Spherical fuzzy Dombi aggregation operators and their application in group decision making problems

Abstract

Spherical fuzzy sets (SFSs), recently proposed by Ashraf, is one of the most important concept to describe the fuzzy information in the process of decision making. In SFSs the sum of the squares of memberships grades lies in close unit interval and hence accommodate more uncertainties. Thus, this set outperforms over the existing structures of fuzzy sets. In real decision making problems, there is often a treat regarding a neutral character towards the membership and non-membership degrees expressed by the decision-makers. To get a fair decision during the process, in this paper, we define some new operational laws by Dombi t-norm and t-conorm. In the present study, we propose Spherical fuzzy Dombi weighted averaging (SFDWA), Spherical fuzzy Dombi ordered weighted averaging (SFDOWA), Spherical fuzzy Dombi hybrid weighted averaging (SFDHWA), Spherical fuzzy Dombi weighted geometric (SFDWG), Spherical fuzzy Dombi ordered weighted geometric (SFDOWG) and Spherical fuzzy Dombi hybrid weighted geometric (SFDHWG) aggregation operators and discuss several properties of these aggregation operators. These aforesaid operators are enormously used to help a successful solution of the decision problems. Then an algorithm by using spherical fuzzy set information in decision-making matrix is developed and applied the algorithm to decision-making problem to illustrate its applicability and effectiveness. Through this algorithm, we proved that our proposed approach is practical and provides decision makers a more mathematical insight before making decisions on their options. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our method. Results indicate that the proposed method is suitable and effective for decision process to evaluate their best alternative.

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References

  1. Ashraf S, Abdullah S (2019) Spherical aggregation operators and their application in multi-attribute group decision-making. Int J Intell Syst 34(3):493–523

    Google Scholar 

  2. Ashraf S, Mahmood T, Abdullah S, Khan Q (2018a) Different approaches to multi-criteria group decision making problems for picture fuzzy environment. Bull Braz Math Soc 50(2):373–397

    MathSciNet  MATH  Google Scholar 

  3. Ashraf S, Abdullah S, Mahmood T (2018b) GRA method based on spherical linguistic fuzzy Choquet integral environment and its application in multi-attribute decision-making problems. Math Sci 12(4):263–75

    MATH  Google Scholar 

  4. Ashraf S, Mehmood T, Abdullah S, Khan Q (2018c) Picture fuzzy linguistic sets and their applications for multi-attribute group. Nucleus 55(2):66–73

    Google Scholar 

  5. Ashraf S, Abdullah S, Mahmood T, Ghani F, Mahmood T (2019a) Spherical fuzzy sets and their applications in multi-attribute decision making problems. J Intell Fuzzy Syst 36:2829–2844. https://doi.org/10.3233/JIFS-172009

    Google Scholar 

  6. Ashraf S, Abdullah S, Aslam M, Qiyas M, Kutbi MA (2019b) Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms. J Intell Fuzzy Syst. https://doi.org/10.3233/JIFS-181941

    Google Scholar 

  7. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    MATH  Google Scholar 

  8. Chen J, Ye J (2017) Some single-valued neutrosophic Dombi weighted aggregation operators for multiple attribute decision-making. Symmetry 9(6):82

    Google Scholar 

  9. Cuong BC (2013a) Picture fuzzy sets-first results, part 1. Seminar neuro-fuzzy systems with applications, Preprint 03/2013, Institute of Mathematics, Hanoi

  10. Cuong BC (2013b) Picture fuzzy sets-first results, part 2. Seminar neuro-fuzzy systems with applications, Preprint 04/2013, Institute of Mathematics, Hanoi

  11. Cuong BC (2014) Picture fuzzy sets. J Comput Sci Cybern 30(4):409–420

    Google Scholar 

  12. Dombi J (1982) A general class of fuzzy operators, the DeMorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets Syst 8(2):149–63

    MathSciNet  MATH  Google Scholar 

  13. Garg H (2017) Some picture fuzzy aggregation operators and their applications to multicriteria decision-making. Arab J Sci Eng 42(12):5275–5290

    MathSciNet  MATH  Google Scholar 

  14. He X (2018) Typhoon disaster assessment based on Dombi hesitant fuzzy information aggregation operators. Nat Hazards 90(3):1153–1175

    Google Scholar 

  15. Jana C, Senapati T, Pal M, Yager RR (2019) Picture fuzzy Dombi aggregation operators: application to MADM process. Appl Soft Comput 74:99–109

    Google Scholar 

  16. Jana C, Pal M, Wang JQ (2018) Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision-making process. J Ambient Intell Hum Comput. https://doi.org/10.1007/s12652-018-1076-9

    Google Scholar 

  17. Klement EP, Mesiar R (eds) (2005) Logical, algebraic, analytic and probabilistic aspects of triangular norms. Elsevier, Amsterdam

    Google Scholar 

  18. Khan Q, Liu P, Mahmood T, Smarandache F, Ullah K (2018) Some interval neutrosophic dombi power bonferroni mean operators and their application in multi-attribute decision-making. Symmetry 10(10):459

