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Pythagorean fuzzy MULTIMOORA method based on distance measure and score function: its application in multicriteria decision making process

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Abstract

The MULTIMOORA method is better than some of the existing decision making methods. However, it has not been improved to process Pythagorean fuzzy sets (PFSs). The decision results of the MULTIMOORA method greatly depend on the distance measure and score function. Although there are many studies focusing on proposing distance measures and score functions for PFSs, they still show some defects. In this paper, we propose two novel distance measures and a novel score function for PFSs for proposing a novel Pythagorean fuzzy MULTIMOORA method. To this end, two distance measures, Dice distance and Jaccard distance, are proposed for computing the deviation degree between two PFSs, and their general forms are also discussed. Afterward, a novel score function based on determinacy degree and indeterminacy degree is put forward for approximately representing PFSs. Then, the original MULTIMOORA method is extended by using the Dice distance and score function and it is used to solve the multicriteria decision making problems under the PFS information context. Finally, a real case for evaluating solid-state disk productions is handled using the proposed Pythagorean fuzzy MULTIMOORA method and another case for evaluating energy projects is given to verify the advantages of our studies by comparing them with the existing Pythagorean fuzzy distance measures, score functions, and decision making methods.

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References

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

    MATH  Google Scholar 

  2. Garg H (2019) New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications. Int J Intell Syst 34(1):82–106

    Google Scholar 

  3. Lin M, Li X, Chen L (2020) Linguistic q-rung orthopair fuzzy sets and their interactional partitioned Heronian mean aggregation operators. International Journal of Intelligent Systems 35(2):217–249

    Google Scholar 

  4. Liu PD, Chen SM, Wang YM (2020) Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators. Inf Sci 512:830–854

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  6. Yager RR (2017) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230

    Google Scholar 

  7. Xu ZS, Xia MM (2011) Induced generalized intuitionistic fuzzy operators. Knowl-Based Syst 24:197–209

    Google Scholar 

  8. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Intell Syst 35(4):417–433

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  10. 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

    MathSciNet  Google Scholar 

  11. Garg H (2018) Some methods for strategic decision-making problems with immediate probabilities in Pythagorean fuzzy environment. Int J Intell Syst 33(4):687–712

    Google Scholar 

  12. Garg H, Chen SM (2020) Multiattribute group decision making based on neutrality aggregation operators of q-rung orthopair fuzzy sets. Inf Sci 517:427–447

    MathSciNet  Google Scholar 

  13. Garg H (2018) New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making. Int J Intell Syst 33(3):653–683

    Google Scholar 

  14. Lin MW, Huang C, Xu ZS (2019) TOPSIS method based on correlation coefficient and entropy measure for linguistic Pythagorean fuzzy sets and its application to multiple attribute decision making. Complexity, Article ID 6967390, 16 pages

  15. Garg H (2019) Neutrality operations-based Pythagorean fuzzy aggregation operators and its applications to multiple attribute group decision-making process. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-019-01448-2

    Article  Google Scholar 

  16. Akram M, Dudek WA, Ilyas F (2019) Group decision-making based on Pythagorean fuzzy TOPSIS method. Int J Intell Syst 34(7):1455–1475

    Google Scholar 

  17. Zhou F, Chen TY (2019) A novel distance measure for Pythagorean fuzzy sets and its applications to the technique for order preference by similarity to ideal solutions. Int J Comput Intell Syst 12(2):955–969

    MathSciNet  Google Scholar 

  18. Liang D, Zhang Y, Xu ZS, Jamaldeen A (2019) Pythagorean fuzzy VIKOR approaches based on TODIM for evaluating internet banking website quality of Ghanaian banking industry. Appl Soft Comput J 78:583–594

    Google Scholar 

  19. 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 

  20. Garg H (2019) Novel neutrality operation-based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis. Int J Intell Syst 34(10):2459–2489

    Google Scholar 

  21. 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 

  22. Lin MW, Wei JH, Xu ZS, Chen RQ (2018) Multiattribute group decision-making based on linguistic Pythagorean fuzzy interaction partitioned Bonferroni mean aggregation operators. Complexity, Article ID 9531064, 24 pages

  23. Brauers WKM, Zavadskas EK (2011) Multimoora optimization used to decide on a bank loan to buy property. Technol Econ Dev Econ 17(1):174–188

    Google Scholar 

  24. Brauers WKM, Zavadskas EK (2010) Project management by multimoora as an instrument for transition economies. Technol Econ Dev Econ 16(1):5–24

    Google Scholar 

  25. Brauers WKM, Zavadskas EK (2012) Robustness of MULTIMOORA: a method for multi-objective optimization. Informatica 23(1):1–25

    MathSciNet  MATH  Google Scholar 

  26. Lin MW, Huang H, Xu ZS (2020) MULTIMOORA based MCDM model for site selection of car sharing station under picture fuzzy environment. Sustain Cities Soc 53:101873

    Google Scholar 

  27. Hafezalkotob A, Hafezalkotob A, Sayadi MK (2016) Extension of MULTIMOORA method with interval numbers: an application in materials selection. Appl Math Model 40(2):1372–1386

