A Pearson-like correlation-based TOPSIS method with interval-valued Pythagorean fuzzy uncertainty and its application to multiple criteria decision analysis of stroke rehabilitation treatments

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Abstract

This paper extends one of the most extensively used multiple criteria decision analysis (MCDA) methods, the technique for order preference by similarity to ideal solutions (TOPSIS), to adapt to highly complicated uncertain environments based on interval-valued Pythagorean fuzzy (IVPF) sets. In contrast to classical TOPSIS methods, this paper develops a novel concept of Pearson-like IVPF correlation coefficients instead of distance measures to not only construct a useful and effective association measure between two IVPF characteristics but also depict the outranking relationship of IVPF information. Moreover, this paper proposes the (weighted) IVPF correlation-based closeness coefficients to establish a Pearson-like correlation-based TOPSIS model to manage MCDA problems within the IVPF environment. In particular, there is a definite improvement in determining the closeness coefficient required in the TOPSIS procedure. This paper considers anchored judgments with respect to the positive- and negative-ideal IVPF solutions and provides new approach- and avoidance-oriented definitions for the IVPF correlation-based closeness coefficient, which is entirely different from the traditional definition of relative closeness in TOPSIS. Furthermore, this paper proposes a comprehensive IVPF correlation-based closeness index to balance the consequences between ultra-approach orientation and ultra-avoidance orientation and acquire the ultimate compromise solution for decision support and aid. The feasibility and practicability of the developed methodology are illustrated by a practical MCDA problem of rehabilitation treatment for hospitalized patients with acute stroke. The application results, along with experimentations and comparative analyses, demonstrate that the developed methods are rational and effective.

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References

  1. 1.

    Ang YH, Chan DK, Heng DM, Shen Q (2003) Patient outcomes and length of stay in a stroke unit offering both acute and rehabilitation services. Med J Australia 178(7):333–336

    Google Scholar 

  2. 2.

    Biswas A, Sarkar B (2019) Interval-valued Pythagorean fuzzy TODIM approach through point operator-based similarity measures for multicriteria group decision making. Kybernetes 48(3):496–519

    Google Scholar 

  3. 3.

    Cabrerizo FJ, Ureña MR, Pedrycz W, Herrera-Viedma E (2014) Building consensus in group decision making with an allocation of information granularity. Fuzzy Sets Syst 255:115–127

    MathSciNet  MATH  Google Scholar 

  4. 4.

    Cayir Ervural B, Zaim S, Demirel OF, Aydin Z, Delen D (2018) An ANP and fuzzy TOPSIS-based SWOT analysis for Turkey’s energy planning. Renew Sustain Energy Rev 82(1):1538–1550

    Google Scholar 

  5. 5.

    Chen T-Y (2018) A novel risk evaluation method of technological innovation using an inferior ratio-based assignment model in the face of complex uncertainty. Expert Syst Appl 95:333–350

    Google Scholar 

  6. 6.

    Chen T-Y (2018) A novel VIKOR method with an application to multiple criteria decision analysis for hospital-based post-acute care within a highly complex uncertain environment. Neural Comput Appl 1:11. https://doi.org/10.1007/s00521-017-3326-8

    Article  Google Scholar 

  7. 7.

    Chen T-Y (2019) Multiple criteria decision analysis under complex uncertainty: a Pearson-like correlation-based Pythagorean fuzzy compromise approach. Int J Intell Syst 34(1):114–151

    Google Scholar 

  8. 8.

    Çoban V, Onar SÇ (2018) Pythagorean fuzzy engineering economic analysis of solar power plants. Soft Comput 22(15):5007–5020

    Google Scholar 

  9. 9.

    Du Y, Hou F, Zafar W, Yu Q, Zhai Y (2017) A novel method for multiattribute decision making with interval-valued Pythagorean fuzzy linguistic information. Int J Intell Syst 32(10):1085–1112

    Google Scholar 

  10. 10.

    Dwivedi G, Srivastava RK, Srivastava SK (2018) A generalised fuzzy TOPSIS with improved closeness coefficient. Expert Syst Appl 96:185–195

    Google Scholar 

  11. 11.

