Fuzzy Set Theory and Rough Set Theory

Part of the Control Engineering book series (CONTRENGIN)


In daily life, we use information obtained to understand our surroundings, to learn new things, and to make plans for the future. Over the years, we have developed the ability to reason on the basis of evidence in order to achieve our goals. However, since we are restricted by our ability to perceive the world, we find ourselves always confronted by uncertainties about how good our inferences are. Uncertainties are one of the sources from which our errors stem since we do not know the exact information about our environment.


Membership Function Linguistic Variable Fuzzy Relation Crisp Relation Fuzzy Proposition 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. Driankov, H. Hellendoorn, and M. Reinfrank, An Introduction to Fuzzy Control, 2nd Ed., New York: Springer-Verlag, 1996.MATHGoogle Scholar
  2. [2]
    G. J. Klir, U. St. Clair, and B. Yuan, Fuzzy Set Theory: Foundations and Applications, Upper Saddle River, NJ: Prentice Hall, 1997.MATHGoogle Scholar
  3. [3]
    H. Liang, H. Zhang, and D. Liu, “Roughness of fuzzy sets based on two new operators,” Proceedings of the IEEE International Conference on Fuzzy Systems, Budapest, Hungary, July 2004, pp 583–586.Google Scholar
  4. [4]
    T. Y. Lin and N. Cercone, Eds., Rough Sets and Data Ming: Analysis of Imprecise Data Norwell, MA: Kluwer Academic Publishers, 1996.Google Scholar
  5. [5]
    K. Passino and S. Yurkovich, Fuzzy Control, Menlo Park, CA: Addison-Wesley, 1998.Google Scholar
  6. [6]
    Z. Pawlak, “Rough sets,” International Journal of Computer and Information Sciences, vol. 11, pp. 341–356, 1982.CrossRefMathSciNetGoogle Scholar
  7. [7]
    Z. Pawlak, Rough Sets-Theoretical Aspects of Reasoning about Data, Boston, MA, USA: Kluwer Academic Publishers, 1991.MATHGoogle Scholar
  8. [8]
    Z. Pawlak, “Rough set theory and its applications to data analysis,” Cybernetics and Systems, vol. 29, no. 7, pp. 661–688, Oct.–Nov. 1998.MATHCrossRefGoogle Scholar
  9. [9]
    L. Polkowski and A. Skowron, Eds., Rough Sets in Knowledge Discovery: Applications, Case Studies and Software Systems, New York: Springer-Verlag, 1998.MATHGoogle Scholar
  10. [10]
    R. Slowinski, Ed., Intelligent Decision Support: Handbook of Applications and Advances of the Rough Set Theory, Norwell, MA: Kluwer Academic Publishers, 1992.Google Scholar
  11. [11]
    L. Wang. A Course in Fuzzy Systems and Control, Upper Saddle River, NJ: Prentice Hall. 1997.MATHGoogle Scholar
  12. [12]
    I. Yen and R. Langari, Fuzzy Logic: Intelligence, Control, and Information, Upper Saddle River, NJ: Prentice Hall, 1999.Google Scholar
  13. [13]
    L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Transaction on Systems. Man. and Cybernetics, vol. SMC-3, no. 1, pp. 28–44, 1973.MathSciNetGoogle Scholar
  14. [14]
    L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning-I, II, III,” Information Sciences, vol. 8, no. 3, pp. 199–249; vol. 8, no. 4, pp. 301–357; vol. 9, no. 1, pp. 43–80, 1975.CrossRefMathSciNetGoogle Scholar
  15. [15]
    H. Zhang, H. Liang, and D. Liu, “Two new operators in rough set theory with applications to fuzzy sets,” Information Sciences, vol. 166, no. 1–4, pp. 147–165. Oct. 2004.MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    H. J. Zimmermann, Fuzzy Set Theory and Its Application, Netherlands: Kluwer-Nijhoff, 1985.Google Scholar
  17. [17]
    K. Zou and Y. Xu, Fuzzy Systems and Expert Systems, Sichuan, China: Southwest Jiaotong University Press, 1989.Google Scholar
  18. [18]
    Proceedings of the 4th International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery, Tokyo, Japan, Nov. 1996.Google Scholar

Copyright information

© Birkhäuser Boston 2006

Personalised recommendations