Soft Computing

, Volume 21, Issue 23, pp 7077–7082 | Cite as

An intuitionistic fuzzy multi-criteria decision-making method based on non-hesitance score for interval-valued intuitionistic fuzzy sets

  • V. Lakshmana Gomathi Nayagam
  • S. JeevarajEmail author
  • P. Dhanasekaran
Methodologies and Application


Fuzzy numbers and intuitionistic fuzzy numbers are introduced in the literature to model problems involving incomplete and imprecise numerical quantities. Researchers from all over the world have been working in ranking of intuitionistic fuzzy numbers since 1985, but till date there is no common methodology that rank any two arbitrary intuitionistic fuzzy numbers. In order to improve the familiar ranking methods, a new non-hesitance score function for the theory of interval-valued intuitionistic fuzzy sets is introduced and the necessity for defining a new non-hesitance score function is explained using illustrative examples. In this paper, a new multi-criteria decision-making algorithm is established for decision problems involving interval-valued intuitionistic fuzzy numbers. Further the practicality of the proposed method is shown by solving an interval-valued intuitionistic fuzzy MCDM problem. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach.


Intuitionistic fuzzy number Interval-valued intuitionistic fuzzy number Non-hesitance score MCDM IFMCDM 



The authors are grateful to the anonymous reviewers whose thoughtful remarks are greatly useful for the improvement of the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRefzbMATHGoogle Scholar
  2. Atanassov KT (2014) Index matrices: towards an augmented matrix calculus. Springer, ChamzbMATHGoogle Scholar
  3. Herrera F, Herrera-Viedma E (2000) Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst 115:67–82CrossRefzbMATHMathSciNetGoogle Scholar
  4. Nayagam VLG, Muralikrishnan S, Sivaraman G (2011) Multi criteria decision making method based on interval valued intuitionistic fuzzy sets. Exp Syst Appl 38(3):1464–1467CrossRefGoogle Scholar
  5. Sahin R (2015) Fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets. Soft Comput 20(7):2557–2563CrossRefzbMATHGoogle Scholar
  6. Xu ZS (2007) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22(2):215–219Google Scholar
  7. Xu ZS (2013) Intuitionistic fuzzy aggregation and clustering. Springer, BerlinzbMATHGoogle Scholar
  8. Yang Y, Liang C, Ji S (2015) Comments on fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets by Ridvan Sahin. Soft Comput. doi: 10.1007/s00500-015-1988-7 Google Scholar
  9. Ye J (2009) Multicriteria fuzzy decision making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Exp Syst Appl 36(6):6899–6902CrossRefGoogle Scholar
  10. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–356CrossRefzbMATHGoogle Scholar
  11. Zhang F, Xu S (2015) Remarks to fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets. Soft Comput. doi: 10.1007/s00500-015-1932-x Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • V. Lakshmana Gomathi Nayagam
    • 1
  • S. Jeevaraj
    • 1
    Email author
  • P. Dhanasekaran
    • 1
  1. 1.Department of MathematicsNational Institute of TechnologyTiruchirappalliIndia

Personalised recommendations