1986, Second Printing
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April 1987, Youngstown State University Printing Office, Youngstown, Ohio, USA.
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[31] S. E. Rodabaugh,Point-set lattice-theoretic topology, Fuzzy Sets and Systems, 40(2) (1991),
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[32] S. E. Rodabaugh,Categorical frameworks for Stone representation theories, in S. E. Rodabaugh,
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E. P. Klement, U. H¨ohle and eds., Applications of Category Theory to Fuzzy Subsets,
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Theory and Decision Library: Series B: Mathematical and Statistical Methods, Kluwer Academic
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Publishers (Boston/Dordrecht/London),14 (1992), 177-231.
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[33] S. E. Rodabaugh,Applications of localic separation axioms, compactness axioms, representations
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and compactifications to poslat topological spaces, Fuzzy Sets and Systems, 73(1)
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(1995), 55-87.
66
[34] S. E. Rodabaugh,Separation axioms: representation theorems, compactness and compactifications,
67
in U. H¨ohle, S. E. Rodabaugh and eds., Mathematics of Fuzzy Sets: Logic, Topology
68
and Measure Theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers,
69
Boston, Dordrecht, London,3 (1999), 481-552.
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[35] F. G. Shi and L. J. Zhao,Pointwise characterizations of HR-regularity, J. Harbin Sci. Technol.
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Univ., in Chinese,1 (1995), 84-85.
72
[36] F. G. Shi,Pointwise uniformities in L-fuzzy set theory, Fuzzy Sets and Systems, 98(1)(1998), 141-146.
73
[37] F. G. Shi,Fuzzy pointwise complete regularity and imbedding theorem, J. Fuzzy Math., 2(1999), 305-310.
74
[38] F. G. Shi,L-fuzzy pointwise metric spaces and T2 axiom, J. Capital Normal University, in
75
Chinese,1 (2000), 8-12.
76
[39] F. G. Shi,Pointwise pseudo-metrics in L-fuzzy set theory, Fuzzy Sets and Systems, 121(2)
77
(2001),209-216.
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[40] F. G. Shi and C. Y. Zheng,Metrization theorems in L-topological spaces, Fuzzy Sets and
79
Systems,149(3) (2005), 455-471.
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[41] F. G. Shi,A new notion of fuzzy compactness in L-topological spaces, Information Sciences,
81
173(2005), 35-48.
82
[42] F. G. Shi,Pointwise pseudo-metric on the L-real line, Iranian Journal of Fuzzy Systems,
83
2(2)(2005), 15-20.
84
[43] F. G. Shi,A new approach to L-T2, L-Urysohn and L-completely hausdorff axioms, Fuzzy
85
Sets and Systems,157(6) (2006), 794-803.
86
[44] G. J. Wang,Theory of topological molecular lattices, Fuzzy Sets and Systems, 47(3) (1992),
87
[45] G. J. Wang,Theory of L-fuzzy topological spaces, Shaanxi Normal University Press, Xi’an,
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93
Sinica,36 (1993), 68-73.
94
ORIGINAL_ARTICLE
CHARACTERIZATION OF L-FUZZIFYING MATROIDS BY
L-FUZZIFYING CLOSURE OPERATORS
An L-fuzzifying matroid is a pair (E, I), where I is a map from2E to L satisfying three axioms. In this paper, the notion of closure operatorsin matroid theory is generalized to an L-fuzzy setting and called L-fuzzifyingclosure operators. It is proved that there exists a one-to-one correspondencebetween L-fuzzifying matroids and their L-fuzzifying closure operators.
http://ijfs.usb.ac.ir/article_160_b9a40ba3ae101fd311f2d462be3c2c23.pdf
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10.22111/ijfs.2010.160
L-fuzzifying matroid
L-fuzzifying rank function
L-fuzzifying closure
operator
Lan
Wang
wanglantongtong@126.com or wanglan@bit.edu.cn
true
1
Department of Mathematics, Beijing Institute of Technology, Beijing
100081, P.R.China; Department of Mathematics, Mudanjiang Teachers college, Heilongjiang
157012, P.R.China
Department of Mathematics, Beijing Institute of Technology, Beijing
100081, P.R.China; Department of Mathematics, Mudanjiang Teachers college, Heilongjiang
157012, P.R.China
Department of Mathematics, Beijing Institute of Technology, Beijing
100081, P.R.China; Department of Mathematics, Mudanjiang Teachers college, Heilongjiang
157012, P.R.China
LEAD_AUTHOR
Fu-Gui
Shi
fuguishi@bit.edu.cn or f.g.shi@263.net
true
2
Department of Mathematics, Beijing Institute of Technology, Beijing,
100081, P. R. China
Department of Mathematics, Beijing Institute of Technology, Beijing,
100081, P. R. China
Department of Mathematics, Beijing Institute of Technology, Beijing,
100081, P. R. China
AUTHOR
[1] A. Borumand Saeid, Interval-valued fuzzy B-algebras, Iranian Journal of Fuzzy Systems, 3
1
(2006), 63-74.
