2010
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Cover Vol.7, No.1, February 2010
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AN INTELLIGENT INFORMATION SYSTEM FOR FUZZY ADDITIVE MODELLING
(HYDROLOGICAL RISK APPLICATION)
AN INTELLIGENT INFORMATION SYSTEM FOR FUZZY ADDITIVE MODELLING
(HYDROLOGICAL RISK APPLICATION)
2
2
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.
1
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.
1
14
L
Iliadis
L
Iliadis
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
Greece
liliadis@fmenr.duth.gr
S
Spartalis
S
Spartalis
Department of Production Engineering & Management, School of Engineering,
Democritus University of Thrace, University Library Building, 67100Xanthi,
Greece
Department of Production Engineering & Management,
Greece
sspart@pme.duth.gr
Fuzzy additive models
fuzzy algebra
Decision support system
Torrential risk
[[1] E. Cox, Fuzzy modeling and genetic algorithms for data mining and exploration, Elsevier ##Morgan Kaufmann Publishers, USA, 2005. ##[2] C. J. Date, An introduction to database systems, AddisonWesley, New York, 1990. ##[3] J. De Vente and J. Poesen, Predicting soil erosion and sediment yield at the basin scale: ##scale issues and semiquantitative models , Earth Science Reviews, Elsevier Science, 71(12) (2005), 95125. ##[4] I. Douglas, Predicting road erosion rates in selectively logged tropical rain forests, Erosion ##Prediction in Ungauged Basins: Integrating Methods and Techniques (Procecdinss of symposium ##IIS01 held during IUGG2003 at Sapporo. July 2003). IAHS Ptibl, 279 (2003). ##[5] S. Gavrilovic, Engineering of torrents flows and erosion, Special edition, Belgrade, 1972. ##[6] Z. Gavrilovic, The use of an empirical method (Erosion potential method for calculating ##sediment production and transportation in unstudied or torrential streams) , International ##Conference on River Regime: Wallingford, England, 1998. ##[7] L. Iliadis, F. Maris and D. Marinos, A decision support system using fuzzy relations for the ##estimation of longterm torrential risk of mountainous watersheds: the case of river evros ##, Proceeding ICNAAM 2004 Conference, Chalkis, Greece, 2004. ##[8] M. T. Jones,AI application programming, Thomson Delmar Learning, 2nd Edition, Boston,2005. ##[9] A. Kandel,Fuzzy expert systems, CRC Press Florida, USA, 1992. ##[10] V. Kecman,Learning and soft computing, MIT Press. London England, 2001. ##[11] B. Kosko,Global stability of generalized additive fuzzy systems, IEEE Transactions on Systems, ##Man and Cybernetics – Part C: Applications and Reviews,28(3) (1998). ##[12] B. Kosko,Neural networks and fuzzy systems: a dynamical systems approach to machine ##learning intelligence, Englewood Cliff, NJ: PrenticeHall, 1991. ##[13] D. Kotoulas,Management of torrents I, Publications of the University of Thessaloniki, 1997. ##[14] E. G. Mansoori, M. J. Zolghadri, S. D. Katebi and H. Mohabatkar,Generating fuzzy rules ##for protein classification, Iranian Journal of Fuzzy Systems, 5(2) (2008). ##[15] F. Maris and L. Iliadis,A computer system using two membership functions and Tnorms ##for the calculation of mountainous watersheds torrential risk: the case of lakes trixonida and ##lisimaxia, Book Series: Developments in Plant and Soil Sciences, Book Title: Ecoand Ground ##BioEngineering: The Use of Vegetation to Improve Slope Stability, Springer Netherlands,103(2007), 247254. ##[16] M. Meidani, G. Habibaghai and S. Katebi,An aggregated fuzzy reliability index for slope ##stability analysis, Iranian Journal of Fuzzy Systems, 1(1) (2004), 17. ##[17] R. Satur , Z. Liu and M. Gahegan,Multilayered FCM’s applied to context dependent learning, ##Proc. IEEE FUZZ95,2 (1992), 561568. ##[18] A. K. Shaymal and M. Pal,Triangular fuzzy matrices, Iranian Journal of Fuzzy Systems,4(1)(2007). ##[19] N. Skermer and D. Van Dine,Debrisflow hazards and related phenomena, Springer Berlin, ##(2005), 2551. ##[20] P. Stefanidis,The torrent problems in mediterranean areas (example from greece), Proc. ##XXIUFRO Congress. Finland, 1995. ##[21] M. Sugeno and G. T. Kang,Structure identification of fuzzy model, Fuzzy Sets and Systems, ##28(1988), 1533. ##[22] T. Takagi and M. Sugeno,Fuzzy identification of systems and its applications to modeling ##and control, IEEE Trans. Syst. Man. Cybern., 15 (1985), 116132. ##[23] A. Tazioli,Evaluation of erosion in equipped basins: preliminary results of a comparison ##between the gavrilovic model and direct measurements of sediment transport ##, Environmental Geology, Springer Berlin,56(5) (2009), 825831. ##[24] R. R. Yager, S. Ovchinnikov, R. M. Tong and H. T. Nguyen,Fuzzy sets and applications: ##selected papers, Wiley New York, 1987. ##[25] L. A. Zadeh, Fuzzy sets, Information Control, 88 (1965), 338353. ##[26] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, ##Part I: Inf. Sci., 8, 199, Part II: Inf. Sci., 8, 301; Part II: Inf. Sci., 9, 43, 1975. ##[27] H. J. Zimmermann, Fuzzy set theory and its applications, 2nd Edition. Boston: Kluwer, 1991.##]
SUBCLASS FUZZYSVM CLASSIFIER AS AN EFFICIENT
METHOD TO ENHANCE THE MASS DETECTION IN
MAMMOGRAMS
SUBCLASS FUZZYSVM CLASSIFIER AS AN EFFICIENT
METHOD TO ENHANCE THE MASS DETECTION IN
MAMMOGRAMS
2
2
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 multiscale 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
rulebased 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 humanlike
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
fuzzySVM 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 fuzzySVM is superior to the other classifiers.
