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On Developing Pythagorean Fuzzy Dombi Geometric Bonferroni Mean Operators with Their Application to Multicriteria Decision Making

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Pythagorean Fuzzy Sets

Abstract

In modeling real-world decision making problems, interrelationship among parameters for describing attributes is usually needed to consider. Bonferroni mean possesses that very characteristic to establish the correlation among parameters of the attributes. Furthermore, Dombi operations have an excellent power of flexibility in information aggregation process due to the presence of general parameters associated with t-conorm and t-norm. Considering both the advantages, in this study, geometric Bonferroni mean operator is combined with Dombi operations to propose new aggregation operators under Pythagorean fuzzy environment, viz., Pythagorean fuzzy Dombi geometric Bonferroni mean and Pythagorean fuzzy weighted Dombi geometric Bonferroni mean operators. Some of the properties and special cases of the newly developed operators are investigated. Due to the presence of several parameters, unlike existing approaches, the proposed operators are very much capable of incorporating interrelationship among input arguments as well as optimistic or pessimistic view of the decision makers based on Pythagorean fuzzy decision situations. Using those operators, a methodology for solving multicriteria decision making problems having interrelated arguments is presented. The developed method is applied to a problem relating to supply chain management and solved. The effects of different parameters associated with the model are investigated. Finally, achieved solutions are compared with the existing methods to establish the efficiency of the proposed method.

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References

  1. Ak MF, Gul M (2019) AHP–TOPSIS integration extended with Pythagorean fuzzy sets for information security risk analysis. Complex Intell Syst 5:113–126

    Google Scholar 

  2. Akram M, Ilyas F, Garg H (2020) Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Comput 24:3425–3453

    Google Scholar 

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

    MATH  Google Scholar 

  4. Aycan K, Büşra Ç, Ferhan Ç (2020) Location selection for WEEE recycling plant by using Pythagorean fuzzy AHP. J Intell Fuzzy Syst 38:1097–1106

    Google Scholar 

  5. Beliakova G, James S, Mordelová J, Rückschlossová T, Yager RR (2010) Generalized Bonferroni mean operators in multicriteria aggregation. Fuzzy Sets Syst 161(17):2227–2242

    MATH  Google Scholar 

  6. Biswas A, Kumar S (2019) Generalization of extent analysis method for solving multicriteria decision making problems involving intuitionistic fuzzy numbers. Opsearch 56(4):1142–1166

    MathSciNet  MATH  Google Scholar 

  7. Biswas A, Sarkar B (2018) Pythagorean fuzzy multi-criteria group decision making through similarity measure based on point operators. Int J Intell Syst 33(8):1731–1744

    Google Scholar 

  8. Biswas A, Sarkar B (2019) Pythagorean fuzzy TOPSIS for multicriteria group decision making with unknown weight information through entropy measure. Int J Intell Syst 34(6):1108–1128

    Google Scholar 

  9. Bonferroni C (1950) Sulle medie multiple di potenze. Bolletino Matematica Italiana 5(3–4):267–270

    MathSciNet  MATH  Google Scholar 

  10. Büyüközkan G, Göçer F (2019) A novel approach integrating AHP and COPRAS under pythagorean fuzzy sets for digital supply chain partner selection. IEEE Trans Eng Manage, 1–18

    Google Scholar 

  11. Cui FB, You XY, Shi H, Liu HC (2018) Optimal siting of electric vehicle charging stations using Pythagorean fuzzy VIKOR approach. Math Probl Eng, Article ID 9262067, 12 pp. https://doi.org/10.1155/2018/9262067

  12. Dombi J (1982) A general class of fuzzy operators, the De-Morgan class of fuzzy operators and fuzziness induced by fuzzy operators. Fuzzy Sets Syst 8(2):149–163

    MathSciNet  MATH  Google Scholar 

  13. Garg H (2016) A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920

    Google Scholar 

  14. Garg H (2016) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision making process. Int J Intell Syst 32(6):597–630

    Google Scholar 

  15. Garg H (2017) Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Comput Math Organ Theory 23:546–571

    Google Scholar 

  16. Garg H (2018) New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications. Int J Intell Syst 34:82–106

    Google Scholar 

  17. Garg H (2019) Novel neutrality operation–based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis. J Intell Syst 34:2459–2489

