Intuitionistic Fuzzy Reasoning under Quotient Space Structure

  • QianSheng ZhangEmail author
  • ShiHua Luo
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 139)


This paper presents a theoretical basis of intuitionistic fuzzy reasoning under quotient space structure induced by an intuitionistic fuzzy equivalence relation. By constructing intuitionistic fuzzy set (IFS) representations of different grain-size spaces, the corresponding intuitionistic fuzzy reasoning method in quotient space and original universe space are studied and their relationships are then discussed.


Intuitionistic fuzzy set Quotient space Intuitionistic fuzzy equivalence relation Approximate reasoning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Atanassov, K.T.: Intuitionistic fuzzy logic. C. R. Acad. Bulgare Sc. 43, 9–12 (1990)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Ciftcibasi, T.: Two-sided (intuitionistic) fuzzy reasoning. IEEE Trans. Systems Man Cybernet. A-28, 662–677 (1998)Google Scholar
  4. 4.
    Lin, T.Y.: Context Free Fuzzy sets and Information Tables. In: European Congress on Intelligent Techniques and Soft Computing, pp. 76–80 (September 1998)Google Scholar
  5. 5.
    Lin, T.Y.: Granular computing on binary relations 1: data mining and neighborhood systems, manuscript. Department of Mathematics and Computer Science, San Jose, California, USA (1998)Google Scholar
  6. 6.
    Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision process. IEEE Trans. Systems. Man Cybernet. 3, 28–44 (1973)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning - II. Information Sciences 8, 301–357 (1975)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Zhang, L., Zhang, B.: Fuzzy reasoning model under quotient space structure. Information Sciences 173, 353–364 (2005)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.School of InformaticsGuangdong University of Foreign StudiesGuangzhouChina
  2. 2.School of StatisticsJiangxi University of Finance and EconomicsNanchangChina

Personalised recommendations