    Farajpour F, Yousefli A (2018) Information flow in supply chain: a fuzzy TOPSIS parameters ranking. Uncertain Supply Chain Manag 6(2):181–194

    Google Scholar 

  12. 12.

    Garg H (2017) A novel improved accuracy function for interval valued Pythagorean fuzzy sets and its applications in the decision-making process. Int J Intell Syst 32(12):1247–1260

    Google Scholar 

  13. 13.

    Garg H (2018) Generalised Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making. J Exp Theor Artif Intell 30(6):763–794

    Google Scholar 

  14. 14.

    Gul M, Ak MF (2018) A comparative outline for quantifying risk ratings in occupational health and safety risk assessment. J Clean Prod 196:653–664

    Google Scholar 

  15. 15.

    Guleria A, Bajaj RK (2018) On Pythagorean fuzzy soft matrices, operations and their applications in decision making and medical diagnosis. Soft Comput 1:11. https://doi.org/10.1007/s00500-018-3419-z

    Article  MATH  Google Scholar 

  16. 16.

    Hwang C-L, Lai Y-J, Liu T-Y (1993) A new approach for multiple objective decision making. Comput Oper Res 20(8):889–899

    MATH  Google Scholar 

  17. 17.

    Hwang C-L, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, Berlin

    MATH  Google Scholar 

  18. 18.

    Khan F, Khan MSA, Shahzad M, Abdullah S (2019) Pythagorean cubic fuzzy aggregation operators and their application to multi-criteria decision making problems. J Intell Fuzzy Syst 36(1):595–607

    Google Scholar 

  19. 19.

    Langhorne P, Pollock A (2002) What are the components of effective stroke unit care? Age Aging 31(5):365–371

    Google Scholar 

  20. 20.

    Liang D, Darko AP, Xu Z, Quan W (2018) The linear assignment method for multicriteria group decision making based on interval-valued Pythagorean fuzzy Bonferroni mean. Int J Intell Syst 33(11):2101–2138

    Google Scholar 

  21. 21.

    Liang D, Xu Z (2017) The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Appl Soft Comput 60:167–179

    Google Scholar 

  22. 22.

    Liang D, Xu Z, Liu D, Wu Y (2018) Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information. Inf Sci 435:282–295

    MathSciNet  Google Scholar 

  23. 23.

    Liang W, Zhang X, Liu M (2015) The maximizing deviation method based on interval-valued Pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis. Discrete Dyn Nat Soc 2015, Article ID 746572: 15 pages. http://dx.doi.org/10.1155/2015/746572

  24. 24.

    Liao H, Xu Z, Herrera-Viedma E, Herrera F (2018) Hesitant fuzzy linguistic term set and its application in decision making: a state-of-the-art survey. Int J Fuzzy Syst 20(7):2084–2110

    MathSciNet  Google Scholar 

  25. 25.

    Lin Y-L, Ho L-H, Yeh S-L, Chen T-Y (2019) A Pythagorean fuzzy TOPSIS method based on novel correlation measures and its application to multiple criteria decision analysis of inpatient stroke rehabilitation. Int J Comput Intell Syst 12(1):410–425

    Google Scholar 

  26. 26.

    Liu Y, Qin Y, Han Y (2018) Multiple criteria decision making with probabilities in interval-valued Pythagorean fuzzy setting. Int J Fuzzy Syst 20(2):558–571

    MathSciNet  Google Scholar 

  27. 27.

    Massanet S, Riera JV, Torrens J, Herrera-Viedma E (2014) A new linguistic computational model based on discrete fuzzy numbers for computing with words. Inf Sci 258:277–290

    MathSciNet  MATH  Google Scholar 

  28. 28.

    Nguyen VQ, PrvuBettger J, Guerrier T, Hirsch MA, Thomas JG, Pugh TM, Rhoads CF (2015) Factors associated with discharge to home versus discharge to institutional care after inpatient stroke rehabilitation. Arch Phys Med Rehabil 96(7):1297–1303

    Google Scholar 

  29. 29.

