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Unifying Rough Set Theories via Large Scaled Granular Computing

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Języki publikacji
EN
Abstrakty
EN
This paper explains the mathematics of large scaled granular computing (GrC), augmented with a new Knowledge theory, by unifying rough set theories (RS) into one single concept, namely, neighborhood systems (NS). NS was first introduced in 1989 by T. Y. Lin to capture the concepts of “near” (topology) and “conflict” (security). Since 1996 when the term Granular Computing (GrC) was coined by T. Y. Lin to label Zadeh's vision, NS has been pushed into the “heart” of GrC. In 2011, LNS, the largest NS, was axiomatized; it implied that this set of axioms defines a new mathematics that realizes Zadeh's vision. The main messages are: this new mathematics is powerful and practical.
Wydawca
Rocznik
Strony
413--428
Opis fizyczny
Bibliogr. 35 poz., rys.
Twórcy
autor
  • Department of Computer Science, San José State University, San José, CA 95192, USA
autor
  • Institute of Cyber-Systems and Control, Zhejiang University, Hanghzou, 310027, PR China
autor
  • China United Network Communication Corporation, 100032 Beijing, China
Bibliografia
  • [1] Bairamian, S.: Goal Search in Relational Databases, 1989.
  • [2] Greco, S., Matarazzo, B., Slowinski, R.: Granular Computing and Data Mining for Ordered Data: The Dominance-Based Rough Set Approach, in: Encyclopedia of Complexity and Systems Science, 2009, 4283-4305.
  • [3] Grzymala-Busse, J. W.: Generalized Parameterized Approximations, RSKT, 2011.
  • [4] Huang, S., Zheng, X., Kang, H., Chen, D.: Word Sense Disambiguation Based on Positional Weighted Context, J. Information Science, 39(2), 2013, 225-237.
  • [5] Kelley, J.: General topology/[by] John L. Kelley, Springer-Verlag, New York :, 1975, ISBN 0387901256.
  • [6] Lin, T. Y.: Chinese Wall security policy -an aggressive model, Proceedings of the Fifth Aerospace Computer Security Application Conference, December 4-8, 1989., 1989.
  • [7] Lin, T. Y.: Neighborhood Systems and Approximation in Database and Knowledge Base Systems, Proceedings of the Fourth International Symposium on Methodologies of Intelligent Systems, Poster Session, October 12-15,1989, 1989.
  • [8] Lin, T. Y.: Topological and Fuzzy Rough Sets, in: Decision Support by Experience - Application of the Rough Sets Theory, R. Slowinski (ed.)., 1992.
  • [9] Lin, T. Y.: Granular Computing on Binary Relations I: Data Mining and Neighborhood Systems., Rough Sets In Knowledge Discovery, PhysicaVerlag, 1998.
  • [10] Lin, T. Y.: Granular Computing on Binary Relations II: Rough set representations and belief functions, Rough Sets In Knowledge Discovery, PhysicaVerlag, 1998.
  • [11] Lin, T. Y.: Granular Computing: Fuzzy Logic and Rough Sets, Computing with words in information/intelligent systems, PhysicaVerlag, 1999.
  • [12] Lin, T. Y.: Data Mining and Machine Oriented Modeling: A Granular Computing Approach, Journal of Applied Intelligence, 13(2), 2000, 113-124.
  • [13] Lin, T. Y.: Attribute (Feature) Completion- The Theory of Attributes from Data Mining Prospect, in: in the Proceedings of International Conference on Data Mining, Maebashi, Japan, Dec 9-12, 2002, 2002, 282-289.
  • [14] Lin, T. Y.: T. Y. Lin: Chinese Wall Security Policy Models: Information Flows and Confining Trojan Horses, DBSec 2003, 2003.
  • [15] Lin, T. Y.: A Roadmap from Rough Set Theory to Granular Computing, RSKT, 2006.
  • [16] Lin, T. Y.: Granular Computing: Practices, Theories, and Future Directions, in: Encyclopedia of Complexity and Systems Science, 2009, 4339-4355.
  • [17] Lin, T. Y.: Uncertainty and knowledge theories new era in Granular Computing, 2012 IEEE International Conference on Granular Computing, 2012.
  • [18] Lin, T. Y, Barot, R., Tsumoto, S.: Some Remarks on the Concept of Approximations from the View of Knowledge Engineering, IJCINI, 4(2), 2010, 1-11.
  • [19] Lin, T. Y, Hsu, J.-D.: Knowledge Based SearchEngine: Granular Computing on the Web, Web Intelligence, 2008.
  • [20] Lin, T. Y, Pan, J.: Granular Computing and Flow Analysis on Discretionary Access Control: Solving the Propagation Problem, IEEE SMC 2009, 2009.
  • [21] Lin, T. Y., Sutojo, A., Hsu, J.-D.: Concept Analysis and Web Clustering using Combinatorial Topology, ICDM Workshops 2006, 2006.
  • [22] Lin, T. Y., Syau, Y-R.: Granular Mathematics foundation and current state, GrC, 2011.
  • [23] Pawlak, Z.: Rough sets, International Journal of Computer and Information Sciences, 11(5), 1982, 341-356.
  • [24] Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data, Mathematics and Its Applications. Soviet Series, Kluwer Academic Publishers, 1991, ISBN 9780792314721.
  • [25] Pawlak, Z., Skowron, A.: Rough sets: Some extensions, Inf. Sci., 177(1), 2007, 28-40.
  • [26] Robinson, A.: Non-standard analysis, North-Holland Pub. Co., 1966.
  • [27] Slowinski, R., Vanderpooten, D.: A Generalized Definition of Rough Approximations Based on Similarity, IEEE Trans. Knowl. Data Eng., 12(2), 2000, 331-336.
  • [28] Spanier, E. H.: Algebraic Topology, McGraw-Hill Book Company, 1966.
  • [29] Stanat, D., McAllister, D.: Discrete Mathematics in Computer Science, Prentice-Hall, 1977.
  • [30] Wang, H.: Toward mechanical mathematics, IBMJ. Res. Dev., 4(1), January 1960, 2-22, ISSN 0018-8646.
  • [31] Xu, X., Lin, T. Y: Neighborhood System of Parameterized Binary Relations, GrC, 2012.
  • [32] Zadeh, L. A.: Fuzzy sets and Information Granularity, Advances in Fuzzy Set Theory and Applications, North-Holland, Amsterdam., 1979.
  • [33] Zadeh, L. A.: Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information/intelligent systems, Soft Comput., 2(1), 1998, 23-25.
  • [34] Zheng, X., Hu, Z., Xu, A., Chen, D., Liu, K., Li, B.: Algorithm for recommending answer providers in community-based question answering, J. Information Science, 38(1), 2012, 3-14.
  • [35] Ziarko, W.: Variable Precision Rough Set Model, J. Comput. Syst. Sci., 46(1), 1993, 39-59.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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