Sufficient Conditions of Cut Sets on Intuitionistic Fuzzy Sets

  • Yiying Shi
  • Xuehai Yuan
  • Yuchun Zhang
  • Yuhong Zhang
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 367)


In this paper, a monomorphism is established from the three-valued fuzzy sets to intuitionistic fuzzy sets, and with this monomorphism, the three-valued fuzzy sets can be embedded in intuitionistic fuzzy sets. Then the general definition of the cut sets on the intuitionistic fuzzy sets is proposed. Finally, the axiomatic descriptions for different cut sets are presented and three most intrinsic properties for each cut sets are listed.


Intuitionistic fuzzy sets Cut sets Sufficient condition Monomorphism 



This work was supported by the National Science Foundation of China (61473327).


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Yiying Shi
    • 1
    • 2
  • Xuehai Yuan
    • 1
    • 3
  • Yuchun Zhang
    • 2
  • Yuhong Zhang
    • 4
  1. 1.School of Control Science and EngineeringDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.School of ScienceShenyang Ligong UniversityShenyangPeople’s Republic of China
  3. 3.School of ScienceDalian University of Technology at PanjinPanjinPeople’s Republic of China
  4. 4.Department of Basic Education, City InstituteDalian University of TechnologyDalianPeople’s Republic of China

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