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Link to original content: https://unpaywall.org/10.1007/S40815-022-01289-W
Aczel–Alsina Weighted Aggregation Operators of Neutrosophic Z-Numbers and Their Multiple Attribute Decision-Making Method | International Journal of Fuzzy Systems Skip to main content
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Aczel–Alsina Weighted Aggregation Operators of Neutrosophic Z-Numbers and Their Multiple Attribute Decision-Making Method

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Abstract

The new operations based on the Aczel–Alsina t-norm and t-conorm show the advantage of flexible operations by adjusting different parameter values. Motivated based on the new operations, we propose the Aczel–Alsina operations and weighted aggregation operators of neutrosophic Z-numbers (NZNs) to solve the flexible decision-making problem by adjusting different parameter values depending on the decision maker’s preference under the environment of NZNs. To do so, this paper first proposes the Aczel–Alsina t-norm and t-conorm operations of NZNs and develops the NZN Aczel–Alsina weighted arithmetic averaging (NZNAAWAA) and NZN Aczel–Alsina weighted geometric averaging (NZNAAWGA) operators to aggregate NZNs. Then, a multiple attribute decision-making (MADM) method is developed by the NZNAAWAA and NZNAAWGA operators under the NZN environment. Finally, a numerical example is provided to verify the influence of different parameter values on decision-making results. Compared with existing MADM methods, the new MADM method shows its feasibility and flexibility in MADM applications. Moreover, the new MADM approach can not only extend the existing MADM methods, but also overcome the lack of decision-making flexibility of the existing MADM methods.

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References

  1. Smarandache, F.: Neutrosophy: Neutrosophic Probability, Set, and Logic. American Research Press, Rehoboth (1998)

    MATH  Google Scholar 

  2. Guo, Y., Sengur, A.: A novel image segmentation algorithm based on neutrosophic similarity clustering. Appl. Soft Comput. 25, 391–398 (2014)

    Article  Google Scholar 

  3. Alia, M., Son, L.H., Thanhc, N.D., Minh, N.V.: A neutrosophic recommender system for medical diagnosis based on algebraic neutrosophic measures. Appl. Soft Comput. 71, 1054–1071 (2018)

    Article  Google Scholar 

  4. Nguyen, G.N., Son, L.H., Ashour, A.S., et al.: A survey of the state-of-the-arts on neutrosophic sets in biomedical diagnoses. Int. J. Mach. Learn. Cyber. 10, 1–13 (2019)

    Article  Google Scholar 

  5. Ye, J.: Single valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine. Soft. Comput. 21(3), 817–825 (2017)

    Article  Google Scholar 

  6. Ye, J.: A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J. Intell. Fuzzy Syst. 26, 2459–2466 (2014)

    Article  MathSciNet  Google Scholar 

  7. Zhang, H.Y., Wang, J.Q., Chen, X.H.: Interval neutrosophic sets and their application in multicriteria decision making problems. Sci. World J. 2014, Article ID 645953 (2014)

  8. Liu, P.D., Wang, Y.M.: Multiple attribute decision making method based on single-valued neutrosophic normalized weighted Bonferroni mean. Neural Comput. Appl. 25(7–8), 2001–2010 (2014)

    Article  Google Scholar 

  9. Peng, J.J., Wang, J.Q., Wang, J., Zhang, H.Y., Chen, X.H.: Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int. J. Syst. Sci. 47(10), 2342–2358 (2016)

    Article  Google Scholar 

  10. Zhou, L.P., Dong, J.Y., Wan, S.P.: Two new approaches for multi-attribute group decision-making with interval-valued neutrosophic Frank aggregation operators and incomplete weights. IEEE Access 7, 102727–102750 (2019)

    Article  Google Scholar 

  11. Singh, P., Huang, Y.P.: A high-order neutrosophic-neuro-gradient descent algorithm-based expert system for time series forecasting. Int. J. Fuzzy Syst. 21(7), 2245–2257 (2019)

    Article  Google Scholar 

  12. Aslam, M., Bantan, R.A.R., Khan, N.: Design of a new attribute control chart under neutrosophic statistics. Int. J. Fuzzy Syst. 21(2), 433–440 (2019)