1
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 multiscale 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
rulebased 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 humanlike
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
fuzzySVM 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 fuzzySVM is superior to the other classifiers.
15
31
Fatemeh
Moayedi
Fatemeh
Moayedi
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
Iran
moayyedi,boostani,kazemi,katebi@cse.shirazu.ac.ir
Ebrahim
Dashti
Ebrahim
Dashti
Board of Science, Azad Universitiy Branch of Jahrom, Iran
Board of Science, Azad Universitiy Branch
Iran
sayed.dashti@jia.ac.ir
Mammography
Support vector based fuzzy neural network
Fuzzy support vector machine
Contourlet
[[1] R. A. Aliev, B. G. Guirimov and R. R. Aliev,A neurofuzzy object classifier with modified ##distance measure estimator, Iranian Journal of Fuzzy Systems, 1(1) (2004), 515. ##[2] K. Bovis, S. Singh, J. Fieldsend and C. Pinder,Identification of masses in digital mammograms ##with MLP and RBF nets, IEEE Trans. on Image Processing, 1 (2005), 342347. ##[3] E. J. Candes and D. L. Donoho,Curvelets: a surprisingly effective non adaptive representation ##for objects with edges, SaintMalo Proceedings, Nashville, TN: Vanderbilt Univ, 2000. ##[4] O. Cordon and M. J. del Jesus and F. Herrera,Genetic learning of fuzzy rule based classification ##systems cooperating with fuzzy reasoning methods, Technical Report, DECSAI970130,1997. ##[5] M. N. Do and M. Vetterli,The contourlet transform: an efficient directional multiresolution ##image representation, IEEE Trans. on Image Processing, 14(12) (2005), 20912106. ##[6] I. ElNaqa, Y. Yang, M. Wernick, N. Galatsanos and R. Nishikawa,A support vector machine ##approach for detection of microcalcifications, IEEE Trans. on Medical Imaging, 21(12)(2002), 15521563. ##[7] E. A. Fischer, J. Y. Lo and M. K. Markey,Bayesian networks of BIRADS descriptors for ##breast lesion classification, IEEE EMBS, San Francisco, 4 (2004), 30313034. ##[8] O. J. Freixenet, A. Bosch, D. Raba and R. Zwiggelaar,Automatic classification of breast ##tissue, Lecture Notes in Computer Science, Pattern Recognition and Image Analysis, (2000),431438. ##[9] W. H. Land, J. L. Wong Daniel, W. McKee, T. Masters and F. R Anderson,Breast cancer ##computer aided diagnosis (CAD) using a recently developed SVM/GRNN oracle hybrid, IEEE ##International Conference on Systems, Man and Cybernetics, 2003. ##[10] C. T. Lin, C. M. Yeh, S. F. Liang, J. F. Chung and N. Kumar, Supportvectorbased fuzzy ##neural network for pattern classification, IEEE Trans. on Fuzzy Systems, 14(1) (2006), 3141. ##[11] A. O. Malagelada, Automatic mass segmentation in mammographic images, PhD Thesis, ##Universitat de Girona, Spain, 2004. ##[12] E. G. Mansoori, M. J. Zolghadri and S. D. Katebi,Using distribution of data to enhance ##prformance of fuzzy classification systems, Iranian Journal of Fuzzy Systems, 4(1) (2007),2136. ##[13] E. G. Mansoori, M. J. Zolghadri, S. D. Katebi, H. Mohabatkar, R. Boostani and M. H.Sadreddini, ##Generating fuzzy for protein classification, Iranian Journal of Fuzzy Systems,5(2)(2008), 