2
[2] P. Dwinger, Characterizations of the complete homomorphic images of a completely distributive
3
complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403-414.
4
[3] J. Fortin, A. Kasperski and P. Zielinski, Efficient methods for computing optimality degrees
5
of elements in fuzzy weighted matroids, in I. Bloch, A. Petrosino, A. Tettamanzi and eds.,
6
Fuzzy Logic and Applications, The 6th International Workshop, WILF, Crema, Italy, (2005),
7
[4] H. L. Huang and F. G. Shi, L-fuzzy numbers and their properties, Information Sciences, 178
8
(2008), 1141-1151.
9
[5] A. Kasperski and P. Zielinski, A possibilistic approach to combinatorial optimization problems
10
on fuzzy-valued matroids, in I. Bloch, A. Petrosino, A. Tettamanzi and eds., Fuzzy Logic and
11
Applications, The 6th International Workshop, WILF, Crema, Italy, (2005), 46-52.
12
[6] A. Kasperski and P. Zielinski, On combinatorial optimization problems on matroids with
13
uncertain weights, European Journal of Operational Research, 177 (2007), 851-864.
14
[7] A. Kasperski and P. Zielinski, Using gradual numbers for solving fuzzy-valued combinatorial
15
optimization problems, in P. Melin, O. Castillo, L.T. Aguilar, J. Kacprzyk, W. Pedrycz and
16
eds., Foundations of Fuzzy Logic and Soft Computing, The 12th International Fuzzy Systems
17
Association World Congress, Cancun, Mexico, (2007), 656-665.
18
[8] S. P. Li, Z. Fang and J. Zhao, P2-connectedness in L-topological spaces, Iranian Journal of
19
Fuzzy Systems, 2 (2005), 29-36.
20
[9] G. N. Raney, Completely distributive complete lattices, Proceedings of the American Mathematical
21
Society, 3 (1952), 677-680.
22
[10] F. G. Shi, Theory of L -nested sets and L -nested sets and its applications, Fuzzy Systems
23
and Mathematics, 4 (1995), 65-72.
24
[11] F. G. Shi, L-fuzzy relation and L-fuzzy subgroup, The Journal of Fuzzy Mathematics, 8
25
(2000), 491-499.
26
[12] F. G. Shi, A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160
27
(2009), 696-705.
28
[13] G. J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992),
29
[14] D. J. A. Welsh, Matroid theory, Academic Press, London, 1976.
30
ORIGINAL_ARTICLE
FUZZY QUASI-METRIC VERSIONS OF A THEOREM OF
GREGORI AND SAPENA
We provide fuzzy quasi-metric versions of a fixed point theorem ofGregori and Sapena for fuzzy contractive mappings in G-complete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.
http://ijfs.usb.ac.ir/article_161_614217821ae8b59f4fcebbf4ac3ae84e.pdf
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59
64
10.22111/ijfs.2010.161
Fuzzy metric space
Non-archimedean fuzzy quasi-metric
Gbicomplete
Domain of words
Dorel
Mihet
mihet@math.uvt.ro
true
1
Department of Mathematics, West University of Timisoara, Bv. V.
Parvan 4, Timisoara, Romania
Department of Mathematics, West University of Timisoara, Bv. V.
Parvan 4, Timisoara, Romania
Department of Mathematics, West University of Timisoara, Bv. V.
Parvan 4, Timisoara, Romania
LEAD_AUTHOR
[1] P. Flajolet, Analytic analysis of algorithms, in Lecture Notes in Computer Science, Springer,
1
Berlin, 623 (1992), 186-210.
2
[2] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1983), 385-389.
3
[3] M. Grabiec, Y. J. Cho and V. Radu, On nonsymmetric topological and probabilistic structures,
4
New York, Nova Science Publishers, Inc., 2006.
5
[4] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,
6
64 (1994), 395-399.
7
[5] V. Gregori and A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and
8
Systems, 125 (2002), 245-252.
9
[6] V. Gregori and S. Romaguera, Fuzzy quasi-metric spaces, Appl. Gen. Topology, 5 (2004),
10
[7] O. Hadˇzi´c and E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Academic
11
Publishers, Dordrecht, 2001.
