Skip to main content
SpringerLink
Log in

New decision-making hybrid model: intuitionistic fuzzy N-soft rough sets

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this paper, we introduce three novel hybrid models, namely, intuitionistic fuzzy N-soft sets (IFNSSs), N-soft rough intuitionistic fuzzy sets and intuitionistic fuzzy N-soft rough sets (IFNSRSs). We discuss some of their respective properties. We also present the lower and upper intuitionistic fuzzy N-soft rough approximation operators and investigate their properties. Furthermore, we present respective new approaches to decision-making problems based on the IFNSS and IFNSRS models in an algorithmic format. Finally, we present illustrative examples in order to show that these decision-making methods can be fruitfully employed to solve real life problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Akram M, Davvaz B, Feng F (2015) Fuzzy soft Lie algebras. J Multivalued Logic Soft Comput 24(5–6):501–520

    MathSciNet  MATH  Google Scholar 

  • Akram M, Ali G, Alshehri NO (2017a) A new multi-attribute decision-making method based on \(m\)-polar fuzzy soft rough sets. Symmetry 9(11):271. https://doi.org/10.3390/sym9110271

    Article  MATH  Google Scholar 

  • Akram M, Feng F, Saeid AB, Fotea V (2017) A new multiple criteria decision-making method based on bipolar fuzzy soft graphs. Iran J Fuzzy Syst. https://doi.org/10.22111/IJFS.2017.3394

    Article  MATH  Google Scholar 

  • Akram M, Adeel A, Alcantud JCR (2018a) Fuzzy N-soft sets: a novel model with applications. J Intell Fuzzy Syst 35(4):4757–4771

    Article  Google Scholar 

  • Akram M, Ali G, Waseem N, Davvaz B (2018b) Decision-making methods based on hybrid mF models. J Intell Fuzzy Syst 35(3):3387–3403

    Article  Google Scholar 

  • Akram M, Adeel A, Alcantud JCR (2019) Group decision-making methods based on hesitant \(N\)-soft sets. Expert Syst Appl 115:95–105

    Article  Google Scholar 

  • Alcantud JCR (2016) A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set. Inf Fusion 29:142–148

    Article  Google Scholar 

  • Alcantud JCR, Laruelle A (2014) Dis&approval voting: a characterization. Soc Choice Welf 43(1):1–10

    Article  MathSciNet  MATH  Google Scholar 

  • Alcantud JCR, Santos-García G (2017) A new criterion for soft set based decision making problems under incomplete information. Int J Comput Intell Syst 10:394–404

    Article  Google Scholar 

  • Ali MI (2011) A note on soft sets, rough soft sets and fuzzy soft sets. Appl Soft Comput 11(4):3329–3332

    Article  Google Scholar 

  • Ali MI, Feng F, Liu XY, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547–1553

    Article  MathSciNet  MATH  Google Scholar 

  • Atanassov KT (1983) Intuitionistic fuzzy sets. VII ITKRs Session, Sofia

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  MATH  Google Scholar 

  • Cagman N, Enginoglu S (2010) Soft matrix theory and decision making. Comput Math Appl 59(10):3308–3314

    Article  MathSciNet  MATH  Google Scholar 

  • Cagman N, Enginoglu S (2012) Fuzzy soft matrix theory and its application in decision-making. Iran J Fuzzy Syst 9(1):109–119

    MathSciNet  MATH  Google Scholar 

  • Chen J, Li S, Ma S, Wang X (2014) \(m\)-polar fuzzy sets: an extension of bipolar fuzzy sets. Sci World J 2014:8 Article ID 416530

    Google Scholar 

  • Fatimah F, Rosadi D, Hakim RBF, Alcantud JCR (2018a) \(N\)-soft sets and their decision making algorithms. Soft Comput 22:3829–3842

    Article  MATH  Google Scholar 

  • Fatimah F, Rosadi D, Hakim RBF, Alcantud JCR (2018b) Probabilistic soft sets and dual probabilistic soft sets in decision-making. Neural Comput Appl (forthcoming)