2133. ##[14] F. Moayedi, Z. Azimifar, R. Boostani and S. Katebi,Contourlet based mammography mass ##classification, Lecture Notes in Computer Science, Image Analysis and Recognition, 4633(2007), 923934. ##[15] F. Moayedi, R. Boostani, Z. Azimifar and S. Katebi,A support vector based fuzzy neural network ##approach for mass classification in mammography, International Conference on Digital ##Signal Processing, Britain, 2007. ##[16] R. Mousa, Q. Munib and A. Mousa,Breast cancer diagnosis system based on wavelet analysis ##and fuzzyneural netwrok, IEEE Trans. on Image Processing, 28(4) (2005), 713723. ##[17] D. Y. Po and N. Do, Directional multiscale modeling of images using the contourlet transform, ##IEEE Trans. on Image Processing, (2006), 111. ##[18] D. Raba, A. Oliver, J. Marti, M. Peracaula and J. Espunya, Breast segmentation with pectoral ##muscle suppression on digital mammograms, SpringerVerlag: Medical Imaging: Pattern ##Recognition and Image Analysis, 3523 (2005), 471478. ##[19] M. Roffilli, Advanced machine learning techniques for digital mammography, Technical Report, ##Department of Computer Science University of Bologna, Italy, 2006. ##[20] M. S. B. Sehgal, I. Gondal and L. Dooley, Support vector machine and generalized regression ##neural network based classification fusion models for cancer diagnosis, proceedings in Fourth ##IEEE International Conference on Hybrid Intelligent System, Computer Society, 2004. ##[21] L. Semler and L. Dettori, A comparison of waveletbased and ridgeletbased texture classification ##of tissues in computed tomography, International Conference on Computer Vision ##Theory and Applications, 2006. ##[22] L. Semler, L. Dettori and J. Furst, Waveletbased texture classification of tissues in computed ##tomography, IEEE International Symposium on ComputerBased Medical Systems, 2005. ##[23] J. L. Starck, E. J. Candes and D. L. Donoho, The curvelet transform for image denoising, ##IEEE Trans. on Image Processing, 11(6) (2002), 670684. ##[24] C. Varelaa, P. G. Tahocesb, A. J. Mndezc, M. Soutoa and J. J. Vidala, Computerized detection ##of breast masses in digitized mammograms, Computers in Biology and Medicine, 37(2)(2007), 214226. ##[25] W. Xiaodan and W. Chongming, Using membership function to improve multiclass SVM ##classification, ICSP Proceeding, China, 2004. ##[26] Z. Yu and C. Bajaj, A fast and adaptive for image contrast enhancement, IEEE International ##Conference on Image Processing, 2004. ##[27] M. Zhu and A. M. Martinez, Subclass discriminant analysis, IEEE Trans. on Pattern Analysis ##and Machine Intelligence, 28(8) (2006), 12471286.##]
THE URYSOHN AXIOM AND THE COMPLETELY HAUSDORFF
AXIOM IN LTOPOLOGICAL SPACES
THE URYSOHN AXIOM AND THE COMPLETELY HAUSDORFF
AXIOM IN LTOPOLOGICAL SPACES
2
2
In this paper, the Urysohn and completely Hausdorff axioms in general topology are generalized to Ltopological spaces so as to be compatible with pointwise metrics. Some properties and characterizations are also derived
1
In this paper, the Urysohn and completely Hausdorff axioms in general topology are generalized to Ltopological spaces so as to be compatible with pointwise metrics. Some properties and characterizations are also derived.
