Neural Computing and Applications

, Volume 29, Issue 7, pp 435–447 | Cite as

Novel intuitionistic fuzzy soft multiple-attribute decision-making methods

Original Article
First Online:
Received:
Accepted:

Abstract

An intuitionistic fuzzy soft set plays a significant role as a mathematical tool for mathematical modeling, system analysis and decision making. This mathematical tool gives more precision, flexibility and compatibility to the system when compared to systems that are designed using fuzzy graphs and fuzzy soft graphs. In this paper, we use intuitionistic fuzzy soft graphs and possibility intuitionistic fuzzy soft graphs for parameterized representation of a system involving some uncertainty. We present novel multiple-attribute decision-making methods based on an intuitionistic fuzzy soft graph and possibility intuitionistic fuzzy soft graph. We also present our methods as algorithms that are used in our applications.

Keywords

Intuitionistic fuzzy soft sets Intuitionistic fuzzy soft graphs Possibility intuitionistic fuzzy soft graphs Decision-making problem 
This is a preview of subscription content, log in to check access

Notes

Acknowledgments

The authors are thankful to Editor-in-Chief, Professor John MacIntyre and the referees for their valuable comments and suggestions for improving the quality of our paper.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this article.

References

  1. 1.
    Akram M, Ashraf A, Sarwar M (2014) Novel applications of intuitionistic fuzzy digraphs in decision support systems. Sci World J 2014:11Google Scholar
  2. 2.
    Akram M, Davvaz B (2012) Strong intuitionistic fuzzy graphs. Filomat 26(1):177–196MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Akram M, Dudek WA (2013) Intuitionistic fuzzy hypergraphs with applications. Inf Sci 218:182–193MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Akram M, Nawaz S (2015) On fuzzy soft graphs. Ital J Pure Appl Math 34:497–514MathSciNetMATHGoogle Scholar
  5. 5.
    Akram M, Nawaz S (2016) Fuzzy soft graphs with applications. J Intell Fuzzy Syst 30(6):3619–3632CrossRefMATHGoogle Scholar
  6. 6.
    Atanassov KT (2012) Intuitionistic fuzzy sets: theory and applications. In: Studies in fuzziness and soft computing. Physica, HeidelbergGoogle Scholar
  7. 7.
    Atanassov KT (1983) Intuitionistic fuzzy sets, VII ITKR’s Session, Deposed in Central for Science-Technical Library of Bulgarian Academy of Sciences, 1697/84, Sofia, Bulgaria (Bulgarian)Google Scholar
  8. 8.
    Bashir M, Salleh AR, Alkhazaleh S (2012) Possibility intuitionistic fuzzy soft set. Adv Decis Sci 2012:1–24. doi: 10.1155/2012/404325 MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Cagman N, Karatas S (2013) Intuitionistic fuzzy soft set theory and its decision making. J Intell Fuzzy Syst 24(4):829–836MathSciNetMATHGoogle Scholar
  10. 10.
    Deli I, Cagman N (2015) Intuitionistic fuzzy parameterized soft set theory and its decision making. Appl Soft Comput 28(4):109–113CrossRefGoogle Scholar
  11. 11.
    Feng F, Jun YB, Liu XY, Li LF (2010) An adjustable approach to fuzzy soft set based decision making. J Comput Appl Math 234:10–20MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Feng F, Akram M, Davvaz B, Fotea VL (2014) Attribute analysis of information systems based on elementary soft implications. Knowl Based Syst 70:281–292CrossRefGoogle Scholar
  13. 13.
    Kauffman A (1973) Introduction to la Theorie des Sous-emsembles Flous. Masson et Cie, vol 1Google Scholar
  14. 14.
    Maji PK, Roy AR, Biswas R (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602MathSciNetMATHGoogle Scholar
  15. 15.
    Maji PK, Biswas R, Roy AR (2001) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–691MathSciNetMATHGoogle Scholar
  16. 16.
    Mordeson JN, Nair PS (1998) Fuzzy graphs and fuzzy hypergraphs. Physica Verlag, Heidelberg. Second Edition 2001Google Scholar
  17. 17.
    Molodtsov DA (1999) Soft set theory-first results. Comput Math Appl 37:19–31MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Qin J, Liu X, Pedrycz W (2015) Hesitant fuzzy maclaurin symmetric mean operators and its application to multiple-attribute decision making. Int J Fuzzy Syst 17(4):509–520MathSciNetCrossRefGoogle Scholar
  19. 19.
    Rao RV (2006) A decision-making framework model for evaluating flexible manufacturing systems using digraph and matrix methods. Int J Adv Manuf Technol 30(11–12):1101–1110CrossRefGoogle Scholar
  20. 20.
    Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203:412–418CrossRefMATHGoogle Scholar
  21. 21.
    Rosenfeld A (1975) Fuzzy sets and their applications. In: Zadeh LA, Fu KS, Tanaka K, Shimura M (eds) Fuzzy graphs. Academic Press, New York, pp 77–95Google Scholar
  22. 22.
    Shahzadi S, Akram M (2016) Edge regular intuitionistic fuzzy soft graphs. J Intell Fuzzy Syst. doi: 10.3233/JIFS-16120 MATHGoogle Scholar
  23. 23.
    Singh PK, Kumar ChA (2014) Bipolar fuzzy graph representation of concept lattice. Inf Sci 288:437–448MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Xu ZS (2004) Uncertain multiple attribute decision making, methods and applications. Tsinghua University Press, BeijingGoogle Scholar
  25. 25.
    Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefMATHGoogle Scholar
  26. 26.
    Zadeh LA (1971) Similarity relations and fuzzy orderings. Inf Sci 3(2):177–200MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Zhu J, Zhan J (2015) Fuzzy parameterized fuzzy soft sets and decision making. Int J Mach Learn Cyber 1–6. doi: 10.1007/s13042-015-0449-z

Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the Punjab, New CampusLahorePakistan

Personalised recommendations