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Pythagorean Fuzzy Multi-Criteria Decision Making Method Based on Multiparametric Similarity Measure

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Abstract

Big data industry decision is supremely important for companies to boost the efficiency of leadership, which can vastly accelerate industrialized. With regard to big data industry decision assessment, the intrinsic problem involves enormous inexactness, fuzziness and ambiguity. Pythagorean fuzzy sets (PFSs), managing the uncertainness depicted in non-membership with membership, are a quite practical way to capture uncertainness. Firstly, the innovative Pythagorean fuzzy score function is given to dispose the comparison issue. Innovative distance measure and similarity measure for PFSs with three parameters are explored, along with corresponding proofs therewith. Later, objective weight is ascertained by deviation-based method. Also, combined weight is skillfully designed, which can tellingly imply both subjective preference and objective preference. In addition, an approach to settle Pythagorean fuzzy problem by multiparametric similarity measure is presented. The efficacy of developed algorithm is elaborated by a big data industry decision issue. Moreover, a comparison of the introduced algorithm with the selected existing methods has been built on the basis of the division by zero issue and counterintuitive phenomena for displaying its effectiveness.

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References

  1. Wang H, Xu Z, Pedrycz W, et al. An overview on the roles of fuzzy set techniques in big data processing: Trends, challenges and opportunities. Knowl-Based Syst. 2017;118:15–30.

    Article  Google Scholar 

  2. Ge M, Bangui H, Buhnova B, et al. Big Data for Internet of Things: A Survey. Future Gener Comp Syst. 2018;87:601–14.

    Article  Google Scholar 

  3. Miah SJ, Vu HQ, Gammack J, McGrath M, et al. A big data analytics method for tourist behaviour analysis. Inform Manage. 2017;54:771–85.

    Article  Google Scholar 

  4. Schlick CJR, Castle JP, Bentrem DJ, et al. Utilizing Big Data in Cancer Care. Surg Oncol Clin N Am. 2018;27:641–52.

    Article  Google Scholar 

  5. Ryan HL, Li-Minn A, Seng KP, Broster JC, Pratley JE, et al. Big data and machine learning for crop protection. Comput Electron Agr. 2018;151:376–83.

    Article  Google Scholar 

  6. Zhao L, Chen Z, Hu Y, Min G, Jiang Z, et al. Distributed feature selection for efficient economic big data analysis. IEEE Trans Big Data. 2018;4:164–76.

    Article  Google Scholar 

  7. Atanassov K. Intuitionistic fuzzy sets. Fuzzy Set Syst. 1986;20:87–96.

    Article  Google Scholar 

  8. Zadeh LA. Fuzzy sets. Inf. Control. 1965;8:338–53.

    Article  MathSciNet  Google Scholar 

  9. Yager RR. Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst. 2014;22:958–65.

    Article  Google Scholar 

  10. Zhang XL, Xu ZS. Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst. 2014;29:1061–78.

    Article  Google Scholar 

  11. Peng XD, Garg H. Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition. Appl Intell. 2019;49:4058–96.

    Article  Google Scholar 

  12. Garg H. Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Comput Math Organ Th. 2017;23:546–71.

    Article  Google Scholar 

  13. Ma ZM, Xu ZS. Symmetric pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst. 2016;31:1198–219.

    Article  Google Scholar 

  14. Khan MSA, Abdullah S, Ali A, Amin F, et al. Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making. Granul Comput. 2019;4:249–63.

    Article  Google Scholar 

  15. Gao H, Lu M, Wei G, Wei Y, et al. Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making. Fund Inform. 2018;159:385–428.

    MathSciNet  MATH  Google Scholar 

  16. Yang Y, Chen ZS, Chen YH, Chin KS, et al. Interval-valued Pythagorean Fuzzy Frank Power Aggregation Operators based on An Isomorphic Frank Dual Triple. Int J Comput Intell Syst. 2018;11:1091–110.

    Article  Google Scholar 

  17. Qin J. Generalized Pythagorean Fuzzy Maclaurin Symmetric Means and Its Application to Multiple Attribute SIR Group Decision Model. Int J Fuzzy Syst. 2018;20:943–57.

    Article  MathSciNet  Google Scholar 

  18. Yang Y, Li YL, Ding H, Qian GS, Lyu HX, et al. The pythagorean fuzzy Frank aggregation operators based on isomorphism Frank t-norm and s-norm and their application. Control Decis. 2018;33:1471–80.