33
45
FuGui
Shi
FuGui
Shi
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing, 100081, P. R. China
Department of Mathematics, School of Science,
China
fuguishi@bit.edu.cn or f.g.shi@263.net
Peng
Chen
Peng
Chen
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing, 100081, P. R. China
Department of Mathematics, School of Science,
China
chenpengbeijing@sina.com
[[1] S. L. Chen,Fuzzy Urysohn spaces and $alpha$stratified fuzzy Urysohn spaces, Proceedings of the ##Fifth IFSA World Congress I, Korea, (1993), 453456. ##[2] S. L. Chen and Z. X.Wu,Urysohn separation property in topological molecular lattices, Fuzzy ##Sets and Systems,123(2) (2001), 177184. ##[3] Z. Deng,Fuzzy pseudometric space, J. Math. Anal. Appl., 86 (1982), 7495. ##[4] P. Dwinger,Characterizations of the complete homomorphic images of a completely distributive ##complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403414. ##[5] M. A. Erceg,Metric space in fuzzy set theory, J. Math. Anal. Appl., 69 (1979), 205230. ##[6] J. Fang,H()completely Hausdorff axiom on Ltopological spaces, Fuzzy Sets and Systems, ##140(3)(2003), 475469. ##[7] J. Fang and Y. Yue,Urysohn closedness on completely distributive lattices, Fuzzy Sets and ##Systems,144(3) (2004), 367381. ##[8] M. H. Ghanim, O. A. Tantawy and F. M. Selim,On lower separation axioms, Fuzzy Sets ##and Systems,85(3) (1997), 385389. ##[9] G. Gierz and et al.,A compendium of continuous lattices, Springer Verlag, Berlin, 1980. ##[10] U. H¨ohle, S. E. Rodabaugh and eds,Mathematics of fuzzy sets: logic, topology and ##measure theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers ##(Boston/Dordrecht/London),3 (1999). ##[11] C. Hu,Fuzzy topological space, J. Math. Anal. Appl., 110 (1985), 141178. ##[12] B. Hutton,Uniformities on fuzzy topological spaces, J. Math. Anal. Appl., 58 (1977), 559571. ##[13] B. Hutton,Normality in fuzzy topological spaces, J. Math.Anal.Appl., 50 (1975), 7479. ##[14] B. Hutton and I. Reilly,Separation axioms in fuzzy topological spaces, Fuzzy Sets and Systems, ##3(1)(1980), 93104. ##[15] O. Kaleva and S. Seikkala,On fuzzy metric spaces, Fuzzy Sets and Systems, 12(3) (1984), ##[16] I. Kramosil and J. Michalek,Fuzzy metric and statistical metric spaces, Kybernetica, 11(1975), 326334. ##[17] W. Kotz´e,Lifting of sobriety concepts with particular reference to (L,M)topological spaces, ##in S. E. Rodabaugh, E. P. Klement and eds., Topological and Algebraic Structures in Fuzzy ##Sets, Kluwer Academic, Publishers (Boston/Dordrecht/London), 2003. ##[18] T. Kubiak,On LTychonoff spaces, Fuzzy Sets and Systems, 73(1) (1995), 2553. ##[19] S. G. Li,H($lambda$)completely regular Lfuzzy sets and their applications, Fuzzy Sets and Systems, ##95(2)(1998), 223231 ##[20] S. G. Li,Separation axioms in Lfuzzy topological spaces (I): T0 and T1, Fuzzy Sets and ##Systems,116(3) (2000), 377383. ##[21] Y. M. Liu and M. K. Luo,Pointwise characterizations of complete regularity and embedding ##theorem in fuzzy topological spaces, Science in China Ser. A, 26 (1983), 138147. ##[22] Y. M. Liu and M. K. Luo,Fuzzy topology, World Scientific Publishing, Singapore, 1997. ##[23] R. Lowen and A. K. Srivastava,Sierpinski objects in subcategories of FTS, Quaestiones ##Mathematicae,11 (1988), 181193. ##[24] R. Lowen and A. K. Srivastava,FTS0: the epireflective hull of the Sierpinski object in FTS, ##Fuzzy Sets and Systems,29(2) (1989), 171176. ##[25] P. M. Pu and Y. M. Liu,Fuzzy topology I, neighborhood structure of a fuzzy point and ##MooreSmith convergence, J. Math. Anal. Appl., 76 (1980), 571599. ##[26] A. Pultr and S. E. Rodabaugh,Lattice valued frames, functor categories and classes of sober ##spaces, in S. E. Rodabaugh, E. P. Klement and eds., Topological and Algebraic Structures in ##Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends ##in Logic, Kluwer Academic Publishers (Boston/Dordrecht/London),20 (2003), 153187. ##[27] A. Pultr and S. E. Rodabaugh,Examples for different sobrieties in fixedbasis topology, in S. ##E. Rodabaugh, E. P. Klement and eds., Topological and Algebraic Structures in Fuzzy Sets: ##A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic, ##Kluwer Academic Publishers (Boston/Dordrecht/London),20 (2003), 427440. ##[28] S. E. Rodabaugh,The Hausdorff separation axiom for fuzzy topological spaces, Topology and ##its Applications,11 (1980), 319334. ##[29] S. E. Rodabaugh,Separation axioms and the Lfuzzy real lines, Fuzzy Sets and Systems, ##11(2)(1983), 163183. ##[30] S. E. Rodabaugh,A pointset latticetheoretic framework T for topology which contains LOC ##as a subcategory of singleton subspaces and in which there are general classes of stone representation ##and compactification theorems, First Printing February 