    Article  Google Scholar 

  13. Ye, J.: Multiple-attribute decision-making method under a single-valued neutrosophic hesitant fuzzy environment. J. Intell. Syst. 24(1), 23–36 (2014)

    Article  Google Scholar 

  14. Deli, I., Ali, M., Smarandache, F.: Bipolar neutrosophic sets and their application based on multi-criteria decision making problems. In: Proceedings of the International Conference on Advanced Mechatronic Systems, Beijing, pp. 249–254 (2015)

  15. Wang, L., Zang, H., Wang, J.: Frank Choquet Bonferroni mean operators of bipolar neutrosophic sets and their application to multi-criteria decision making problems. Int. J. Fuzzy Syst. 20, 13–28 (2018)

    Article  MathSciNet  Google Scholar 

  16. Maji, P.K.: A neutrosophic soft set approach to a decision making problem. Ann. Fuzzy Math. Inform. 3(2), 313–319 (2012)

    MathSciNet  MATH  Google Scholar 

  17. Zhao, A., Jie, H., Guan, H., et al.: A multi-attribute fuzzy fluctuation time series model based on neutrosophic soft sets and information entropy. Int. J. Fuzzy Syst. 22(2), 636–652 (2020)

    Article  Google Scholar 

  18. Yang, H.L., Zhang, C.L., Guo, Z.L., et al.: A hybrid model of single valued neutrosophic sets and rough sets: single valued neutrosophic rough set model. Soft. Comput. 21, 6253–6267 (2017)

    Article  Google Scholar 

  19. Du, S.G., Ye, J., Yong, R., Zhang, F.W.: Simplified neutrosophic indeterminate decision making method with decision makers’ indeterminate ranges. J. Civ. Eng. Manag. 26(6), 590–598 (2020)

    Article  Google Scholar 

  20. Chen, J.Q., Ye, J., Du, S.G.: Vector similarity measures between refined simplified neutrosophic sets and their multiple attribute decision making method. Symmetry 9(8), 153 (2017). https://doi.org/10.3390/sym9070153-11

    Article  Google Scholar 

  21. Ye, J., Du, S.G., Yong, R., Zhang, F.W.: Arccosine and arctangent similarity measures of refined simplified neutrosophic indeterminate sets and their multicriteria decision-making method. J. Intell. Fuzzy Syst. (2021). https://doi.org/10.3233/JIFS-201571

    Article  Google Scholar 

  22. Ye, J., Song, J.M., Du, S.G.: Correlation coefficients of consistency neutrosophic sets regarding neutrosophic multi-valued sets and their multi-attribute decision-making method. Int. J. Fuzzy Syst. (2021). https://doi.org/10.1007/s40815-020-00983-x

    Article  Google Scholar 

  23. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

  24. Zadeh, L.A.: A note on z-numbers. Inf. Sci. 181(14), 2923–2932 (2011)

    Article  Google Scholar 

  25. Jiang, W., Xie, C., Zhuang, M., Shou, Y., Tang, Y.: Sensor data fusion with z-numbers and its application in fault diagnosis. Sensors 16(9), 1–22 (2016)

    Article  Google Scholar 

  26. Kang, B., Hu, Y., Deng, Y., Zhou, D.: A new methodology of multicriteria decision-making in supplier selection based on z-numbers. Math. Probl. Eng. 2016, 1–17 (2016)

    MathSciNet  MATH  Google Scholar 

  27. Wang, J.Q., Cao, Y.X., Zhang, H.Y.: Multi-criteria decision-making method based on distance measure and choquet integral for linguistic z-numbers. Cogn. Comput. 9(6), 82–842 (2017)

    Article  Google Scholar 

  28. Aliev, R.A., Huseynov, O.H., Serdaroglu, R.: Ranking of Z-Numbers and its application in decision making. Int. J. Inf. Technol. Decis. Mak. 15(06), 1503–1519 (2016)

    Article  Google Scholar 

  29. Jabbarova, A.I.: Application of Z-number concept to supplier selection problem. Proc. Comput. Sci. 120, 473–477 (2017)

    Article  Google Scholar 

  30. Aboutorab, H., Saberi, M., Asadabadi, M.R., Hussain, O., Chang, E.: ZBWM: the Z-number extension of Best Worst Method and its application for supplier development. Expert Syst. Appl. 107, 115–125 (2018)