    Google Scholar 

  18. Garg H (2020) Neutrality operations-based Pythagorean fuzzy aggregation operators and its applications to multiple attribute group decision-making process. J Ambient Intell Human Comput 11:3021–3041

    Google Scholar 

  19. Garg H (2018) New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making. Int J Intell Syst 33:653–683

    Google Scholar 

  20. Gou X, Xu Z, Ren P (2016) The properties of continuous Pythagorean fuzzy information. Int J Intell Syst 31(5):401–424

    Google Scholar 

  21. Gul M, Ak MF, Guneri AF (2019) Pythagorean fuzzy VIKOR-based approach for safety risk assessment in mine industry. J Saf Res 69:135–153

    Google Scholar 

  22. He X (2017) Typhoon disaster assessment based on Dombi hesitant fuzzy information aggregation operators. Nat Hazards 90(3):1153–1175

    Google Scholar 

  23. He YD, He Z, Chen HY (2015) Intuitionistic fuzzy interaction Bonferroni means and its application to multiple attribute decision making. IEEE Trans Cybern 45(1):116–128

    Google Scholar 

  24. Jana C, Pal M, Wang JQ (2019) Bipolar fuzzy Dombi aggregation operators and its application in multiple attribute decision making process. J Ambient Intell Human Comput 10:3533–3549. https://doi.org/10.1007/s12652-018-1076-9

    Article  Google Scholar 

  25. 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 11:383

    MATH  Google Scholar 

  26. Khan MJ, Kumam P, Ashraf S, Kumam W (2019) Generalized picture fuzzy soft sets and their application in decision support systems. Symmetry 11:415

    MATH  Google Scholar 

  27. Khan MJ, Kumam P, Liu P, Kumam W (2019c) Another view on generalized interval valued intuitionistic fuzzy soft set and its applications in decision support system. J Int Fuzzy Syst, 1–15

    Google Scholar 

  28. Khan MJ, Kumam P, Liu P, Kumam W, Ashraf S (2019) A novel approach to generalized intuitionistic fuzzy soft sets and its application in decision support system. Mathematics 7:742

    Google Scholar 

  29. Khan MJ, Kumam P, Liu P, Kumam W, Rehman H (2020) An adjustable weighted soft discernibility matrix based on generalized picture fuzzy soft set and its applications in decision making. J Int Fuzzy Syst 38:2103–2118

    Google Scholar 

  30. Kumar R, Edalatpanah SA, Jha S, Singh R (2019) A Pythagorean fuzzy approach to the transportation problem. Complex Intell Syst 5:255–263

    Google Scholar 

  31. Li N, Garg H, Wang L (2019) Some novel interactive hybrid weighted aggregation operators with Pythagorean fuzzy numbers and their applications to decision making. Mathematics 7:1150

    Google Scholar 

  32. Li XH, Huang L, Li Q, Liu HC (2020) Passenger satisfaction evaluation of public transportation using Pythagorean fuzzy MULTIMOORA method under large group environment. Sustainability 12:4996. https://doi.org/10.3390/su12124996

    Article  Google Scholar 

  33. Li Z, Wei G, Lu M (2018) Pythagorean fuzzy Hamy mean operators in multiple attribute group decision making and their application to supplier selection. Symmetry 10:505

    Google Scholar 

  34. Liang D, Xu Z, Darko AP (2017) Projection model for fusing the information of Pythagorean fuzzy multicriteria group decision making based on geometric Bonferroni mean. Int J Intell Syst 32(9):966–987

    Google Scholar 

  35. Liang D, Zhang XZ, Darko AP (2018) Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading. Int J Intell Syst 33(3):615–633

    Google Scholar 

  36. Liu P, Chen Y, Chu Y (2014) Intuitionistic uncertain linguistic weighted Bonferroni OWA operator and its application to multiple attribute decision making. Cybern Syst 45(5):418–438

    MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  38. Mete S, Serin F, Oz NE, Gul M (2019) A decision-support system based on Pythagorean fuzzy VIKOR for occupational risk assessment of a natural gas pipeline construction. J Nat Gas Sci Eng 71:102979. https://doi.org/10.1016/j.jngse.2019.102979