1986, Second Printing ##April 1987, Youngstown State University Printing Office, Youngstown, Ohio, USA. ##[31] S. E. Rodabaugh,Pointset latticetheoretic topology, Fuzzy Sets and Systems, 40(2) (1991), ##[32] S. E. Rodabaugh,Categorical frameworks for Stone representation theories, in S. E. Rodabaugh, ##E. P. Klement, U. H¨ohle and eds., Applications of Category Theory to Fuzzy Subsets, ##Theory and Decision Library: Series B: Mathematical and Statistical Methods, Kluwer Academic ##Publishers (Boston/Dordrecht/London),14 (1992), 177231. ##[33] S. E. Rodabaugh,Applications of localic separation axioms, compactness axioms, representations ##and compactifications to poslat topological spaces, Fuzzy Sets and Systems, 73(1) ##(1995), 5587. ##[34] S. E. Rodabaugh,Separation axioms: representation theorems, compactness and compactifications, ##in U. H¨ohle, S. E. Rodabaugh and eds., Mathematics of Fuzzy Sets: Logic, Topology ##and Measure Theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, ##Boston, Dordrecht, London,3 (1999), 481552. ##[35] F. G. Shi and L. J. Zhao,Pointwise characterizations of HRregularity, J. Harbin Sci. Technol. ##Univ., in Chinese,1 (1995), 8485. ##[36] F. G. Shi,Pointwise uniformities in Lfuzzy set theory, Fuzzy Sets and Systems, 98(1)(1998), 141146. ##[37] F. G. Shi,Fuzzy pointwise complete regularity and imbedding theorem, J. Fuzzy Math., 2(1999), 305310. ##[38] F. G. Shi,Lfuzzy pointwise metric spaces and T2 axiom, J. Capital Normal University, in ##Chinese,1 (2000), 812. ##[39] F. G. Shi,Pointwise pseudometrics in Lfuzzy set theory, Fuzzy Sets and Systems, 121(2) ##(2001),209216. ##[40] F. G. Shi and C. Y. Zheng,Metrization theorems in Ltopological spaces, Fuzzy Sets and ##Systems,149(3) (2005), 455471. ##[41] F. G. Shi,A new notion of fuzzy compactness in Ltopological spaces, Information Sciences, ##173(2005), 3548. ##[42] F. G. Shi,Pointwise pseudometric on the Lreal line, Iranian Journal of Fuzzy Systems, ##2(2)(2005), 1520. ##[43] F. G. Shi,A new approach to LT2, LUrysohn and Lcompletely hausdorff axioms, Fuzzy ##Sets and Systems,157(6) (2006), 794803. ##[44] G. J. Wang,Theory of topological molecular lattices, Fuzzy Sets and Systems, 47(3) (1992), ##[45] G. J. Wang,Theory of Lfuzzy topological spaces, Shaanxi Normal University Press, Xi’an, ##[46] M. D. Weiss,Fixed points, separation and induced topologies for fuzzy sets, J. Math. Anal. ##Appl.,50 (1975), 142150. ##[47] P. Wuyts and R. Lowen,On local and global measures of separation in fuzzy topological ##spaces, Fuzzy Sets and Systems, 19(1) (1986), 5180. ##[48] D. Zhang and Y. Liu,Weakly induced modifications of Lfuzzy topological spaces, Acta Math. ##Sinica,36 (1993), 6873.##]
CHARACTERIZATION OF LFUZZIFYING MATROIDS BY
LFUZZIFYING CLOSURE OPERATORS
CHARACTERIZATION OF LFUZZIFYING MATROIDS BY
LFUZZIFYING CLOSURE OPERATORS
2
2
An Lfuzzifying 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 Lfuzzy setting and called Lfuzzifyingclosure operators. It is proved that there exists a onetoone correspondencebetween Lfuzzifying matroids and their Lfuzzifying closure operators.
1
An Lfuzzifying 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 Lfuzzy setting and called Lfuzzifyingclosure operators. It is proved that there exists a onetoone correspondencebetween Lfuzzifying matroids and their Lfuzzifying closure operators.
58
47
Lan
Wang
Lan
Wang
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
China
wanglantongtong@126.com or wanglan@bit.edu.cn
FuGui
Shi
FuGui
Shi
Department of Mathematics, Beijing Institute of Technology, Beijing,
100081, P. R. China
Department of Mathematics, Beijing Institute
China
fuguishi@bit.edu.cn or f.g.shi@263.net
Lfuzzifying matroid
Lfuzzifying rank function
Lfuzzifying closure operator
[[1] A. Borumand Saeid, Intervalvalued fuzzy Balgebras, Iranian Journal of Fuzzy Systems, 3##(2006), 6374.##[2] P. Dwinger, Characterizations of the complete homomorphic images of a completely distributive##complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403414.##[3] J. Fortin, A. Kasperski and P. Zielinski, Efficient methods for computing optimality degrees##of elements in fuzzy weighted matroids, in I. Bloch, A. Petrosino, A. Tettamanzi and eds.,##Fuzzy Logic and Applications, The 6th International Workshop, WILF, Crema, Italy, (2005),##[4] H. L. Huang and F. G. Shi, Lfuzzy numbers and their properties, Information Sciences, 178##(2008), 11411151.##[5] A. Kasperski and P. Zielinski, A possibilistic approach to combinatorial optimization problems##on fuzzyvalued matroids, in I. Bloch, A. Petrosino, A. Tettamanzi and eds., Fuzzy Logic and##Applications, The 6th International Workshop, WILF, Crema, Italy, (2005), 4652.