    Article  Google Scholar 

  31. Ding, X.F., Zhu, L.X., Lu, M.S., Wang, Q., Feng, Y.Q.: A novel linguistic Z-number QUALIFLEX method and its application to large group emergency decision making. Sci. Program. (2020). https://doi.org/10.1155/2020/1631869

    Article  Google Scholar 

  32. Ye, T., Bingyi, K.: A modified method of generating Z-number based on OWA weights and maximum entropy. Soft. Comput. (2020). https://doi.org/10.1007/s00500-020-04914-8

    Article  MATH  Google Scholar 

  33. Kang, B., Chhipi-Shrestha, G., Deng, Y., Hewage, K., Sadiq, R.: Stable strategies analysis based on the utility of z-number in the evolutionary games. Appl. Math. Comput. 324, 202–217 (2018)

    Article  MathSciNet  Google Scholar 

  34. Ren, Z., Liao, H., Liu, Y.: Generalized Z-numbers with hesitant fuzzy linguistic information and its application to medicine selection for the patients with mild symptoms of the COVID-19. Comput. Ind. Eng. (2020). https://doi.org/10.1016/j.cie.2020.106517

    Article  Google Scholar 

  35. Kang, B., Zhang, P., Gao, Z., Chhipi-Shrestha, G., Hewage, K., Sadiq, R.: Environmental assessment under uncertainty using Dempster-Shafer theory and Z-numbers. J. Ambient. Intell. Humaniz. Comput. 11(5), 2041–2060 (2020)

    Article  Google Scholar 

  36. Li, Y., Garg, H., Deng, Y.: A new uncertainty measure of discrete Z-numbers. Int. J. Fuzzy Syst. 22, 760–776 (2020)

    Article  Google Scholar 

  37. Teng, F., Wang, L., Rong, L., et al.: Probabilistic linguistic Z number decision-making method for multiple attribute group decision-making problems with heterogeneous relationships and incomplete probability information. Int. J. Fuzzy Syst. (2021). https://doi.org/10.1007/s40815-021-01161-3

    Article  Google Scholar 

  38. Peng, H.G., Wang, X.K., Wang, J.Q.: New MULTIMOORA and pairwise evaluation-based MCDM methods for hotel selection based on the projection measure of Z-numbers. Int. J. Fuzzy Syst. (2021). https://doi.org/10.1007/s40815-021-01141-7

    Article  Google Scholar 

  39. Du, S.G., Ye, J., Yong, R., Zhang, F.W.: Some aggregation operators of neutrosophic Z-numbers and their multicriteria decision making method. Complex Intell. Syst. 7, 429–438 (2021)

    Article  Google Scholar 

  40. Yong, R., Ye, J., Du, S.G.: Multicriteria decision making method and application in the setting of trapezoidal neutrosophic Z-numbers. J. Math. (2021). https://doi.org/10.1155/2021/6664330

    Article  MathSciNet  Google Scholar 

  41. Aczel, J., Alsina, C.: Characterization of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements. Aequ. Math. 25(1), 313–315 (1982)

    Article  MathSciNet  Google Scholar 

  42. Alsina, C., Frank, M.J., Schweizer, B.: Associative functions: triangular norms and copulas. World Scientific Publishing, Danvers, MA (2006)

    Book  Google Scholar 

  43. Ashraf, S., Abdullah, S., Zeng, S., et al.: fuzzy decision support modeling for hydrogen power plant selection based on single valued neutrosophic sine trigonometric aggregation operators. Symmetry 12, 298 (2020). https://doi.org/10.3390/sym12020298

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Civil and Environmental Engineering, Ningbo University, Ningbo, 315211, People’s Republic of China

    Jun Ye, Shigui Du & Rui Yong

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  1. Jun Ye
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  2. Shigui Du
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  3. Rui Yong
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Correspondence to Jun Ye.

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Ye, J., Du, S. & Yong, R. Aczel–Alsina Weighted Aggregation Operators of Neutrosophic Z-Numbers and Their Multiple Attribute Decision-Making Method. Int. J. Fuzzy Syst. 24, 2397–2410 (2022). https://doi.org/10.1007/s40815-022-01289-w

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