    Article  Google Scholar 

  39. Muhammet G (2018) Application of Pythagorean fuzzy AHP and VIKOR methods in occupational health and safety risk assessment: the case of a gun and rifle barrel external surface oxidation and colouring unit. Int J Occu Saf Ergon (In Press). https://doi.org/10.1080/10803548.2018.1492251

    Article  Google Scholar 

  40. Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30(11):1133–1160

    MathSciNet  Google Scholar 

  41. Peng XD, Smarandache F (2019) Novel neutrosophic Dombi Bonferroni mean operators with mobile cloud computing industry evaluation. Expert Syst 36:e12411 (Online Published). https://doi.org/10.1111/exsy.12411

  42. Peng XD, Yang Y (2016) Pythagorean fuzzy Choquet integral based MABAC method for multiple attribute group decision making. Int J Intell Syst 31(10):989–1020

    Google Scholar 

  43. Rahman K, Abdullah S, Ahmed R, Ullah M (2017) Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision-making. J Intell Fuzzy Syst 33(1):635–647

    MATH  Google Scholar 

  44. Rani P, Mishra AR, Pardasani KR, Mardani A, Liao H, Streimikiene D (2019) A novel VIKOR approach based on entropy and divergence measures of Pythagorean fuzzy sets to evaluate renewable energy technologies in India. J Cleaner Prod 238:117936. https://doi.org/10.1016/j.jclepro

    Article  Google Scholar 

  45. Ren P, Xu Z, Gou X (2016) Pythagorean fuzzy TODIM approach to multi-criteria decision making. Appl Soft Comput 42:246–259

    Google Scholar 

  46. Wang J, Zhang R, Shang X, Chen D, Buchmeister B (2017) Pythagorean fuzzy Bonferroni mean operators with their application to supply chain management. In: 2017 IEEE international conference on systemss, man, cybernet (SMC), Banff, AB, 734–739. https://doi.org/10.1109/SMC.2017.8122695

  47. Wei G (2017) Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 33(4):2119–2132

    MATH  Google Scholar 

  48. Wei G, Lu M (2018) Pythagorean fuzzy power aggregation operators in multiple attribute decision-making. Int J Intell Syst 33:169–186

    Google Scholar 

  49. Wei G, Zhao X, Lin R, Wang H (2013) Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making Appl. Appl Math Model 37(7):5277–5285

    MathSciNet  MATH  Google Scholar 

  50. Wu SJ, Wei GW (2017) Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Int J Knowl Based Intell Eng Syst 21(3):189–201

    Google Scholar 

  51. Xia M, Xu Z, Zhu B (2013) Geometric Bonferroni means with their application in multi-criteria decision making. Knowl Based Syst 40:88–100

    Google Scholar 

  52. Xu Q, Yu K, Zeng S, Liu J (2017) Pythagorean fuzzy induced generalized OWA operator and its application to multi-attribute group decision-making. Int J Innov Comput Inf Control 13:1527–1536

    Google Scholar 

  53. Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of joint IFSA world congress and NAFIPS annual meeting, Edmonton, Canada, 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375

  54. Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

    Google Scholar 

  55. Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers and decision making. Int J Intell Syst 28:436–452

    Google Scholar 

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

    MATH  Google Scholar 

  57. Zeng S, Mu Z, Baležentis T (2017) A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making. Int J Intell Syst 33(3):573–585

    Google Scholar 

  58. Zhang XL, Xu ZS (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078

    Google Scholar 

  59. Zhang XL (2016) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31:593–611

    Google Scholar 

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Acknowledgements

The authors remain grateful to the anonymous reviewers for their comments and suggestions to improve the quality of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, University of Kalyani, Kalyani, 741235, India

    Nayana Deb & Animesh Biswas

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  1. Nayana Deb
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  2. Animesh Biswas
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Correspondence to Animesh Biswas .

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Editors and Affiliations

  1. School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala, Punjab, India

    Harish Garg

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Deb, N., Biswas, A. (2021). On Developing Pythagorean Fuzzy Dombi Geometric Bonferroni Mean Operators with Their Application to Multicriteria Decision Making. In: Garg, H. (eds) Pythagorean Fuzzy Sets. Springer, Singapore. https://doi.org/10.1007/978-981-16-1989-2_9

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