Skip to main content
SpringerLink
Log in

Some m-polar fuzzy operators and their application in multiple-attribute decision-making process

  • Published:
Sādhanā Aims and scope Submit manuscript

Abstract

In this study, Dombi operations are introduced on two m-polar fuzzy sets (mFSs). Here, Dombi operation on m-polar fuzzy numbers (mFNs), some new averaging and geometric averaging operators, namely mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid weighted averaging (mFDHWA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi ordered weighted geometric (mFDOWG) operator, and mF Dombi hybrid weighted geometric (mFDHWGA) operator, have been proposed. Further, some properties like idempotency, boundedness, monotonicity, and commutativity are established. Next, a multi-attribute decision-making (MADM) method in mFNs environment based on mFDWA and mFDWG operators is constructed. Finally, an application of the present MADM method for selecting the best location for the construction of thermal power stations is presented. The present approach with the existing procedure is also compared and a sensitivity analysis of the proposed plan is given.

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

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. Zadeh L A 1965 Fuzzy sets. Information and Control 8: 338–353

    Article  MathSciNet  Google Scholar 

  2. Atanassov K T 1999 On intuitionistic fuzzy sets theory. Studies in Fuzziness and Soft Computing 283. Berlin– Heidelberg: Springer-Verlag

  3. Garg H 2018 Generalised Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making. Journal of Experimental and Theoretical Artificial Intelligence 30: 763–794

    Article  Google Scholar 

  4. Jana C, Pal M, Karaaslan F and Wang J Q 2020 Trapezoidal neutrosophic aggregation operators and its application in multiple attribute decision making process. Scientia Iranica E 27(3): 1655–1673

    Google Scholar 

  5. Jana C and Pal M 2019 Assessment of enterprise performance based on picture fuzzy Hamacher aggregation operators. Symmetry 11(1): 75, https://doi.org/10.3390/sym11010075

    Article  MATH  Google Scholar 

  6. Zhao H, Xu Z S, Ni M F and Liu S S 2010 Generalized aggregation operators for intuitionistic fuzzy sets. International Journal of Intelligent Systems 25(1): 1–30

    Article  Google Scholar 

  7. Zhao X F and Wei G W 2013 Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making. Knowledge-Based Systems 37: 472–479

    Article  Google Scholar 

  8. Xu Z S 2007 Intuitionistic fuzzy aggregation operators. IEEE Transaction on Fuzzy Systems 15(6): 1179–1187

    Article  Google Scholar 

  9. Xu Z S and Yager R R 2006 Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems 35(4): 417–433

    Article  MathSciNet  Google Scholar 

  10. Yager R R 1998 On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics 18(1): 183–190

    Article  Google Scholar 

  11. Yager R R and Kacprzyk J 1997 The ordered weighted averaging operators: theory and applications. Boston, M.A.: Kluwer

    Book  Google Scholar 

  12. Zhang W R 1994 Bipolar fuzzy sets and relations: a computational framework for cognitive modelling and multiagent decision analysis. In: Proceedings of the IEEE Conference, pp. 305–309

  13. Zhang W R 1998 Bipolar fuzzy sets. In: Proceedings of FUZZYIEEE, pp. 835–840

  14. Jana C, Pal M and Wang J Q 2019a Bipolar fuzzy Dombi aggregation operators and its application in multiple attribute decision making process. Journal of Ambient Intelligence and Humanized Computing 10: 3533–3549

    Article  Google Scholar 

  15. Jana C, Pal M and Wang J Q 2020 Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making. Soft Computing 24: 3631–3646

    Article  Google Scholar 

  16. Wei G W, Alsaedi F E, Tasawar H and Alsaedi A 2018 Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making. International Journal of Fuzzy Systems 20(1): 1–12

    Article  MathSciNet  Google Scholar 

  17. Gao H, Wei G W and Huang Y H 2018 Dual hesitant bipolar fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. IEEE Access 6(1): 11508–11522