##[6] A. Kasperski and P. Zielinski, On combinatorial optimization problems on matroids with##uncertain weights, European Journal of Operational Research, 177 (2007), 851864.##[7] A. Kasperski and P. Zielinski, Using gradual numbers for solving fuzzyvalued combinatorial##optimization problems, in P. Melin, O. Castillo, L.T. Aguilar, J. Kacprzyk, W. Pedrycz and##eds., Foundations of Fuzzy Logic and Soft Computing, The 12th International Fuzzy Systems##Association World Congress, Cancun, Mexico, (2007), 656665.##[8] S. P. Li, Z. Fang and J. Zhao, P2connectedness in Ltopological spaces, Iranian Journal of##Fuzzy Systems, 2 (2005), 2936.##[9] G. N. Raney, Completely distributive complete lattices, Proceedings of the American Mathematical##Society, 3 (1952), 677680.##[10] F. G. Shi, Theory of L nested sets and L nested sets and its applications, Fuzzy Systems##and Mathematics, 4 (1995), 6572. ##[11] F. G. Shi, Lfuzzy relation and Lfuzzy subgroup, The Journal of Fuzzy Mathematics, 8##(2000), 491499.##[12] F. G. Shi, A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160##(2009), 696705.##[13] G. J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992),##[14] D. J. A. Welsh, Matroid theory, Academic Press, London, 1976.##]
FUZZY QUASIMETRIC VERSIONS OF A THEOREM OF
GREGORI AND SAPENA
FUZZY QUASIMETRIC VERSIONS OF A THEOREM OF GREGORI AND SAPENA
2
2
We provide fuzzy quasimetric versions of a fixed point theorem ofGregori and Sapena for fuzzy contractive mappings in Gcomplete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.
1
We provide fuzzy quasimetric versions of a fixed point theorem ofGregori and Sapena for fuzzy contractive mappings in Gcomplete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.
59
64
Dorel
Mihet
Dorel
Mihet
Department of Mathematics, West University of Timisoara, Bv. V.
Parvan 4, Timisoara, Romania
Department of Mathematics, West University
Turkey
mihet@math.uvt.ro
Fuzzy metric space
Nonarchimedean fuzzy quasimetric
Gbicomplete
Domain of words
[[1] P. Flajolet, Analytic analysis of algorithms, in Lecture Notes in Computer Science, Springer,##Berlin, 623 (1992), 186210.##[2] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1983), 385389.##[3] M. Grabiec, Y. J. Cho and V. Radu, On nonsymmetric topological and probabilistic structures,##New York, Nova Science Publishers, Inc., 2006.##[4] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,##64 (1994), 395399.##[5] V. Gregori and A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and##Systems, 125 (2002), 245252.##[6] V. Gregori and S. Romaguera, Fuzzy quasimetric spaces, Appl. Gen. Topology, 5 (2004),##[7] O. Hadˇzi´c and E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Academic##Publishers, Dordrecht, 2001.##[8] O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11##(1975), 336344.##[9] D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems,##144 (2004), 431439.##[10] D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems,##158 (2007), 915921.##[11] M. Rafi and M. S. M. Noorani, Fixed point theorem in intuitionistic fuzzy metric spaces,##Iranian Journal of Fuzzy Systems, 3(1) (2006), 2329.##[12] A. Razani and M. Shirdaryazdi, Erratum to:” On fixed point theorems of Gregori and##Sapena”, Fuzzy Sets and Systems, 153(2) (2005), 301302.##[13] A. Razani, A contraction theorem in fuzzy metric spaces, Fixed Point Theory Applications,##3 (2005), 257265.##[14] S. Romaguera, A. Sapena and P. Tirado, The banach fixed point theorem in fuzzy quasimetric##spaces with application to the domain of words, Topology and its Applications, 154(10)##(2007), 21962203.##[15] R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for weakly commuting##maps in Lfuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5(1) (2008), 4754.##[16] B. Schweizer and A. Sklar, Probabilistic metric spaces, NorthHolland, Amsterdam, 1983.##[17] R.Vasuki and P. Veeramani, Fixed point theorems and Cauchy sequences in fuzzy metric##spaces, Fuzzy Sets and Systems, 135 (2003), 415417.##[18] T. Zikic, On fixed point theorems of Gregori and Sapena, Fuzzy Sets and Systems, 144(3)##(2004), 421429.##]
BIMATRIX GAMES WITH INTUITIONISTIC FUZZY GOALS
BIMATRIX GAMES WITH INTUITIONISTIC FUZZY GOALS
2
2
In this paper, we present an application of intuitionistic fuzzyprogramming to a two person bimatrix game (pair of payoffs matrices) for thesolution with mixed strategies using linear membership and nonmembershipfunctions. 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.
1
In this paper, we present an application of intuitionistic fuzzyprogramming to a two person bimatrix game (pair of payoffs matrices) for thesolution with mixed strategies using linear membership and nonmembershipfunctions. 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.
