Induced Intuitionistic Fuzzy Ordered Weighted Averaging Operator and Its Application to Multiple Attribute Group Decision Making

  • Guiwu Wei
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5009)


With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic fuzzy numbers, a new group decision making analysis method is developed. Firstly, some operational laws of intuitionistic fuzzy numbers, score function and accuracy function of intuitionistic fuzzy numbers are introduced. Then a new aggregation operator called induced intuitionistic fuzzy ordered weighted averaging (I-IFOWA) operator is proposed, and some desirable properties of the I-IFOWA operators are studied, such as commutativity, idempotency and monotonicity. An I-IFOWA and IFWA (intuitionistic fuzzy weighted averaging) operators-based approach is developed to solve the MAGDM under the intuitionistic fuzzy environment. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.


Group decision making Intuitionistic fuzzy numbers Induced intuitionistic fuzzy ordered weighted averaging (I-IFOWA) operator 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Atanassov, K.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20, 87–96 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Atanassov, K.: More on Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 33, 37–46 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–356 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Gau, W.L., Buehrer, D.J.: Vague Sets. IEEE Transactions on Systems, Man and Cybernetics 23(2), 610–614 (1993)zbMATHCrossRefGoogle Scholar
  5. 5.
    Bustine, H., Burillo, P.: Vague Sets are Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 79, 403–405 (1996)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Xu, Z.S., Yager, R.R.: Some Geometric Aggregation Operators Based on Intuitionistic Fuzzy Sets. International Journal of General System 35(4), 417–433 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Xu, Z.S.: Intuitionistic Fuzzy Aggregation Operators. IEEE Transations on Fuzzy Systems 15(6), 1179–1187 (2007)CrossRefGoogle Scholar
  8. 8.
    Yager, R.R., Filev, D.P.: Induced Ordered Weighted Averaging Operators. IEEE Transactions on Systems, Man, and Cybernetics- Part B 29, 141–150 (1999)CrossRefGoogle Scholar
  9. 9.
    Chen, S.M., Tan, J.M.: Handling Multicriteria Fuzzy Decision-making Problems Based on Vague Set Theory. Fuzzy Sets and Systems 67, 163–172 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Hong, D.H., Choi, C.H.: Multicriteria Fuzzy Problems Based on Vague Set Theory. Fuzzy Sets and Systems 114, 103–113 (2000)zbMATHCrossRefGoogle Scholar
  11. 11.
    Herrera, F., Herrera-Viedma, E.: Linguistic Decision Analysis: Steps for Solving Decision Problems under Linguistic Information. Fuzzy Sets and Systems 115, 67–82 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Yager, R.R., Kacprzyk, J.: The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer, Boston (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Guiwu Wei
    • 1
  1. 1.Department of Economics and ManagementChongqing University of Arts and SciencesYongchuanP.R. China

Personalised recommendations