    MathSciNet  MATH  Google Scholar 

  28. Lin MW, Huang C, Xu ZS, Chen RQ (2020) Evaluating IoT platforms using integrated probabilistic linguistic MCDM method. IEEE Internet Things J. https://doi.org/10.1109/JIOT.2020.2997133

    Article  Google Scholar 

  29. Li D, Zeng W (2018) Distance measure of Pythagorean fuzzy sets. Int J Intell Syst 33(2):348–361

    MathSciNet  Google Scholar 

  30. Zeng W, Li D, Yin Q (2018) Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making. Int J Intell Syst 33(11):2236–2254

    Google Scholar 

  31. 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(11):1187–1214

    Google Scholar 

  32. Gündoǧdu FK, Cengiz K (2019) Spherical fuzzy sets and spherical fuzzy TOPSIS method. J Intell Fuzzy Syst 36(1):337–352

    Google Scholar 

  33. Xiao FY, Ding WP (2019) Divergence measure of Pythagorean fuzzy sets and its application in medical diagnosis. Appl Soft Comput J 79:254–267

    Google Scholar 

  34. Zeng SZ, Chen SM, Kuo LW (2019) Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method. Inf Sci 488:76–92

    Google Scholar 

  35. Lin MW, Chen ZY, Liao HC, Xu ZS (2019) ELECTRE II method to deal with probabilistic linguistic term sets and its application to edge computing. Nonlinear Dyn 96:2125–2143

    MATH  Google Scholar 

  36. 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(12):1198–1219

    Google Scholar 

  37. Peng XD (2019) Algorithm for pythagorean fuzzy multi-criteria decision making based on WDBA with new score function. Fundamenta Informaticae 165(2):99–137

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  39. Dice LR (1945) Measures of the amount of ecologic association between species. Ecology 26(3):297–302

    Google Scholar 

  40. Jaccard P (1976) étude comparative de la distribution florale dans une portion des Alpes et des Jura. Bulletin Société Vaudoise Science Nature 3:547–579

    Google Scholar 

  41. Luo L, Zhang C, Liao HC (2019) Distance-based intuitionistic multiplicative MULTIMOORA method integrating a novel weight-determining method for multiple criteria group decision making. Comput Ind Eng 131:82–98

    Google Scholar 

  42. Hafezalkotob A, Hafezalkotob A, Liao H, Herrera F (2019) An overview of MULTIMOORA for multi-criteria decision-making: theory, developments, applications, and challenges. Inf Fus 51:145–177

    Google Scholar 

  43. Wei GW (2019) The generalized dice similarity measures for multiple attribute decision making with hesitant fuzzy linguistic information. Econ Res Ekonomska Istraživanja 32(1):1498–1520

    Google Scholar 

  44. 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(2):437–466

    Google Scholar 

  45. Ye J (2014) Vector similarity measures of hesitant fuzzy sets and their multiple attribute decision making. Econ Comput Econ Cybernet Stud Res 48(4):215–226

    Google Scholar 

  46. Lin MW, Wang HB, Xu ZS (2019) TODIM-based multi-criteria decision-making method with hesitant fuzzy linguistic term sets. Artif Intell Rev. https://doi.org/10.1007/s10462-019-09774-9

    Article  Google Scholar 

  47. Garg H (2020) Kaur G (2020) Quantifying gesture information in brain hemorrhage patients using probabilistic dual hesitant fuzzy sets with unknown probability information. Comput Ind Eng 140:106211

    Google Scholar 

  48. Lin MW, Xu ZS, Zhai YL, Yao ZQ (2018) Multi-attribute group decision-making under probabilistic uncertain linguistic environment. J Oper Res Soc 69(2):157–170

    Google Scholar 

  49. Yang J, Shi B (1992) Joining method in group appraising. Syst Eng Theory Pract 12(1):49–51

    Google Scholar 

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

    Google Scholar 

  51. Garg H (2017) Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Comput Math Org Theory 23(4):546–571

    Google Scholar 

  52. Peng X (2019) New operations for interval-valued Pythagorean fuzzy set. Scientia Iranica 26(2C):1049–1076

    Google Scholar 

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

    Google Scholar 

  54. Wan SP, Jin Z, Dong JY (2020) A new order relation for Pythagorean fuzzy numbers and application to multi-attribute group decision making. Knowl Inf Syst 62:751–785

    Google Scholar 

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

    Google Scholar 

Download references

Acknowledgments

This research work was supported by the National Natural Science Foundation of China under Grant Nos. 61872086 and U1805263.

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Authors and Affiliations

  1. College of Mathematics and Informatics, Fujian Normal University, Fuzhou, 350117, Fujian, China

    Chao Huang & Mingwei Lin

  2. Digital Fujian Internet-of-Things Laboratory of Environmental Monitoring, Fujian Normal University, Fuzhou, 350117, Fujian, China

    Chao Huang & Mingwei Lin

  3. Business School, Sichuan University, Chengdu, 610064, Sichuan, China

    Zeshui Xu

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  1. Chao Huang
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  2. Mingwei Lin
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  3. Zeshui Xu
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Correspondence to Mingwei Lin.

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Huang, C., Lin, M. & Xu, Z. Pythagorean fuzzy MULTIMOORA method based on distance measure and score function: its application in multicriteria decision making process. Knowl Inf Syst 62, 4373–4406 (2020). https://doi.org/10.1007/s10115-020-01491-y

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