12
[8] O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11
13
(1975), 336-344.
14
[9] D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems,
15
144 (2004), 431-439.
16
[10] D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems,
17
158 (2007), 915-921.
18
[11] M. Rafi and M. S. M. Noorani, Fixed point theorem in intuitionistic fuzzy metric spaces,
19
Iranian Journal of Fuzzy Systems, 3(1) (2006), 23-29.
20
[12] A. Razani and M. Shirdaryazdi, Erratum to:” On fixed point theorems of Gregori and
21
Sapena”, Fuzzy Sets and Systems, 153(2) (2005), 301-302.
22
[13] A. Razani, A contraction theorem in fuzzy metric spaces, Fixed Point Theory Applications,
23
3 (2005), 257-265.
24
[14] S. Romaguera, A. Sapena and P. Tirado, The banach fixed point theorem in fuzzy quasi-metric
25
spaces with application to the domain of words, Topology and its Applications, 154(10)
26
(2007), 2196-2203.
27
[15] R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for -weakly commuting
28
maps in L-fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5(1) (2008), 47-54.
29
[16] B. Schweizer and A. Sklar, Probabilistic metric spaces, North-Holland, Amsterdam, 1983.
30
[17] R.Vasuki and P. Veeramani, Fixed point theorems and Cauchy sequences in fuzzy metric
31
spaces, Fuzzy Sets and Systems, 135 (2003), 415-417.
32
[18] T. Zikic, On fixed point theorems of Gregori and Sapena, Fuzzy Sets and Systems, 144(3)
33
(2004), 421-429.
34
ORIGINAL_ARTICLE
BI-MATRIX GAMES WITH INTUITIONISTIC FUZZY GOALS
In this paper, we present an application of intuitionistic fuzzyprogramming to a two person bi-matrix game (pair of payoffs matrices) for thesolution with mixed strategies using linear membership and non-membershipfunctions. We also introduce the intuitionistic fuzzy(IF) goal for a choiceof a strategy in a payoff matrix in order to incorporate ambiguity of humanjudgements; a player wants to maximize his/her degree of attainment of the IFgoal. It is shown that this solution is the optimal solution of a mathematicalprogramming problem. Finally, we present a numerical example to illustratethe methodology.
http://ijfs.usb.ac.ir/article_162_2cfcb7b16ba7eb37bf63f20ae72666b8.pdf
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65
79
10.22111/ijfs.2010.162
Bi-matrix game
Nash equilibrium
Intuitionistic fuzzy sets
Fuzzy
optimization
Intuitionistic fuzzy optimization
Prasun Kumar
Nayak
nayak prasun@rediffmail.com
true
1
Department of Mathematics, Bankura Christian College,
P.O.+ Dist- Bankura, West Bengal,722101, India
Department of Mathematics, Bankura Christian College,
P.O.+ Dist- Bankura, West Bengal,722101, India
Department of Mathematics, Bankura Christian College,
P.O.+ Dist- Bankura, West Bengal,722101, India
LEAD_AUTHOR
Madhumangal
Pal
mmpalvu@gmail.com
true
2
Department of Applied Mathematics with Oceanology and Computer
Programming, Vidyasagar University, Midnapore-721 102, India
Department of Applied Mathematics with Oceanology and Computer
Programming, Vidyasagar University, Midnapore-721 102, India
Department of Applied Mathematics with Oceanology and Computer
Programming, Vidyasagar University, Midnapore-721 102, India
AUTHOR
[1] K. Atanassov, Intuitionistic fuzzy sets: theory and applications, Physica-Verlag, 1999.
1
[2] P. P. Angelov,Optimization in an intuitinistic fuzzy enviornment, Fuzzy Sets and Systems,
2
86 (1997), 299-306.
3
[3] C. R. Bector, S. Chandra and V. Vijay, Bi-matrix games with fuzzy payoffs and fuzzy goals,
4
Fuzzy Optimization and Decision Making, 3 (2004), 327-344.
5
[4] T. Basar and G. J. Olsder, Dynamic non-cooperative game theory, Academic Press, New
6
York, 1995.
7
[5] L. Campos, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets and
8
Systems, 32 (1989), 275-289.
9
[6] D. Dubois and H. Prade, Fuzzy sets and systems, Academic Press, New York, 1980.
10
[7] T. Maeda, Characterization of the equilibrium strategy of bi-matrix games with fuzzy payoffs,
11
Journal of Mathematical Analysis and Applications, 251 (2000), 885-896.
