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Granular Computing pp 125–142Cite as

Granulation and Nearest Neighborhoods: Rough Set Approach

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 70))

Abstract

“Nearest” neighborhoods are informally used in many areas of AI and database. Mathematically, a “nearest” neighborhood system that maps each object p a unique crisp/fuzzy subset of data, representing the “nearest” neighborhood, is a binary relation between the object and data spaces. “Nearest” neighborhood consists of data that are semantically related to p, and represents an elementary granule (atoms) of the system under consideration. This paper examines “rough set theory” of these elementary granules. Applications to databases, fuzzy sets and pattern recognition are used to illustrate the idea.

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References

  1. S. Bairamian, Goal Search in Relational Databases, Thesis, California State University at Northridge, 1989.

    Google Scholar 

  2. T. Back, Evolutionary Algorithm in Theory and Practice, Oxford University Press, 1996.

    Google Scholar 

  3. Cattaneo, G.: Mathematical foundations of roughness and fuzziness. In: S. Tsumoto, S. Kobayashi, T. Yokomori, H. Tanaka and A.Nakamura (eds.), The fourth International Workshop on Rough Sets Fuzzy Sets, and Machine Discovery, PROCEEDINGS (RS96FD), November 6–8, The University of Tokyo (1996) 241–247

    Google Scholar 

  4. W. Chu, Neighborhood and associative query answering, Journal of Intelligent Information Systems, 1, 355–382, 1992.

    Article  Google Scholar 

  5. K. Fukunaga, “Statistical Pattern Recognition,” Academic Press 7 1990.

    Google Scholar 

  6. K. Engesser, Some connections between topological and Modal Logic, Mathematical Logic Quarterlyi 41, 49–64, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  7. Halmos, P., Measure Theory, Van Nostrand, 1950.

    Google Scholar 

  8. John Kelly. General topology, 1955.

    Google Scholar 

  9. Alexander Hinneburg and Daniel A. Keim “An Efficeint Approach to Clustering in Large Multimedia Databases with Noise.” In: Proceedings of the 4th International Conference on Knowledge Discovery Data Mining,“ Agrawahl, Stolorz, and Pistetsky-Shapiro (eds), Aug 27–31, 1998, 58–65.

    Google Scholar 

  10. T. Y. Lin, Neighborhood Systems and Relational Database. In: Proceedings of 1988 ACM Sixteen Annual Computer Science Conference, February 23–25, 1988, 725

    Google Scholar 

  11. Topological Data Models and Approximate Retrieval and Reasoning, in: Proceedings of 1989 ACM Seventeenth Annual Computer Science Conference, February 21–23, Louisville, Kentucky, 1989, 453.

    Google Scholar 

  12. T. Y. Lin, 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, pp. 75–86, 1989.

    Google Scholar 

  13. T. Y. Lin, Topological and Fuzzy Rough Sets. In: Decision Support by Experience–Application of the Rough Sets Theory, R, Slowinski (ed.), Kluwer Academic Publishers, 287–304, 1992

    Google Scholar 

  14. A Logic System for Approximate Reasoning via Rough Sets and Topology,“ Methodologies of Intelligent Systems, Lecture notes in Artificial Intelligence 869, ed. By Z. Ras, and M. Zemankova, 1994, 65–74. Co-author: Q. Liu and Y. Y. Yao)

    Google Scholar 

  15. T. Y. Lin, and Q. Liu, Rough Approximate Operators-Axiomatic Rough Set Theory. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, W. Ziarko (ed), Springer-Verlag, 256–260, 1994. Also in: The Proceedings of Second International Workshop on Rough Sets and Knowledge Discovery, Banff, Oct. 12–15, 255–257, 1993.

    Google Scholar 

  16. T. Y. Lin and S. Tsumoto, Qualitative Fuzzy Sets Revisited: Granulation on the Space of Membership Functions., Atlanta, July 13–15, 2000

    Google Scholar 

  17. Universal Approximator,-Turing computability,“ The First Annual International Conference Computational Intelligence & Neuroscience, Proceedings of Second Annual Joint Conference on Information Science, Wrightsville Beach, North Carolina, Sept. 28-Oct. 1, 1995, 157–160.

