A Development of Inclusion-degree-based Rough Fuzzy Random Sets

• Autorzy: Ha M. , Pedrycz W. , Zhang A. , Fan Y.
• Języki publikacji: EN

Abstrakty

EN

Given a widespread interest in rough sets as being applied to various tasks of data analysis, it is not surprising at all that we have witnessed a wave of further generalizations and algorithmic enhancements of this original concept. In this study, we investigate an idea of rough fuzzy random sets. This construct provides us with a certain generalization of rough sets by introducing the concept of inclusion degree. The underlying objective behind this development is to address the problems which involve co-existing factors of fuzziness and randomness thus giving rise to a notion of the fuzzy random approximation space based on inclusion degree. Some essential properties of rough approximation operators of such rough fuzzy random sets are discussed. Further theoretical foundations for the formation of rules constructed on a basis of available decision tables are offered as well.

Słowa kluczowe

EN

rough sets; fuzzy random sets; inclusion degree; rough approximation operators; decision table

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2008
• Tom: Vol. 86, nr 4
• Strony: 481--502
• Opis fizyczny: bibliogr.44 poz., tab.

Twórcy

autor

Ha M.

autor

Pedrycz W.

autor

Zhang A.

autor

Fan Y.

• Department of Electrical & Computer Engineering, University of Alberta Edmonton Canada and Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland,