12
[8] J. V. Neumann and O. Morgenstern, Theory of games and economic behaviour, Princeton
13
University Press, Princeton, New Jersey, 1944 .
14
[9] J. F. Nash, Non cooperative games, Annals of Mathematics, 54 (1951), 286-295.
15
[10] P. K. Nayak and M. Pal, Solution of interval games using graphical method, Tamsui Oxford
16
Journal of Mathematical Sciences, 22(1) (2006), 95-115.
17
[11] P. K. Nayak and M. Pal, Bi-matrix games with intuitionistic fuzzy payoffs, Notes on Intuitionistic
18
Fuzzy Sets, 13(3) (2007), 1-10.
19
[12] P. K. Nayak and M. Pal, Bi-matrix games with interval payoffs and its Nash equilibrium
20
strategy, Asia specific Journal of Operational Research, 26(2) (2009), 285-305.
21
[13] P. K. Nayak and M. Pal, Bi-matrix games with interval payoffs and its Nash equyilibrium
22
strategy, Journal of Fuzzy Mathematics, 17(2) (2009).
23
[14] Z. Peng, L. Dagang and W. Guangyuan, Idea and principle of intuitionistic fuzzy optimization,
24
htpp://www.paper.edu.cn.
25
[15] S. K. Roy, M. P. Biswal and R. N. Tiwari, An approach to multi-objective bimatrix games of
26
Nash equilibrium solutions, Ricerca Operativa , 30(93) (2001), 47-64.
27
[16] M. Sakawa and I. Nishizaki, Max-min solution for fuzzy multiobjective matrix games, Fuzzy
28
Sets and Systems, 67 (1994), 53-69.
29
[17] M. Sakawa and I. Nishizaki, Equilibrium solution in bi-matrix games with fuzzy payoffs,
30
Japanse Fuzzy Theory and Systems, 9(3) (1997), 307-324.
31
[18] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-352.
32
ORIGINAL_ARTICLE
CATEGORICAL RELATIONS AMONG MATROIDS, FUZZY
MATROIDS AND FUZZIFYING MATROIDS
The aim of this paper is to study the categorical relations betweenmatroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids.It is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. The category of matroids can be embedded in that offuzzifying matroids as a simultaneously concretely reflective and coreflectivesubcategory.
http://ijfs.usb.ac.ir/article_163_26f26b535f5ffeeed74f751fe9378466.pdf
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81
89
10.22111/ijfs.2010.163
Matroid
Fuzzy matroid
Closed fuzzy matroid
Fuzzifying matroid.
This paper is supported by the national natural science foundation of china(10926055)
Ling-Xia
Lu
lulingxia1214@gmail.com
true
1
School of Mathematics and Science, Shijiazhuang University of Technology,
Shijiazhuang 050031, P.R. China
School of Mathematics and Science, Shijiazhuang University of Technology,
Shijiazhuang 050031, P.R. China
School of Mathematics and Science, Shijiazhuang University of Technology,
Shijiazhuang 050031, P.R. China
LEAD_AUTHOR
Wei-Wei
Zheng
zww@nwpu.edu.cn
true
2
School of Science, Xi’an Polytechnic University, Xi’an 710048, P.R.
China
School of Science, Xi’an Polytechnic University, Xi’an 710048, P.R.
China
School of Science, Xi’an Polytechnic University, Xi’an 710048, P.R.
China
AUTHOR
[1] J. Ad´amek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New
1
York, 1990.
2
[2] K. R. Bhutani, J. Mordeson and A. Rosenfeld, On degrees of end nodes and cut nodes in
3
fuzzy graphs, Iranian Journal of Fuzzy Systems, 1 (2004), 57-64.
4
[3] J. Edmonds, Matroids and the greedy algorithm, Mathematical Programming, 1 (1971), 125-
5
[4] D. Gale, Optimal assignments in an ordered set: an application of matroid theory, Journal
6
of Combinatoral Theory, 4 (1968), 176-180.
7
[5] R. Goetschel and W. Voxman, Bases of fuzzy matroids, Fuzzy Sets and Systems, 31 (1989),
8
[6] R. Goetschel and W. Voxman, Fuzzy circuits, Fuzzy Sets and Systems, 32 (1989), 35-43.
9
[7] R. Goetschel and W. Voxman, Fuzzy matroids, Fuzzy Sets and Systems, 27 (1988), 291-302.
10
[8] R. Goetschel and W. Voxman, Fuzzy rank functions, Fuzzy Sets and Systems, 42 (1991),
11
[9] S. G. Li, X. Xin and Y. L. Li, Closure axioms for a class of fuzzy matroids and the co-tower
12
of matroids, Fuzzy Sets and Systems, 158 (2007), 1246-1257.