  • Feng F (2011) Soft rough sets applied to multicriteria group decision making. Ann Fuzzy Math Inform 2(1):69–80

    MathSciNet  MATH  Google Scholar 

  • Feng F, Li C, Davvaz B, Ali MI (2010a) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14(9):899–911

    Article  MATH  Google Scholar 

  • Feng F, Jun YB, Liu X, Li L (2010b) An adjustable approach to fuzzy soft set based decision-making. J Comput Appl Math 234(1):10–20

    Article  MathSciNet  MATH  Google Scholar 

  • Feng F, Liu X, Leoreanu-Fotea V, Jun YB (2011) Soft sets and soft rough sets. Inf Sci 181(6):1125–1137

    Article  MathSciNet  MATH  Google Scholar 

  • Gong K, Xiao Z, Zhang X (2010) The bijective soft set with its operations. Comput Math Appl 60(8):2270–2278

    Article  MathSciNet  MATH  Google Scholar 

  • Herawan T, Deris MM (2009) On multi-soft sets construction in information systems. Springer, Berlin, pp 101–110

    MATH  Google Scholar 

  • Kong Z, Gao L, Wang L (2009) Comment on: A fuzzy soft set theoretic approach to decision-making problem. J Comput Appl Math 223(2):540–542

    Article  MATH  Google Scholar 

  • Ma X, Liu Q, Zhan J (2017) A survey of decision making methods based on certain hybrid soft set models. Artif Intell Rev 47:507–530

    Article  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2001a) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692

    MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2001b) Fuzzy soft sets. J Fuzzy Math 9(3):589–602

    MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2002) An application of soft sets in a decision-making problem. Comput Math Appl 44(8):1077–1083

    Article  MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(4–5):555–562

    Article  MathSciNet  MATH  Google Scholar 

  • Molodtsov DA (1999) Soft set theory—first results. Comput Math Appl 37(4–5):19–31

    Article  MathSciNet  MATH  Google Scholar 

  • Naz M, Shabir M (2014) On fuzzy bipolar soft sets, their algebraic structures and applications. J Intell Fuzzy Syst 26(4):1645–1656

    Article  MathSciNet  MATH  Google Scholar 

  • Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):145–172

    Article  MATH  Google Scholar 

  • Pawlak Z (1996) Rough sets, rough relations and rough functions. Fundam Inform 27(2):103–108

    Article  MathSciNet  MATH  Google Scholar 

  • Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203(2):412–418

    Article  MATH  Google Scholar 

  • Saleem A, Aslam M, Ullah K (2014) Bipolar fuzzy soft sets and its applications in decision making problem. J Intell Fuzzy Syst 27(2):729–742

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  • Zhan J, Alcantud JCR (2018) A survey of parameter reduction of soft sets and corresponding algorithms. Artif Intell Rev (forthcoming)

  • Zhang H, Shu L, Liao S (2014) Intuitionistic fuzzy soft rough set and its application in decision-making. Abstr Appl Anal. https://doi.org/10.1155/2014/287314

    Article  MathSciNet  MATH  Google Scholar 

  • Zou Y, Xiao Z (2008) Data analysis approaches of soft sets under incomplete information. Knowl Based Syst 21(8):941–945

    Article  Google Scholar 

Download references

Acknowledgements

The authors are very grateful to the editor and the anonymous referees for their valuable comments and helpful suggestions which helped us to improve the original version of this paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

    Muhammad Akram & Ghous Ali

  2. BORDA Research Unit and IME, University of Salamanca, 37007, Salamanca, Spain

    José Carlos R. Alcantud

Authors
  1. Muhammad Akram
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ghous Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. José Carlos R. Alcantud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José Carlos R. Alcantud.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

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

Informed consent

It is submitted with the consent of all the authors.

Additional information

Communicated by A. Di Nola.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akram, M., Ali, G. & Alcantud, J.C.R. New decision-making hybrid model: intuitionistic fuzzy N-soft rough sets. Soft Comput 23, 9853–9868 (2019). https://doi.org/10.1007/s00500-019-03903-w

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-019-03903-w

Keywords

Search

Navigation