• Zhinan HaoEmail author
  • Zeshui Xu
  • Hua Zhao
Part of the Uncertainty and Operations Research book series (UOR)


This chapter briefly presents the basic concept, the formulation, the basic operation laws, and aggregation operators of the intuitionistic fuzzy set (IFS). These methods and theory are the preliminary knowledge which will be used in the intuitionistic fuzzy decision-making methods in this book.


  1. Atanassov KT (2009) Remark on operations “subtraction” over intuitionistic fuzzy sets. Notes Intuitionistic Fuzzy Sets 15(3):20–24Google Scholar
  2. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96Google Scholar
  3. Atanassov KT (2012) On intuitionistic fuzzy sets theory. Springer, BerlinCrossRefGoogle Scholar
  4. Bustince H, Fernandez J, Kolesárová A, Mesiar R (2013a) Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst 220:69–77CrossRefGoogle Scholar
  5. Bustince H, Galar M, Bedregal B, Kolesarova A, Mesiar R (2013b) A new approach to interval-valued choquet integrals and the problem of ordering in interval-valued fuzzy set applications. IEEE Trans Fuzzy Syst 21(6):1150–1162CrossRefGoogle Scholar
  6. Chen SM, Tan JM (1994) Handling multicriteria fuzzy decision-making problems based on vague set-theory. Fuzzy Sets Syst 67(2):163–172CrossRefGoogle Scholar
  7. Chen TY (2007) Remarks on the subtraction and division operations over intuitionistic fuzzy sets and interval-valued fuzzy sets. Int J Fuzzy Syst 9(3):169–172Google Scholar
  8. De SK, Biswas R, Roy AR (2000) Some operations on intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):477–484CrossRefGoogle Scholar
  9. Hong DH, Choi CH (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114(1):103–113CrossRefGoogle Scholar
  10. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187CrossRefGoogle Scholar
  11. Xu ZS (2010) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180(5):726–736CrossRefGoogle Scholar
  12. Xu ZS, Xia MM (2011) Induced generalized intuitionistic fuzzy operators. Knowl-Based Syst 24(2):197–209CrossRefGoogle Scholar
  13. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J General Syst 35(4):417–433CrossRefGoogle Scholar
  14. Xu ZS, Yager RR (2011) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst Man Cybern Part B Cybern 41(2):568–578CrossRefGoogle Scholar
  15. Zhao H, Xu ZS, Ni MF, Liu SS (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25(1):1–30CrossRefGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Command and Control Engineering CollegeArmy Engineering University of PLANanjingChina
  2. 2.Business SchoolSichuan UniversityChengduChina
  3. 3.Department of General EducationArmy Engineering University of PLANanjingChina

Personalised recommendations