Advertisement

Information Distribution

  • Chongfu Huang
  • Yong Shi
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 99)

Abstract

This chapter presents the concept of information distribution. Through information distribution, we can change the crisp observations of a given sample into fuzzy sets. Hence, fuzzy sets are employed to describe the fuzzy transition information in a small sample. It is useful to improve the estimation of the probability distribution. Based on this estimation, we can construct fuzzy relationships, directly, without any assumptions. In detail, we discuss the method of 1-dimension linear-information-distribution. Computer simulation shows the work efficiency of the new method is about 23% higher than the histogram method for the estimation of a probability distribution. The chapter is organized as follows: in section 4.1, we introduce the concept of information distribution. In section 4.2, we give the mathematical definition of information distribution. Section 4.3 gives the method of 1-dimension linear-information-distribution. Section 4.4 demonstrates the benefit of information distribution for probability distribution estimation. In section 4.5, we construct a fuzzy relation matrixes with the method of information distribution. In section 4.6, we discuss approximate inference based on information distribution.

Keywords

Factor Space Information Distribution Fuzzy Relation Linear Distribution Work Efficiency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berkan, R. C. and Trubatch, S. L. (1997]), Fuzzy Systems Design Principles: Building Fuzzy If-Then Rule Bases. IEEE, New YorkGoogle Scholar
  2. 2.
    Gupta, M. M. and Qi, J. (1991), Theory of T-norms and fuzzy inference methods. Fuzzy Sets and Systems, Vol. 40, pp. 431–450MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Jang, J. -S. R. (1993), ANFIS: Adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man, and Cybernetics, Vol.23, No., pp. 665–685Google Scholar
  4. 4.
    Kullback, S. (1959), Information Theory and Statistics. Wiley, New YorkMATHGoogle Scholar
  5. 5.
    Luo, C. Z. (1993), The Fundamental Theory of Fuzzy Sets(II). Beijing Normal University Press, Beijing (in Chinese)Google Scholar
  6. 6.
    Mamdani, E. H. (1977), Application of fuzzy logic to approximate reasoning using linguistic synthesis. IEEE Trans. Computers, Vol.26, No.12, pp. 11821191Google Scholar
  7. 7.
    Peng, X. T., Kandel, A., Wang, P. Z. (1991), Concepts, rules, and fuzzy reasoning: a factor space approach. IEEE Trans. Systems, Man, and Cybernetics, Vol. 21, No. 2, pp. 194–205MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Peng, X. T., Wang, P. Z., and Kandel, A. (1996), Knowledge acquisition by random sets. International Journal of Intelligent Systems, Vol.11, No.3, pp. 113147Google Scholar
  9. 9.
    Pérez-Neira, A., Sueiro, J. C., Rota, J., and Lagunas, M. A. (1998), A dynamic non-singleton fuzzy logic system for DSKDMA communications. Proceedings of FUZZ-IEEE’98, Anchorage, USA, pp. 1494–1499Google Scholar
  10. 10.
    Tanaka, H. (1996), Possibility model and its applications. in: Ruan, D. Ed., Fuzzy Logic Foundations and Industrial Applications, Kluwer Academic Publishers, Boston, pp. 93–110Google Scholar
  11. 11.
    Wang, L. X. and Mendel, J. M. (1992), Generating fuzzy rules by learning through examples. IEEE Trans. on Systems, Man, and Cybernetics, Vol. 22, No. 6, pp. 1414–1427MathSciNetCrossRefGoogle Scholar
  12. 12.
    Wang, P. Z. (1983), Fuzzy Sets Theory and Applications. Shanghai Publishing House of Science and Technology, Shanghai (in Chinese)Google Scholar
  13. 13.
    Wang, P. Z. (1985), Fuzzy Sets and Falling Shadows of Random Sets. Beijing Normal University Press, Beijing (in Chinese)Google Scholar
  14. 14.
    Wang, P. Z. (1990), A factor space approach to knowledge representation. Fuzzy Sets and Systems, Vol. 36, pp. 113–124MathSciNetMATHCrossRefGoogle Scholar
  15. Wang, P. Z, Huang, M. and Zhang, D. Z. (1992), Reeaxmining fuzziness and randomness using falling shadow theory. Proceedings of the Tenth International Conference on Multiple Criteria Decision Making, Taipei, pp. 101–110Google Scholar
  16. 16.
    Wang, P. Z., Liu, X. H. and Sanchez E. (1986), Set-valued statistics and its application to earthquake engineering. Fuzzy sets and Systems, Vol.18, pp. 347356Google Scholar
  17. 17.
    Wang, P. Z. and Sugeno, M. (1982), The factor fields and background structure for fuzzy subsets. Fuzzy Mathematics, Vol. 2, pp. 45–54MathSciNetMATHGoogle Scholar
  18. 18.
    Yager, R. R. and Filev, D. P. (1994), Essentials of Fuzzy Modeling and Control, John Wiley, New YorkGoogle Scholar
  19. 19.
    Zsutty, T. C. (1985), A deterministic and fuzzy method or relating intensity, building damage, and earthquake ground motion. Fen Deyi and Liu Xihui (eds): Fuzzy Mathematics in Earthquake Researches. Seismological Press, Beijing, pp. 79–94Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Chongfu Huang
    • 1
  • Yong Shi
    • 2
  1. 1.Institute of Resources ScienceBeijing Normal UniversityBeijingChina
  2. 2.College of Information Science and TechnologyUniversity of Nebraska at OmahaOmahaUSA

Personalised recommendations