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Pythagorean Fuzzy MCDM Method Based on CODAS

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Pythagorean Fuzzy Sets

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Abstract

As an extension of intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PFS) is more appropriate for seizing the uncertainty of preference information. This paper is designed to set a novel approach based on CODAS (COmbinative Distance-based ASsessment) for dealing multi-criteria decision-making (MCDM) problem under Pythagorean fuzzy environment. It can not only be sorted without complicated processes, but also without counterintuition to get the best choice.

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References

  1. Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–356

    MATH  Google Scholar 

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

    Article  Google Scholar 

  3. Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, 24–28 June 2013, pp 57–61

    Google Scholar 

  4. Yager RR, Abbasov AM (2014) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28:436–452

    Google Scholar 

  5. Peng XD, Selvachandran G (2019) Pythagorean fuzzy set: state of the art and future directions. Artif Intell Rev 52:1873–1927

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  8. Peng XD, Yang Y (2015) Some results for pythagorean fuzzy sets. Int J Intell Syst 30:1133–1160

    Google Scholar 

  9. Zhang XL (2016) Multicriteria pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking methods. Inf Sci 330:104–124

    Google Scholar 

  10. Peng XD, Dai JG (2017) Approaches to Pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function. Int J Intell Syst 32:1187–1214

    Google Scholar 

  11. Ren PJ, Xu ZS, Gou XJ (2016) Pythagorean fuzzy TODIM approach to multi-criteria decision making. Appl Soft Comput 42:246–259

    Google Scholar 

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

    Google Scholar 

  13. Wan SP, Jin Z, Dong JY (2018) Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degrees. Knowl Inf Syst 55:437–466

    Google Scholar 

  14. Chen TY (2018) A novel PROMETHEE-based outranking approach for multiple criteria decision analysis with Pythagorean fuzzy information. IEEE Access 6:54495–54506

    Google Scholar 

  15. Chen TY (2018) A mixed-choice-strategy-based consensus ranking method for multiple criteria decision analysis involving pythagorean fuzzy information. IEEE Access 6:79174–79199

    Google Scholar 

  16. Khan MSA, Abdullah S (2018) Interval-valued Pythagorean fuzzy GRA method for multiple-attribute decision making with incomplete weight information. Int J Intell Syst 33:1689–1716

    Google Scholar 

  17. Khan MSA, Abdullah S, Ali YM, Hussain I, Farooq M (2018) Extension of TOPSIS method base on Choquet integral under interval-valued Pythagorean fuzzy environment. J Intell Fuzzy Syst 34:267–282

    Google Scholar 

  18. Khan MSA, Abdullah S, Lui P (2019) Gray method for multiple attribute decision making with incomplete weight information under the Pythagorean fuzzy setting. J Intell Syst 29:858–876

    Google Scholar 

  19. Khan MSA, Ali A, Abdullah S, Amin F, Hussain F (2018) New extension of TOPSIS method based on Pythagorean hesitant fuzzy sets with incomplete weight information. J Intell Fuzzy Syst 35:5435–5448

    Google Scholar 

  20. Khan MSA, Abdullah S, Ali A, Siddiqui N, Amin F (2017) Pythagorean hesitant fuzzy sets and their application to group decision making with incomplete weight information. J Intell Fuzzy Syst 33:3971–3985

    Google Scholar 

  21. Lu J, Tang X, Wei G, Wei C, Wei Y (2019) Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision-making and their application to performance assessment of new rural construction. Int J Intell Syst 34:1920–1934

    Google Scholar 

  22. Peng XD, Li WQ (2019) Algorithms for interval-valued Pythagorean fuzzy sets in emergency decision making based on multiparametric similarity measures and WDBA. IEEE Access 7:7419–7441

    Google Scholar 

  23. Peng XD (2019) Algorithm for Pythagorean fuzzy multi-criteria decision making based on WDBA with new score function. Fund Inform 165:99–137

    MathSciNet  MATH  Google Scholar 

  24. Peng XD, Yuan HY (2016) Fundamental properties of Pythagorean fuzzy aggregation operators. Fund Inform 147:415–446

    MathSciNet  MATH  Google Scholar 

  25. Yang W, Pang Y (2018) New pythagorean fuzzy interaction Maclaurin symmetric mean operators and their application in multiple attribute decision making. IEEE Access 6:39241–39260

    Google Scholar 

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

    Google Scholar 

  27. Garg H (2017) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process. Int J Intell Syst 32:597–630

    Google Scholar 

  28. Zeng SZ, Chen JP, Li XS (2016) A hybrid method for Pythagorean fuzzy multiple-criteria decision making. Int J Inf Tech Decis 15:403–422

    Google Scholar 

  29. Ma ZM, Xu ZS (2016) Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst 31:1198–1219

    Google Scholar 

  30. Zeng S (2017) Pythagorean fuzzy multiattribute group decision making with probabilistic information and OWA approach. Int J Intell Syst 32:1136–1150

    Google Scholar 

  31. Peng XD, Yang Y (2016) Fundamental properties of interval-valued pythagorean fuzzy aggregation operators. Int J Intell Syst 31:444–487