65
79
Prasun Kumar
Nayak
Prasun Kumar
Nayak
Department of Mathematics, Bankura Christian College,
P.O.+ Dist Bankura, West Bengal,722101, India
Department of Mathematics, Bankura Christian
India
nayak prasun@rediffmail.com
Madhumangal
Pal
Madhumangal
Pal
Department of Applied Mathematics with Oceanology and Computer
Programming, Vidyasagar University, Midnapore721 102, India
Department of Applied Mathematics with Oceanology
India
mmpalvu@gmail.com
Bimatrix game
Nash equilibrium
Intuitionistic fuzzy sets
Fuzzy optimization
Intuitionistic fuzzy optimization
[[1] K. Atanassov, Intuitionistic fuzzy sets: theory and applications, PhysicaVerlag, 1999.##[2] P. P. Angelov,Optimization in an intuitinistic fuzzy enviornment, Fuzzy Sets and Systems,##86 (1997), 299306.##[3] C. R. Bector, S. Chandra and V. Vijay, Bimatrix games with fuzzy payoffs and fuzzy goals,##Fuzzy Optimization and Decision Making, 3 (2004), 327344.##[4] T. Basar and G. J. Olsder, Dynamic noncooperative game theory, Academic Press, New##York, 1995.##[5] L. Campos, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets and##Systems, 32 (1989), 275289.##[6] D. Dubois and H. Prade, Fuzzy sets and systems, Academic Press, New York, 1980.##[7] T. Maeda, Characterization of the equilibrium strategy of bimatrix games with fuzzy payoffs,##Journal of Mathematical Analysis and Applications, 251 (2000), 885896.##[8] J. V. Neumann and O. Morgenstern, Theory of games and economic behaviour, Princeton##University Press, Princeton, New Jersey, 1944 .##[9] J. F. Nash, Non cooperative games, Annals of Mathematics, 54 (1951), 286295.##[10] P. K. Nayak and M. Pal, Solution of interval games using graphical method, Tamsui Oxford##Journal of Mathematical Sciences, 22(1) (2006), 95115. ##[11] P. K. Nayak and M. Pal, Bimatrix games with intuitionistic fuzzy payoffs, Notes on Intuitionistic##Fuzzy Sets, 13(3) (2007), 110.##[12] P. K. Nayak and M. Pal, Bimatrix games with interval payoffs and its Nash equilibrium##strategy, Asia specific Journal of Operational Research, 26(2) (2009), 285305.##[13] P. K. Nayak and M. Pal, Bimatrix games with interval payoffs and its Nash equyilibrium##strategy, Journal of Fuzzy Mathematics, 17(2) (2009).##[14] Z. Peng, L. Dagang and W. Guangyuan, Idea and principle of intuitionistic fuzzy optimization,##htpp://www.paper.edu.cn.##[15] S. K. Roy, M. P. Biswal and R. N. Tiwari, An approach to multiobjective bimatrix games of##Nash equilibrium solutions, Ricerca Operativa , 30(93) (2001), 4764.##[16] M. Sakawa and I. Nishizaki, Maxmin solution for fuzzy multiobjective matrix games, Fuzzy##Sets and Systems, 67 (1994), 5369.##[17] M. Sakawa and I. Nishizaki, Equilibrium solution in bimatrix games with fuzzy payoffs,##Japanse Fuzzy Theory and Systems, 9(3) (1997), 307324.##[18] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338352.##]
CATEGORICAL RELATIONS AMONG MATROIDS, FUZZY
MATROIDS AND FUZZIFYING MATROIDS
CATEGORICAL RELATIONS AMONG MATROIDS, FUZZY MATROIDS AND FUZZIFYING MATROIDS
2
2
The aim of this paper is to study the categorical relations betweenmatroids, GoetschelVoxman’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.
1
The aim of this paper is to study the categorical relations betweenmatroids, GoetschelVoxman’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.
81
89
LingXia
Lu
LingXia
Lu
School of Mathematics and Science, Shijiazhuang University of Technology,
Shijiazhuang 050031, P.R. China
School of Mathematics and Science, Shijiazhuang
China
lulingxia1214@gmail.com
WeiWei
Zheng
WeiWei
Zheng
School of Science, Xi’an Polytechnic University, Xi’an 710048, P.R.