    Google Scholar 

  18. T. Y Lin, A Set Theory for Soft Computing. In: Proceedings of 1996 IEEE International Conference on Fuzzy Systems, New Orleans, Louisiana, September 8–11, 1140–1146, 1996.

    Google Scholar 

  19. T. Y. Lin, Rough Set Theory in Very Large Databases, Symposium on Modeling, Analysis and Simulation, IMACS Multi Conference (Computational Engineering in Systems Applications), Lille, France, July 9–12, 1996, Vol. 2 of 2, 936–941.

    Google Scholar 

  20. The Power and Limit of Neural Networks,“ Proceedings of the 1996 Engineering Systems Design and Analysis Conference, Montpellier, France, July 1–4, 1996, Vol. 7, 49–53.

    Google Scholar 

  21. T. Y. Lin, and Y. Y. Yao, Mining Soft Rules Using Rough Sets and Neighborhoods. In: Symposium on Modeling, Analysis and Simulation, CESA’96 IMACS Multiconference (Computational Engineering in Systems Applications), Lille, France, 1996, Vol. 2 of 2, 1095–1100, 1996.

    Google Scholar 

  22. T. Y. Lin, and M. Hadjimichaelm M., Non-classificatory Generalization in Data Mining. In: Proceedings of The Fourth Workshop on Rough Sets, Fuzzy Sets and Machine Discovery, Tokyo, Japan, November 8–10, 404–411, 1996.

    Google Scholar 

  23. T. Y. Lin and Rayne Chen, Supporting Rough Set Theory in Very Large Database Using ORACLE RDBMS, Soft Computing in Intelligent Systems and Information Processing, Proceedings of 1996, Asian Fuzzy Systems Symposium, Kenting, Taiwan, December 11–14, 1996, 332–337 ( Co-author: R. Chen )

    Google Scholar 

  24. T. Y. Lin and Rayne Chen, Finding Reducts in Very Large Databases, Proceedings of Joint Conference of Information Science,Research Triangle Park, North Carolina, March 1–5, 1997, 350–352.

    Google Scholar 

  25. T. Y. Lin, Neighborhood Systems -A Qualitative Theory for Fuzzy and Rough Sets. In: Advances in Machine Intelligence and Soft Computing, Volume IV. Ed. Paul Wang, 132–155, 1997. Also in Proceedings of Second Annual Joint Conference on Information Science, Wrightsville Beach, North Carolina, Sept. 28-Oct. 1, 1995, 257–260, 1995.

    Google Scholar 

  26. T. Y. Lin, “Granular Computing on Binary Relations I: Data Mining and Neighborhood Systems.” In: Rough Sets In Knowledge Discovery, A. Skoworn and L. Polkowski (eds), Springer-Verlag, 1998, 107–121

    Google Scholar 

  27. T. Y. Lin, “Granular Computing on Binary Relations II: Rough Set Representations and Belief Functions.” In: Rough Sets In Knowledge Discovery, A. Skoworn and L. Polkowski (eds), Springer-Verlag, 1998, 121–140.

    Google Scholar 

  28. T. Y. Lin, “Granular Computing: Fuzzy Logic and Rough Sets. ” In: Computing with words in information/intelligent systems, L.A. Zadeh and J. Kacprzyk (eds), Springer-Verlag, 183–200, 1999

    Chapter  Google Scholar 

  29. T. Y. Lin, Data Mining and Machine Oriented Modeling: A Granular Computing Approach Journal of Applied Intelligence, 2000

    Google Scholar 

  30. A. Motro, Supporting Goal Queries in Relational Databases. In: Kerschberg (ed) Proceedings of the First International Conference on Expert Database Systems, Charleston, South Carolina, April 1–4, 1986

    Google Scholar 

  31. J. Park and I. W. Sandberg, Universal Approximation Using radial-Basis- Function Networks, Neural Computation 3, 1991, pp. 246–257.