    Nie R-X, Tian Z-P, Wang J-Q, Hu J-H (2019) Pythagorean fuzzy multiple criteria decision analysis based on Shapley fuzzy measures and partitioned normalized weighted Bonferroni mean operator. Int J Intell Syst 34(2):297–324

    Google Scholar 

  30. 30.

    Peng X, Li W (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 

  31. 31.

    Peng X, Yang Y (2016) Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 31(5):444–487

    Google Scholar 

  32. 32.

    Rahman K, Ali A, Abdullah S, Amin F (2018) Approaches to multi-attribute group decision making based on induced interval-valued Pythagorean fuzzy Einstein aggregation operator. New Math Nat Comput 14(3):343–361

    MathSciNet  MATH  Google Scholar 

  33. 33.

    Rahman K, Khan MA, Ullah M, Fahmi A (2017) Multiple attribute group decision making for plant location selection with Pythagorean fuzzy weighted geometric aggregation operator. Nucleus 54(1):66–74

    Google Scholar 

  34. 34.

    Rice DB, McIntyre A, Mirkowski M, Janzen S, Viana R, Britt E, Teasell R (2017) Patient-centered goal setting in a hospital-based outpatient stroke rehabilitation center. PM & R 9(9):856–865

    Google Scholar 

  35. 35.

    Ringelstein EB, Chamorro A, Kaste M, Langhorne P, Leys D, Lyrer P, Thijs V, Thomassen L, Toni D (2013) European Stroke Organisation recommendations to establish a stroke unit and stroke center. Stroke 44(3):828–840

    Google Scholar 

  36. 36.

    Sadic S, de Sousa JP, Crispim JA (2018) A two-phase MILP approach to integrate order, customer and manufacturer characteristics into dynamic manufacturing network formation and operational planning. Expert Syst Appl 96:462–478

    Google Scholar 

  37. 37.

    Sangaiah AK, Gopal J, Basu A, Subramaniam PR (2017) An integrated fuzzy DEMATEL, TOPSIS, and ELECTRE approach for evaluating knowledge transfer effectiveness with reference to GSD project outcome. Neural Comput Appl 28(1):111–123

    Google Scholar 

  38. 38.

    Sawabe M, Momosaki R, Hasebe K, Sawaguchi A, Kasuga S, Asanuma D, Suzuki S, Miyauchi N, Abo M (2018) Rehabilitation characteristics in high-performance hospitals after acute stroke. J Stroke Cerebrovasc Dis 27(9):2431–2435

    Google Scholar 

  39. 39.

    Shen F, Ma X, Li Z, Xu Z, Cai D (2018) An extended intuitionistic fuzzy TOPSIS method based on a new distance measure with an application to credit risk evaluation. Inf Sci 428:105–119

    MathSciNet  Google Scholar 

  40. 40.

    Singh S, Garg H (2017) Distance measures between type-2 intuitionistic fuzzy sets and their application to multicriteria decision-making process. Appl Intell 46(4):788–799

    Google Scholar 

  41. 41.

    Viswanathan A, Rakich SM, Engel C, Snider R, Rosand J, Greenberg SM, Smith EE (2006) Antiplatelet use after intracerebral hemorrhage. Neurology 66(2):206–209

    Google Scholar 

  42. 42.

    Walczak D, Rutkowska A (2017) Project rankings for participatory budget based on the fuzzy TOPSIS method. Eur J Oper Res 260(2):706–714

    MathSciNet  MATH  Google Scholar 

  43. 43.

    Wan S-P, Li S-Q, Dong J-Y (2018) A three-phase method for Pythagorean fuzzy multi-attribute group decision making and application to haze management. Comput Ind Eng 123:348–363

    Google Scholar 

  44. 44.

    Wan S-P, Qin Y-L, Dong J-Y (2017) A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees. Knowl Based Syst 138:232–248

    Google Scholar 

  45. 45.