    Google Scholar 

  32. Wei GW, Lu M (2018) Pythagorean fuzzy Maclaurin Symmetric mean operators in multiple attribute decision making. Int J Intell Syst 33:1043–1070

    Google Scholar 

  33. Zhang RT, Wang J, Zhu XM, Xia MM, Yu M (2017) Some generalized Pythagorean fuzzy Bonferroni mean aggregation operators with their application to multiattribute group decision-making. Complexity. https://doi.org/10.1155/2017/5937376

  34. Liu WF, Du YX, Chang J (2017) Pythagorean fuzzy interaction aggregation operators and applications in decision making. Control Decis 32:1033–1040

    MATH  Google Scholar 

  35. Liang DC, Xu ZS, 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 32:966–987

    Google Scholar 

  36. Khan MSA, Abdullah S, Ali A, Amin F, Hussain F (2019) Pythagorean hesitant fuzzy Choquet integral aggregation operators and their application to multi-attribute decision-making. Soft Comput 23:251–267

    MATH  Google Scholar 

  37. Khan MSA, Abdullah S, Ali A (2019) Multiattribute group decision-making based on Pythagorean fuzzy Einstein prioritized aggregation operators. Int J Intell Syst 34:1001–1033

    Google Scholar 

  38. Gao H (2018) Pythagorean fuzzy hamacher prioritized aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst 35:2229–2245

    Google Scholar 

  39. Tang X, Wei G (2019) Multiple attribute decision-making with dual hesitant Pythagorean fuzzy information. Cogn Comput 11:193–211

    Google Scholar 

  40. Wei GW (2019) Pythagorean fuzzy Hamacher power aggregation operators in multiple attribute decision making. Fund Inform 166:57–85

    MathSciNet  MATH  Google Scholar 

  41. Peng XD (2019) New operations for interval-valued Pythagorean fuzzy set. Sci Iran 26:1049–1076

    Google Scholar 

  42. Wang L, Li N (2019) Continuous interval-valued Pythagorean fuzzy aggregation operators for multiple attribute group decision making. J Intell Fuzzy Syst 36:6245–6263

    Google Scholar 

  43. Garg H (2016) A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst 31:1234–1252

    Google Scholar 

  44. Peng XD, Yuan HY, Yang Y (2017) Pythagorean fuzzy information measures and their applications. Int J Intell Syst 32:991–1029

    Google Scholar 

  45. 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 

  46. Wang J, Gao H, Wei G (2019) The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making. Int J Intell Syst 34:1158–1183

    Google Scholar 

  47. Peng XD, Garg H (2019) Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition. Appl Intell 49:4058–4096

    Google Scholar 

  48. Hadi-Vencheh A, Mirjaberi M (2014) Fuzzy inferior ratio method for multiple attribute decision making problems. Inf Sci 277:263–272

    MathSciNet  MATH  Google Scholar 

  49. Ghorabaee MK, Zavadskas EK, Turskis Z, Antucheviciene J (2016) A new combinative distance-based assessment (CODAS) method for multi-criteria decision-making. Econ Comput Econ Cyb 50:25–44

    Google Scholar 

  50. Yoon K (1987) A reconciliation among discrete compromise solutions. J Oper Res Soc 38:277–286

    MATH  Google Scholar 

  51. Ghorabaee MK, Amiri M, Zavadskas EK, Hooshmand R, Antuchevi\(\breve{c}\)ien\(\dot{e}\) J (2017) Fuzzy extension of the CODAS method for multi-criteria market segment evaluation. J Bus Econ Manage 18:1–19

    Google Scholar 

  52. Akram M, Garg H, Zahid K (2020) Extensions of ELECTRE-I and TOPSIS methods for group decision making under complex Pythagorean fuzzy environment. Iranian J Fuzzy Syst 5:147–164

    Google Scholar 

  53. Ma X, Akram M, Zahid et al (2020) Group decision-making framework using complex Pythagorean fuzzy information. Neural Comput Appl. https://doi.org/10.1007/s00521-020-05100-5

  54. Akram M, Ilyasa 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 

  55. Akram M, Dudek W, Ilyas F (2019) Group decision making based on Pythagorean fuzzy TOPSIS method. Int J Intell Syst 34:1455–1475

    Google Scholar 

  56. Wang L, Garg H, Li N (2020) Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weights. Soft Comput. https://doi.org/10.1007/s00500-020-05193-z

  57. Garg H (2020) Linguistic interval-valued Pythagorean fuzzy sets and their application to multiple attribute group decision-making process. Cognitive Comput. https://doi.org/10.1007/s12559-020-09750-4

  58. Garg H (2018) Linguistic Pythagorean fuzzy sets and its applications in multi attribute decision making process. Int J Intell Syst 33:1234–1263

    Google Scholar 

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

    Google Scholar 

  60. Garg H (2019) New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications. Int J Intell Syst 34:82–106

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Shaoguan University, Shaoguan, 512005, China

    Xindong Peng

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  1. Xindong Peng
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Correspondence to Xindong Peng .

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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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Peng, X. (2021). Pythagorean Fuzzy MCDM Method Based on CODAS. In: Garg, H. (eds) Pythagorean Fuzzy Sets. Springer, Singapore. https://doi.org/10.1007/978-981-16-1989-2_11

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