    MATH  Google Scholar 

  19. Yang W, Pang Y. New Pythagorean Fuzzy Interaction Maclaurin Symmetric Mean Operators and Their Application in Multiple Attribute Decision Making. IEEE Access. 2018;6:39241–60.

    Article  Google Scholar 

  20. Peng X, Ma X. Pythagorean fuzzy multi-criteria decision making method based on CODAS with new score function. J Intell Fuzzy Syst. 2020;38:3307–18.

    Article  Google Scholar 

  21. Chen TY. Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis. Inf Fusion. 2018;41:129–50.

    Article  Google Scholar 

  22. Peng X, Selvachandran G. Pythagorean fuzzy set: State of the art and future directions. Artif Intell Rev. 2019;52:1873–927.

    Article  Google Scholar 

  23. Chen TY. 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. 2019;31:3969–99.

    Article  Google Scholar 

  24. Chen TY. An outranking approach using a risk attitudinal assignment model involving Pythagorean fuzzy information and its application to financial decision making. Appl Soft Comput. 2018;71:460–87.

    Article  Google Scholar 

  25. Lin M, Huang C, Xu Z, et al. TOPSIS Method Based on Correlation Coefficient and Entropy Measure for Linguistic Pythagorean Fuzzy Sets and Its Application to Multiple Attribute Decision Making. Complexity. 2019;2019:1–16.

    MATH  Google Scholar 

  26. Zhan J, Sun B, Zhang X, et al. PF-TOPSIS method based on CPFRS models: An application to unconventional emergency events. Comput Ind Eng. 2020;139:106192.

    Article  Google Scholar 

  27. Peng X. New similarity measure and distance measure for Pythagorean fuzzy set. Complex Intell Syst. 2019;5:101–11.

    Article  Google Scholar 

  28. Chen SM. Similarity measures between vague sets and between elements. IEEE Trans Syst Man Cyber. 1997;27:153–8.

    Article  Google Scholar 

  29. Chen SM, Chang CH. A novel similarity measure between Atanssov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf Sci. 2015;291:96–114.

    Article  Google Scholar 

  30. Hong DH, Kim C. A note on similarity measures between vague sets and between elements. Inf Sci. 1999;115:83–96.

    Article  MathSciNet  Google Scholar 

  31. Li F, Xu ZY. Measures of similarity between vague sets. J Softw. 2001;12:922–7.

    Google Scholar 

  32. Liang ZZ, Shi PF. Similarity measures on intuitionistic fuzzy sets. Pattern Recognit Lett. 2003;24:2687–93.

    Article  Google Scholar 

  33. Mitchell HB. On the Dengfeng-Chuntian similarity measure and its application to pattern recognition. Pattern Recognit Lett. 2003;24:3101–4.

    Article  Google Scholar 

  34. Ye J. Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model. 2011;53:91–7.

    Article  MathSciNet  Google Scholar 

  35. Keshavarz GM, Zavadskas EK, Amiri M, Antucheviciene J, et al. A new method of assessment based on fuzzy ranking and aggregated weights (AFRAW) for MCDM problems under type-2 fuzzy environment. Econ Comput Econ Cyb. 2016;50:39–68.

    Google Scholar 

  36. Wang X, Triantaphyllou E. Ranking irregularities when evaluating alternatives by using some electre methods. Omega. 2008;36:45–63.

    Article  Google Scholar 

  37. Lin M, Huang C, Xu Z, Chen R, et al. Evaluating IoT Platforms Using Integrated Probabilistic Linguistic MCDM Method. IEEE Internet Things. 2020. https://doi.org/10.1109/JIOT.2020.2997133.

    Article  Google Scholar 

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Funding

This study was funded by National Natural Science Foundation of China (grant number 62006155), MOE (Ministry of Education in China) Project of Humanities and Social Sciences (grant number 18YJCZH054), Natural Science Foundation of Guangdong Province (grant number 2018A030307033), and the General Project of Shaoguan University (grant number SY2016KJ11).

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Authors and Affiliations

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

    Xindong Peng & Huiyong Yuan

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  1. Xindong Peng
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  2. Huiyong Yuan
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Correspondence to Xindong Peng.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Peng, X., Yuan, H. Pythagorean Fuzzy Multi-Criteria Decision Making Method Based on Multiparametric Similarity Measure. Cogn Comput 13, 466–484 (2021). https://doi.org/10.1007/s12559-020-09781-x

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  • DOI: https://doi.org/10.1007/s12559-020-09781-x

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