    Article  Google Scholar 

  32. Z. Pawlak, Rough sets. Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, 1991

    Book  MATH  Google Scholar 

  33. Polkowski, L., Skowron, A., and Zytkow, J., (1995), Tolerance based rough sets. In: T.Y. Lin and A. Wildberger (eds.), Soft Computing: Rough Sets } Fuzzy Logic Neural Networks, Uncertainty Management, Knowledge Discovery, Simulation Councils, Inc. San Diego CA, 55–58.

    Google Scholar 

  34. W. Sierpenski and C. Krieger, General Topology, University of Torranto Press 1956.

    Google Scholar 

  35. Slowinski, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. ICS Research Report 53/95, Warsaw Unviersity of Technology (1995)

    Google Scholar 

  36. E. Spanier, Algebraic Topology,McGraw-Hill.

    Google Scholar 

  37. Stefanowski, J.: Using valued closeness relation in classification support of new objects. In: T. Y. Lin, A. Wildberger (eds.), Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, Knowledge Discovery, Simulation Councils, Inc., San Diego CA=20 (1995) 324–327

    Google Scholar 

  38. Helmut Thiele: On the Concept of Qualitative Fuzzy Set, University of Dortmund, Pre-print, 1998

    Google Scholar 

  39. M. Viveros, Extraction of Knowledge from Databases, Thesis, California State University at Northridge, 1989.

    Google Scholar 

  40. Y. Y. Yao and T. Y. Lin, Yao, Y.Y., and Lin, T.Y. Generalization of rough sets using modal logic. Intelligent Automation and Soft Computing, An International Journal, 2, No. 2, pp. 103–120, 1996.

    Google Scholar 

  41. Y. Y. Yao, M. S. K. Wong, and T. Y. Lin, “A Review of Rough Set Models,” Rough Sets and Data Mining: Analysis of Imprecise Data, Kluwer Academic Publisher, 1997, 47–75

    Book  Google Scholar 

  42. Y. Y. Yao, Binary Relation Based Neighborhood Operators. In: Proceedings of the Third Annual Joint Conference in Information Sciences, Research Triangle Park, March 1–5, 169–172, 1997.

    Google Scholar 

  43. Lotfi Zadeh, Fuzzy Graph, Rough sets and Information Ganularity. In: Proceedings of the Third Internatiorial Workshop on Rough Sets and Soft Computings, San Jose, Nov. 10–12, 1, 1994

    Google Scholar 

  44. Lotfi Zadeh, The Key Roles of Information Granulation and Fuzzy logic in Human Reasoning. In: 1996 IEEE International Conference on Fuzzy Systems, September 8–11, 1, 1996.

    Google Scholar 

  45. L.A. Zadeh, Fuzzy Sets and Information Granularity, in: M. Gupta, R. Ragade, and R. Yager, (Eds), Advances in Fuzzy Set Theory and Applications, North- Holland, Amsterdam, 1979, 3–18.

    Google Scholar 

  46. H. Zimmerman, Fuzzy Set Theory -and its Applications, Second Ed., Kluwer Acdamic Publisher, 1991.

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, San Jose State University, San Jose, California, 95192-0103, USA

    T. Y. Lin

  2. Berkeley Initiative in Soft Computing, University of California, Berkeley, California, 94720, USA

    T. Y. Lin

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  1. T. Y. Lin
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Alberta, T6R 2G7, Edmonton, Alberta, Canada

    Witold Pedrycz

  2. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Witold Pedrycz

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© 2001 Springer-Verlag Berlin Heidelberg

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Lin, T.Y. (2001). Granulation and Nearest Neighborhoods: Rough Set Approach. In: Pedrycz, W. (eds) Granular Computing. Studies in Fuzziness and Soft Computing, vol 70. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1823-9_6

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  • DOI: https://doi.org/10.1007/978-3-7908-1823-9_6

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2487-2

  • Online ISBN: 978-3-7908-1823-9

  • eBook Packages: Springer Book Archive

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