China
School of Science, Xi’an Polytechnic University,
China
zww@nwpu.edu.cn
Matroid
Fuzzy matroid
Closed fuzzy matroid
Fuzzifying matroid. This paper is supported by the national natural science foundation of china(10926055)
[[1] J. Ad´amek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New##York, 1990.##[2] K. R. Bhutani, J. Mordeson and A. Rosenfeld, On degrees of end nodes and cut nodes in##fuzzy graphs, Iranian Journal of Fuzzy Systems, 1 (2004), 5764.##[3] J. Edmonds, Matroids and the greedy algorithm, Mathematical Programming, 1 (1971), 125##[4] D. Gale, Optimal assignments in an ordered set: an application of matroid theory, Journal##of Combinatoral Theory, 4 (1968), 176180.##[5] R. Goetschel and W. Voxman, Bases of fuzzy matroids, Fuzzy Sets and Systems, 31 (1989),##[6] R. Goetschel and W. Voxman, Fuzzy circuits, Fuzzy Sets and Systems, 32 (1989), 3543.##[7] R. Goetschel and W. Voxman, Fuzzy matroids, Fuzzy Sets and Systems, 27 (1988), 291302.##[8] R. Goetschel and W. Voxman, Fuzzy rank functions, Fuzzy Sets and Systems, 42 (1991),##[9] S. G. Li, X. Xin and Y. L. Li, Closure axioms for a class of fuzzy matroids and the cotower##of matroids, Fuzzy Sets and Systems, 158 (2007), 12461257.##[10] J. G. Oxley, Matroid Theory, Oxford Universty Press, 1992.##[11] F. G. Shi, A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160##(2009), 696705.##[12] M. S. Ying, A new approach to fuzzy topologies (I), Fuzzy Sets and Systems, 39 (1991),##]
SOME FIXED POINT THEOREMS FOR SINGLE AND MULTI
VALUED MAPPINGS ON ORDERED NONARCHIMEDEAN
FUZZY METRIC SPACES
SOME FIXED POINT THEOREMS FOR SINGLE AND MULTI
VALUED MAPPINGS ON ORDERED NONARCHIMEDEAN
FUZZY METRIC SPACES
2
2
In the present paper, a partial order on a non Archimedean fuzzymetric space under the Lukasiewicz tnorm is introduced and fixed point theoremsfor single and multivalued mappings are proved.
1
In the present paper, a partial order on a non Archimedean fuzzymetric space under the Lukasiewicz tnorm is introduced and fixed point theoremsfor single and multivalued mappings are proved.
91
96
Ishak
Altun
Ishak
Altun
Department of Mathematics, Faculty of Science and Arts, Kirikkale
University, 71450 Yahsihan, Kirikkale , Turkey
Department of Mathematics, Faculty of Science
Turkey
ialtun@kku.edu.tr, ishakaltun@yahoo.com
Fixed point
Partial order
Fuzzy metric space
[[1] S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung and S. M. Kang, Coincidence point and##minimization theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 88 (1997), 119128.##[2] Y. J. Cho, Fixed points in fuzzy metric spaces, J. Fuzzy Math., 5 (1997), 949962.##[3] J. X. Fang, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 46##(1992), 107 113.##[4] Y. Feng and S. Liu, Fixed point theorems for multivalued increasing operators in partially##ordered spaces, Soochow J. Math., 30(4) (2004), 461469.##[5] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,##64 (1994), 395399.##[6] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385389.##[7] V. Gregori and A. Sapena, On fixedpoint theorem in fuzzy metric spaces, Fuzzy Sets and##Systems, 125 (2002), 245252.##[8] O. Hadzic, Fixed point theorems for multivalued mappings in some classes of fuzzy metric##spaces, Fuzzy Sets and Systems, 29 (1989), 115125.##[9] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),##[10] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11##(1975), 326334.##[11] D. Mihet, A banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems,##114 (2004), 431 439.##[12] D. Mihet, On the existence and the uniqueness of fixed points of Sehgal contractions, Fuzzy##Sets and Systems, 156 (2005), 135141.##[13] D. Mihet, Fuzzy  contractive mappings in Nonarchimedean fuzzy metric spaces, Fuzzy##Sets and Systems, 159 (2008), 739744.##[14] S. N. Mishra , S. N. Sharma and S. L. Singh, Common fixed points of maps in fuzzy metric##spaces, Internat. J. Math. Math. Sci., 17 (1994), 253258.##[15] V. Radu, Some remarks on the probabilistic contractions on fuzzy Menger spaces, The Eighth##International Conference on Appl. Math. Comput. Sci., ClujNapoca, Automat. Comput.##Appl. Math., 11 (2002) 125131.##[16] M. Rafi and M. S. M. Noorani, Fixed point theorem on intuitionistic fuzzy metric spaces,##Iran. J. Fuzzy Syst., 3(1) (2006), 2329.##[17] R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for weakly commuting##maps in Lfuzzy metric spaces, Iran. J. Fuzzy Syst., 5(1) (2008), 4753.##[18] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313334.##[19] S. Sedghi, K. P. R. Rao and N. Shobe, A common fixed point theorem for six weakly compatible##mappings in Mfuzzy metric spaces, Iran. J. Fuzzy Syst., 5(2) (2008), 4962.##[20] Z. Q. Xia and F. F. Gou, Fuzzy metric spaces, J. Appl. Math. Computing, 16(12) (2004),##]
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