Bibliografia

• [1] Cock, M.D. , Cornelis, C. , Kerre, E.E. : Fuzzy rough sets: the forgotten step, IEEE Transactions on Fuzzy Systems, 15(1), 2007, 121-130.
• [2] Deng, T. Q. , Chen, Y. M. , Xu, W. L. , Dai, Q. H. : A novel approach to fuzzy rough sets based on a fuzzy covering, Information Sciences, 177(11), 2007, 2308-2326.
• [3] Dubois, D. , Prade, H. : Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems, 17(2), 1990, 191-209.
• [4] Gil, M.A. , Dłaz, M.L. , Ralescu, D.A. : Overview on the development of fuzzy random variables, Fuzzy Sets and Systems, 157 (19), 2006, 2546-2557.
• [5] Gomoli´nska, A. : Variable-precision compatibility spaces, Electronic Notes in Theoretical Computer Science, 82(4), 2003, 120-131.
• [6] Gong, Z.T. , Sun, B.Z. , Chen, D.G. : Rough set theory for the interval-valued fuzzy information systems, Information Sciences, 178(8), 2008, 1968-1985.
• [7] Hu, Q.H. , Xie, Z.X. , Yu, D.R. : Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation, Pattern Recognition, 40, 2007, 3509-3521.
• [8] Jensen, R. , Shen, Q. : Fuzzy-rough sets assisted attribute selection, IEEE Transactions on Fuzzy Systems, 15(1), 2007, 73-89.
• [9] Kendall, D.G. : Foundation of a theory of random sets, Stochastic Geometry, 1973, 332-376.
• [10] Krätschmer, V. : Constraints on belief functions imposed by fuzzy random variables: some technical remarks on Romer-Kandel, IEEE Transactions on Systems, Man and Cybernetics, Part B, 28(6), 1998, 881-883.
• [11] Leung, Y. , Wu, W.Z. , Zhang, W.X. : Knowledge acquisition in incomplete information systems: A rough set approach, European Journal of Operational Research , 168, 2006, 164-180.
• [12] Lin, T.Y. : Neighborhood systems and approximation in database and knowledge base systems, Proceedings of the Fourth International Symposium on Methodologies of Intelligent Systems, New York: North-Holland, 1989.
• [13] Mitchell,T. M. : Machine Learning, Beijing: China Machine Press, 2003.
• [14] Nguyen, H. , Wu, B. : Random and fuzzy sets in coarse data analysis, Computational Statistics and Data Analysis, 51, 2006, 70-85.
• [15] Nguyen, H.T.: Fuzzy and random sets, Fuzzy Sets and Systems, 156(3), 2005, 349-356.
• [16] Nguyen, H.T. : On random sets and belief functions, Journal of Mathematical Analysis and Applications, 65, 1978, 531-542.
• [17] Pal, S. K. , Mitra, P.: Multispectral image segmentation using the rough-set-initialized EM algorithm, IEEE Transactions on Geoscience and Remote Sensing, 40(11), 2002, 2495-2501.
• [18] Pawlak, Z. , Skowron, A. : Rough membership functions, Advances in the Dempster-Shafer Theory of Evidence, 1994, 251-271.
• [19] Pawlak, Z. , Skowron, A. : Rough sets: some extensions, Information Sciences, 177, 2007, 28-40.
• [20] Pawlak, Z. : Rough sets, International Journal of Computer and Information Science, 11(5), 1982, 341-356.
• [21] Pawlak, Z. : Rough Sets: Theoretical Aspects of Reasoning about Data, Netherlands: Kluwer Academic Publishers, 1991.
• [22] Pawlak, Z., Wong, S.K.M. , Ziarko, W. : Rough sets: probabilistic versus deterministic approach, International Journal of Man-Machine Studies, 29, 1988, 81-95.
• [23] Polkowski, L. , Skowron, A. : Roughmereology. Proceedings of the 8th International SymposiumonMethodologies for Intelligent Systems on Methodologies for Intelligent Systems, LNCS 869, Berlin, Heidelberg: Springer-Verlag, 1994. 85-94.
• [24] Polkowski, L. , Skowron, A. : Rough mereology: a new paradigm for approximate reasoning, International Journal of Approximate Reasoning, 15(4), 1996, 333-365.
• [25] Puri, M.L. , Ralescu, D.A. : Fuzzy random variables, Journal of Mathematical Analysis and Applications, 114, 1986, 409-422.
• [26] Ren, Y.X. , Suo, X.Y. , Zhai, J.R. : Random fuzzy sets and random sets, Fuzzy Systems and Mathematics, 12(1), 1998, 66-70.
• [27] Shi, K.Q. , Xia, J. R. : Function S-rough sets and mining-discovery of rough law in systems, Journal of Systems Engineering and Electronics, 17(4), 2006, 919-926.
• [28] Skowron, A. , Polkowski, L. : Rough mereological foundations for design, analysis, synthesis, and control in distributed systems, Information Sciences, 104(1-2), 1998,129-156.
• [29] Skowron, A. , Stepaniuk, J. : Generalized Approximation Spaces, Proceedings of the Third International Workshop on Rough Sets and Soft Computing, San Jose, 1994, 156-163.
• [30] Skowron, A. , Stepaniuk, J. : Tolerance approximation spaces. Fundamenta Informaticae, 27, 1996, 245-253.
• [31] Su, C.T. , Hsu, J.H. : Precision parameter in the variable precision rough sets model: an application, Omega, 34 (2), 2006, 149-157.
• [32] We1, D. , Tang, L. : Attribute reduction based on inclusion degree for incomplete and fuzzy decision information systems, Journal of Communication and Computer, 3(5), 2006, 22-28.
• [33] Wojcik, Z. : Rough approximation of shapes in pattern recognition, Computer Vision, Graphics, and Image Processing, 40(2), 1987, 228-249.
• [34] Wong, S.K.M. ,Wang, L.S. and Yao, Y.Y. : On modeling uncertainty with interval structures, Computational Intelligence, 11(2), 1995, 406-426.
• [35] Wong, S.K.M. , Ziarko, W. : Comparison of the probabilistic approximate classification and the fuzzy set model, Fuzzy Sets and Systems, 21, 1987,357-362.
• [36] Wu, W.Z. : Rough set model based on inclusion degree, Journal of Zhejiang Ocean University (Natural Science), 19(4), 2000, 311-315.
• [37] Xu, Z.B. , Liang, J.Y. , Dang, C.Y. , et al. : Inclusion degree: a perspective on measures for rough set data analysis, Information Sciences, 141, 2002, 227-236.
• [38] Yao, Y.Y. : Constructive and algebraic approaches for generalized rough set models, Bulletin of International Rough Set Society, 1, 1997, 22-29.
• [39] Yao, Y.Y. : Probabilistic approaches to rough sets, Expert Systems, 20(5), 2003, 287-297.
• [40] Yao, Y.Y. : Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences, 111, 1998, 239-259.
• [41] Yao, Y.Y. , Lin, T.Y. : Generalization of rough sets using model logics, Intelligent Automation and Soft Computing, 2(2), 1996, 103-120.
• [42] Zadeh, L.A. : Fuzzy Sets, Information Control, 8, 1965, 338-353.
• [43] Ziarko,W. : Variable precision rough set model, Journal of Computer and System Science, 46, 1993, 39-59.
• [44] Zhang, W.X, Wu, W.Z., Liang J.Y., et al.: Theory and Method of Rough Sets, Beijing: Science Press, 2001, 132-157.