13
[10] J. G. Oxley, Matroid Theory, Oxford Universty Press, 1992.
14
[11] F. G. Shi, A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160
15
(2009), 696-705.
16
[12] M. S. Ying, A new approach to fuzzy topologies (I), Fuzzy Sets and Systems, 39 (1991),
17
ORIGINAL_ARTICLE
SOME FIXED POINT THEOREMS FOR SINGLE AND MULTI
VALUED MAPPINGS ON ORDERED NON-ARCHIMEDEAN
FUZZY METRIC SPACES
In the present paper, a partial order on a non- Archimedean fuzzymetric space under the Lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.
http://ijfs.usb.ac.ir/article_165_dedba155defd976c6a33406b81aa9208.pdf
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91
96
10.22111/ijfs.2010.165
Fixed point
Partial order
Fuzzy metric space
Ishak
Altun
ialtun@kku.edu.tr, ishakaltun@yahoo.com
true
1
Department of Mathematics, Faculty of Science and Arts, Kirikkale
University, 71450 Yahsihan, Kirikkale , Turkey
Department of Mathematics, Faculty of Science and Arts, Kirikkale
University, 71450 Yahsihan, Kirikkale , Turkey
Department of Mathematics, Faculty of Science and Arts, Kirikkale
University, 71450 Yahsihan, Kirikkale , Turkey
LEAD_AUTHOR
[1] S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung and S. M. Kang, Coincidence point and
1
minimization theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 88 (1997), 119-128.
2
[2] Y. J. Cho, Fixed points in fuzzy metric spaces, J. Fuzzy Math., 5 (1997), 949-962.
3
[3] J. X. Fang, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 46
4
(1992), 107- 113.
5
[4] Y. Feng and S. Liu, Fixed point theorems for multi-valued increasing operators in partially
6
ordered spaces, Soochow J. Math., 30(4) (2004), 461-469.
7
[5] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,
8
64 (1994), 395-399.
9
[6] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389.
10
[7] V. Gregori and A. Sapena, On fixed-point theorem in fuzzy metric spaces, Fuzzy Sets and
11
Systems, 125 (2002), 245-252.
12
[8] O. Hadzic, Fixed point theorems for multi-valued mappings in some classes of fuzzy metric
13
spaces, Fuzzy Sets and Systems, 29 (1989), 115-125.
14
[9] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
15
[10] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11
16
(1975), 326-334.
17
[11] D. Mihet, A banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems,
18
114 (2004), 431- 439.
19
[12] D. Mihet, On the existence and the uniqueness of fixed points of Sehgal contractions, Fuzzy
20
Sets and Systems, 156 (2005), 135-141.
21
[13] D. Mihet, Fuzzy - contractive mappings in Non-archimedean fuzzy metric spaces, Fuzzy
22
Sets and Systems, 159 (2008), 739-744.
23
[14] S. N. Mishra , S. N. Sharma and S. L. Singh, Common fixed points of maps in fuzzy metric
24
spaces, Internat. J. Math. Math. Sci., 17 (1994), 253-258.
25
[15] V. Radu, Some remarks on the probabilistic contractions on fuzzy Menger spaces, The Eighth
26
International Conference on Appl. Math. Comput. Sci., Cluj-Napoca, Automat. Comput.
27
Appl. Math., 11 (2002) 125-131.
28
[16] M. Rafi and M. S. M. Noorani, Fixed point theorem on intuitionistic fuzzy metric spaces,
29
Iran. J. Fuzzy Syst., 3(1) (2006), 23-29.
30
[17] R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for -weakly commuting
31
maps in L-fuzzy metric spaces, Iran. J. Fuzzy Syst., 5(1) (2008), 47-53.
32
[18] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334.
33
[19] S. Sedghi, K. P. R. Rao and N. Shobe, A common fixed point theorem for six weakly compatible
34
mappings in M-fuzzy metric spaces, Iran. J. Fuzzy Syst., 5(2) (2008), 49-62.
35
[20] Z. Q. Xia and F. F. Gou, Fuzzy metric spaces, J. Appl. Math. Computing, 16(1-2) (2004),
36
ORIGINAL_ARTICLE
Persian-translation Vol.7, No.1, February 2010
http://ijfs.usb.ac.ir/article_2883_7ccdb12e0be3e8f2b2dbcd7ece66e8e3.pdf
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99
106
10.22111/ijfs.2010.2883