    Article  Google Scholar 

  18. Xu X R and Wei G W 2017 Dual hesitant bipolar fuzzy aggregation operators in multiple attribute decision making. International Journal of Knowledge-Based and Intelligent Engineering Systems 21: 155–164

    Article  Google Scholar 

  19. Jana C, Pal M and Wang J Q 2019 A robust aggregation operator for multi-criteria decision-making method with bipolar fuzzy soft environment. Iranian Journal of Fuzzy Systems 16(6): 1–16

    MathSciNet  MATH  Google Scholar 

  20. Chen J, Li S, Ma S and Wang X 2014 m-polar fuzzy sets: an extension of bipolar fuzzy sets. Scientific World Journal 2014: 416530

    Google Scholar 

  21. Al-Masarwah A and Ahmad A G 2019 m-Polar fuzzy ideals of \(BCK/BCI\)-algebras. Journal of King Saud University-Science 31(4): 1220–1226

    Article  Google Scholar 

  22. Akram M, Farooq A and Shum K P 2016 On m-polar fuzzy Lie subalgebras. Italian Journal of Pure and Applied Mathematics 36: 445–454

    MathSciNet  MATH  Google Scholar 

  23. Ghorai G and Pal M 2016 Some properties of m-polar fuzzy graphs. Pacific Science Review A: Natural Science and Engineering 18(1): 38–46

    MATH  Google Scholar 

  24. Khameneh A Z and Kilicman A 2018 m-polar fuzzy soft weighted aggregation operators and their applications in group decision-making. Symmetry 10: 636

    Article  Google Scholar 

  25. Akram M and Waseem N 2019 Novel approach in decision-making with m-polar fuzzy ELECTRE-I. International Journal of Fuzzy Systems 21: 1117–1129

    Article  MathSciNet  Google Scholar 

  26. Akram M 2019 m-polar fuzzy graphs. In: Studies in Fuzziness and Soft Computing. Cham, Switzerland: Springer, p. 371

  27. Waseem N, Akram M and Alcantud J C R 2019 Multi-attribute decision-making based on m-polar fuzzy Hamacher aggregation operators. Symmetry 11: 1498

    Article  Google Scholar 

  28. Akram M, Adeel A and Alcantud J C R 2019 Multi-criteria group decision-making using an m-polar hesitant fuzzy TOPSIS approach. Symmetry 11(6): 795

    Article  Google Scholar 

  29. Akram M, Shumaiza and Alcantud J C R 2020 An m-polar fuzzy PROMETHEE approach for AHP-assisted group decision-making. Mathematical and Computational Applications 25(2): 26

  30. Dombi J 1982 A general class of fuzzy operators, the DeMorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets and Systems 8: 149–163

    Article  MathSciNet  Google Scholar 

  31. Liu P D, Liu J L and Chen S M 2017 Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making. Journal of the Operational Research Society, https://doi.org/10.1057/s41274-017-0190-y

  32. Jana C, Senapati T, Pal M and Yager R R 2019 Picture fuzzy Dombi aggregation operators: application to MADM process. Applied Soft Computing 74(1): 99–109

    Article  Google Scholar 

  33. Jana C, Senapati T and Pal M 2019 Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision-making. International Journal of Intelligent Systems 34(9): 2019–2038

    Article  Google Scholar 

  34. Jana C, Muhiuddin G and Pal M 2019 Some Dombi aggregation of q-rung orthopair fuzzy numbers in multiple-attribute decision making. International Journal of Intelligent Systems 34(12): 3220–3240

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank the anonymous reviewers for their insightful and constructive comments and suggestions that have been helpful for providing a better version of the present work.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Chiranjibe Jana & Madhumangal Pal

Authors
  1. Chiranjibe Jana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Madhumangal Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chiranjibe Jana.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jana, C., Pal, M. Some m-polar fuzzy operators and their application in multiple-attribute decision-making process. Sādhanā 46, 95 (2021). https://doi.org/10.1007/s12046-021-01599-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12046-021-01599-z

Keywords

Search

Navigation