    Google Scholar 

  19. Khan AA, Ashraf S, Abdullah S, Qiyas M, Luo J, Khan SU (2019) Pythagorean fuzzy Dombi aggregation operators and their application in decision support system. Symmetry 11(3):383

    MATH  Google Scholar 

  20. Liang WZ, Zhao GY, Luo SZ (2018) An integrated EDAS-ELECTRE method with picture fuzzy information for cleaner production evaluation in gold mines. IEEE Access 6:65747–65759

    Google Scholar 

  21. Li DX, Dong H, Jin X (2017) Model for evaluating the enterprise marketing capability with picture fuzzy information. J Intell Fuzzy Syst 33(6):3255–3263

    Google Scholar 

  22. Liu P, Liu J, Chen SM (2018) Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making. J Oper Res Soc 69(1):1–24

    Google Scholar 

  23. Lu X, Ye J (2018) Dombi aggregation operators of linguistic cubic variables for multiple attribute decision making. Information 9(8):188

    Google Scholar 

  24. Phong PH, Cuong BC (2016) Multi-criteria group decision making with picture linguistic numbers. VNU J Sci Comput Sci Commun Eng 32(3):

  25. Rafiq M, Ashraf S, Abdullah S, Mahmood T, Muhammad S (2019) The cosine similarity measures of spherical fuzzy sets and their applications in decision making. J Intell Fuzzy Syst. https://doi.org/10.3233/JIFS-181922

    Google Scholar 

  26. Shi L, Ye J (2018) Dombi aggregation operators of neutrosophic cubic sets for multiple attribute decision-making. Algorithms 11(3):29

    Google Scholar 

  27. Thong PH (2017) Some novel hybrid forecast methods based on picture fuzzy clustering for weather nowcasting from satellite image sequences. Appl Intell 46(1):1–5

    MathSciNet  Google Scholar 

  28. Van Viet P, Van Hai P (2017) Picture inference system: a new fuzzy inference system on picture fuzzy set. Appl Intell 46(3):652–669

    Google Scholar 

  29. Son LH (2016) Generalized picture distance measure and applications to picture fuzzy clustering. Appl Soft Comput 46(C):284–295

    Google Scholar 

  30. Wang C, Zhou X, Tu H, Tao S (2017) Some geometric aggregation operators based on picture fuzzy sets and their application in multiple attribute decision making. Ital J Pure Appl Math 37:477–492

    MathSciNet  MATH  Google Scholar 

  31. Wei G (2017) Picture fuzzy aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 33(2):713–724

    MATH  Google Scholar 

  32. Wei G (2018) Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Fund Inform 157(3):271–320

    MathSciNet  MATH  Google Scholar 

  33. Wei G, Wei Y (2018) Some single-valued neutrosophic Dombi prioritized weighted aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst (Preprint):1–3

  34. Yager RR (2013a) Pythagorean fuzzy subsets. In: 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS) 2013 Jun 24. IEEE, pp. 57–61

  35. Yager RR (2013b) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

    Google Scholar 

  36. Yager RR, Walker CL, Walker EA (2015) Generalizing Leximin to t-norms and t-conorms: the LexiT and LexiS orderings. Fuzzy Sets Syst 151(2):327–340

    MathSciNet  MATH  Google Scholar 

  37. Yager RR (2004a) Modeling prioritized multicriteria decision making. IEEE Trans Syst Man Cybern Part B Cybern 34(6):2396–2404

    Google Scholar 

  38. Yager RR (2004b) Generalized OWA aggregation operators. Fuzzy Optim Decis Mak 3(1):93–107

    MathSciNet  MATH  Google Scholar 

  39. Yager RR (2004c) On some new classes of implication operators and their role in approximate reasoning. Inf Sci 167(1–4):193–216

    MathSciNet  MATH  Google Scholar 

  40. Yang Y, Liang C, Ji S, Liu T (2015) Adjustable soft discernibility matrix based on picture fuzzy soft sets and its applications in decision making. J Intell Fuzzy Syst 29(4):1711–1722

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  42. Zeng S, Asharf S, Arif M, Abdullah S (2019) Application of exponential jensen picture fuzzy divergence measure in multi-criteria group decision making. Mathematics 7(2):191

    MathSciNet  Google Scholar 

  43. Zhang H, Zhang R, Huang H, Wang J (2018) Some picture fuzzy dombi heronian mean operators with their application to multi-attribute decision-making. Symmetry 10(11):593

    MATH  Google Scholar 

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Acknowledgements

This work was supported by Higher Education Commission, Pakistan under National Research Program for Universities (NRPU), Project no. 10701/KPK/ NRPU/R&D/HEC/ 2017.

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Correspondence to Shahzaib Ashraf.

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Ashraf, S., Abdullah, S. & Mahmood, T. Spherical fuzzy Dombi aggregation operators and their application in group decision making problems. J Ambient Intell Human Comput 11, 2731–2749 (2020). https://doi.org/10.1007/s12652-019-01333-y

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