The framework of axiomatics fuzzy sets based fuzzy classifiers

Journal of Industrial and Management Optimization

Volumn 4, Issue 3, 2008, Pages 581-609

  Liu, Xiaodong ^a   Liu, Wanquan ^b  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b CURTIN UNIVERSITY   (Australia)

Author keywords

AFS algebra; AFS structure; Fuzzy classification; Molecular lattice; Sub preference relation

Indexed keywords

EID: 56649107939     PISSN: 15475816     EISSN: 1553166X     Source Type: Journal    
DOI: 10.3934/jimo.2008.4.581     Document Type: Article

References (47)

1. L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
2. J. M. Keller, M. Gray and J. Givens, A fuzzy k-nearest neighbor algorithm, IEEE Trans.Syst., Man, Cybern., vol. 15 (1985), 580-585.
3. J. C. Bezdek, "Pattern Recognition with Fuzzy Objective Function Algorithms," New York: Plenum, 1981.
4. X. D. Liu, The fuzzy theory based on AFS algebras and AFS structure, Journal of Mathematical Analysis and Applications, 217 (1998), 459-478.
5. X. D. Liu, The topology on AFS algebra and AFS structure, Journal of Mathematical Analysis and Applications, 217 (1998), 479-489.
6. X. D. Liu, The structure of fuzzy matrices, Journal of Fuzzy Mathematics, 2 (1994), 311-325.
7. X. D. Liu, The fuzzy sets and systems based on AFS structure, EI algebra and EII algebra, Fuzzy Sets and Systems, 95 (1998), 179-188.
8. K. H. Kim, "Boolean matrix Theory and Applications," Inc.: Marcel Dekker, 1982.
9. Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11 (1982), 341-356.
10. Y. Y. Yao, Semantics of fuzzy set in rough set theory, Transactions on Rough Sets II, LNCS 3135 (2004), 297-318.
11. A. Radzikowska and EE Kerre, A comparative study of fuzzy rough sets, Fuzzy Sets and Systems, 126 (2002), 137-155.
12. J. M. Fernandez Salido and S. Murakami, Rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations, Fuzzy Sets and Systems, 139 (2003), 635-660.
13. G. J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992), 351-376.
14. J. E. Graver and M. E. Watkins, "Combinatorics with Emphasis on the Theory of Graphs," New York, Springer-Verlag, 1977.
15. W. Pedrycz and G. Vukovich, logic-oriented fuzzy clustering, Pattern Recognition Letters, 23 (2002), 1515-1527.
16. R. Bellman, R. Kalaba and L. A. Zadeh, Abstraction and pattern classification, J. Math. Anal. Appl., 13 (1966), 1-7.
17. J. C. Bezdek, "Pattern Recognition with Fuzzy Objective Function Algorithms," Plenum Press, New York, 1981.
18. M. S. Yang, A survey of fuzzy clustering, Math. Comput. Modelling, 18 (1993), 1-16.
19. M. S. Yang and C. H. Ko, On cluster-wise fuzzy regression analysis, IEEE Transactions Systems Man Cyberenet, Part B, 27 (1997), 1-13.
20. X. D. Liu, A new fuzzy model of pattern recognition and hitch diagnoses of complex systems, Fuzzy Sets and Systems, 104 (1999), 289-297.
21. B. Q. Hu and S. Wang, A novel approach in uncertain programming I: New arithmetic and order relations for interval numbers, Journal of Industrial and Management Optimization, 2 (2006), 351-371.
22. B. Q. Hu and S. Wang, A novel approach in uncertain programming part II: A class of constrained nonlinear programming problems with interval objective functions, Journal of Industrial and Management Optimization, 2 (2006), 373-385.
23. E. H. Ruspini, A new approach to clustering, Information and Control, 15 (1969), 22-32.
24. W. Pedrycz and Z. A. Sosnowski, The design of decision trees in the framework of granular data and their application to software quality models, Fuzzy Sets and Systems, 123 (2001), 271-290.
25. X. D. Liu and Q. L. Zhang, AFS Fuzzy logic and its applications to fuzzy information processing, Dongbei Daxue Xuebao, (in Chinese), 23 (2002), 321-323.
26. X. D. Liu, W. Pedrycz and Q. L. Zhang, Axiomatics fuzzy sets logic, IEEE International Conference on Fuzzy Systems, 1 (2003), 55-60.
27. X. D. Liu and Q. L. Zhang, The EI algebra representations of fuzzy concept, Fuzzy Systems and Mathematics, 16 (2002), 27-35.
28. X. D. Liu, K. Zhu and H. Z. Huang, The representations of fuzzy concepts based on the fuzzy matrix theory and the AFS theory, IEEE International Symposium on Intelligent Control, October 5-8, 2003, Texas, USA.
29. L. A. Zadeh, Fuzzy logic=computing with word, IEEE Transactions on Fuzzy Systems, 4 (1996), 103-111.
30. M. Ait Kbir, H. Benkirane, K. Maalmi and R. Benslimane, Hierarchical fuzzy partition for pattern classification with fuzzy if-then rules, Pattern Recognition Letters, 21 (2000), 503-509.
31. J. Abonyi, J. A. Roubos and F. Szeifert, Data-driven generation of compact accurate and linguistically sound fuzzy classifiers based on a decision-tree initialization, International Journal of Approximate Reasoning, 32 (2003), 1-21.
32. J. A. Roubos, M. Setnes and J. Abonyi, Learning fuzzy classification rules from labeled data, Information Sciences, 150 (2003), 77-93.
33. H. Roubos and M. Setnes, Compact and transparent fuzzy models and classifiers through iterative complexity reduction, IEEE Transations on Fuzzy Systems, 9 (2001), 516-524.
34. B. Carse, T. C. Fogarty and A. Munro, Evolving fuzzy rule based controllers using genetic algorithms, Fuzzy Sets Syst., 80 (1996), 273-293.
35. T. Takagi and M. Sugeno, Fuzzy identification of systems and its application to modeling and control, IEEE Transactions on Systems, Man, and Cybernetics-part B: Cybernetics, 15 (1985), 116-132.
36. S. K. Pal and S. Mitra, Multilayer perceptron, fuzzy sets, and classification, IEEE Trans. Neural Networks, 3 (1992), 683-697.
37. T. M. Mitchell, "Machine Learning," McGraw-Hill, 1997.
38. S. K. Halgamuge, W. Poechmueller and M. Glesner, An alternative approach for generation of membership functions and fuzzy rules based on radial and cubic basis function networks, Int. J. Approx. Reas., 12 (1995), 279-298.
39. R. Bajcsy and S. Kovacic, Multi-resolution elastic matching, Computer Vision Graphics Image Processing, 46 (1989), 1-21.
40. U. Grenander, "General Pattern Theory," Oxford University Press, 1993.
41. A. K. Jain, R. P. W. Duin and J. C. Mao, Statistical pattern recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, 22 (2000), 4-37.
42. L. I. Perlovsky, Conundrum of combinatorial complexity, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20 (1998), 666-670.
43. A. K. Jain, J. Mao and K. M. Mohiuddin, Artificial neural networks, Computer, (1996), 628-633.
44. I. Kohonen, "Self-Organizing Maps," Springer Series in Information Sciences, 30, Berlin, 1995.
45. K. Ciesielski, "Set Theory for the Working Mathematician," Cambridge University Press, 1997.
46. S. J. Roberts, R. Everson and I. rezek, Maximum certainty data partitioning, Pattern Recognition, 33 (2000), 833-839.
47. M. Girolami, Mercer kernel-based clustering in feature space, IEEE Transactions on Neural Networks, 13 (2002), 780-784.