    Wu T, Liu X, Liu F (2018) An interval type-2 fuzzy TOPSIS model for large scale group decision making problems with social network information. Inf Sci 432:392–410

    MathSciNet  Google Scholar 

  46. 46.

    Xing Y, Zhang R, Wang J, Zhu X (2018) Some new Pythagorean fuzzy Choquet–Frank aggregation operators for multi-attribute decision making. Int J Intell Syst 33(11):2189–2215

    Google Scholar 

  47. 47.

    Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of the 2013 joint IFSA world congress and NAFIPS annual meeting, Edmonton, Canada, June 24–28, pp 57–61

  48. 48.

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

    Google Scholar 

  49. 49.

    Yager RR (2016) Properties and applications of Pythagorean fuzzy sets. In: Angelov P, Sotirov S (eds) Imprecision and uncertainty in information representation and processing, studies in fuzziness and soft computing, vol 332. Springer, Basel, pp 119–136

    Google Scholar 

  50. 50.

    Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28(5):436–452

    Google Scholar 

  51. 51.

    Yilmazlar S, Abas F, Korfali E (2005) Comparison of ventricular drainage in poor grade patients after intracranial hemorrhage. Neurol Res 27(6):653–656

    Google Scholar 

  52. 52.

    Yoon K (1987) A reconciliation among discrete compromise solutions. J Oper Res Soc 38(3):277–286

    MATH  Google Scholar 

  53. 53.

    Yu C, Shao Y, Wang K, Zhang L (2019) A group decision making sustainable supplier selection approach using extended TOPSIS under interval-valued Pythagorean fuzzy environment. Expert Syst Appl 121:1–17

    Google Scholar 

  54. 54.

    Zavadskas EK, Mardani A, Turskis Z, Jusoh A, Nor KM (2016) Development of TOPSIS method to solve complicated decision-making problems—an overview on developments from 2000 to 2015. Int J Inf Technol Decis Mak 15(3):645–682

    Google Scholar 

  55. 55.

    Zeng S, Chen J, Li X (2016) A hybrid method for Pythagorean fuzzy multiple-criteria decision making. Int J Inf Technol Decis Mak 15(2):403–422

    Google Scholar 

  56. 56.

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

    Google Scholar 

  57. 57.

    Zhang X (2017) Pythagorean fuzzy clustering analysis: a hierarchical clustering algorithm with the ratio index-based ranking methods. Int J Intell Syst 33(9):1798–1822

    Google Scholar 

  58. 58.

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

    MathSciNet  Google Scholar 

  59. 59.

    Zhou J, Su W, Baležentis T, Streimikiene D (2018) Multiple criteria group decision-making considering symmetry with regards to the positive and negative ideal solutions via the Pythagorean normal cloud model for application to economic decisions. Symmetry 10(5):140. https://doi.org/10.3390/sym10050140

    Article  Google Scholar 

  60. 60.

    Zyoud SH, Fuchs-Hanusch D (2017) A bibliometric-based survey on AHP and TOPSIS techniques. Expert Syst Appl 78:158–181

    Google Scholar 

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Acknowledgements

The authors acknowledge the assistance of the respected editor and the anonymous referees for their insightful and constructive comments, which helped to improve the overall quality of the paper. The authors are grateful for grant funding support from the Taiwan Ministry of Science and Technology (MOST 105-2410-H-182-007-MY3) and Linkou Chang Gung Memorial Hospital (BMRP 574 and CMRPD2F0203) during the completion of this study.

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Correspondence to Ting-Yu Chen.

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Ho, LH., Lin, YL. & Chen, TY. A Pearson-like correlation-based TOPSIS method with interval-valued Pythagorean fuzzy uncertainty and its application to multiple criteria decision analysis of stroke rehabilitation treatments. Neural Comput & Applic 32, 8265–8295 (2020). https://doi.org/10.1007/s00521-019-04304-8

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Keywords

  • Multiple criteria decision analysis
  • TOPSIS
  • Interval-valued Pythagorean fuzzy set
  • Pearson-like IVPF correlation coefficient
  • Correlation-based closeness coefficient
  • Rehabilitation treatment