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MADM Strategies Based on Arithmetic and Geometric Mean Operator Under Rough-Bipolar Neutrosophic Set Environment

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Transactions on Rough Sets XXIII

Abstract

The main focus of this paper is to introduce some aggregation operators namely, Rough-Bipolar Neutrosophic Arithmetic Mean (RBNAM) operator and Rough-Bipolar Neutrosophic Geometric Mean (RBNGM) operator under Rough-Bipolar Neutrosophic Set (RBNS) environment. Besides, we present the concept of score and accuracy functions under the RBNS environment. Further, we propose two multi-attribute decision-making (MADM) strategies based on RBNAM operator and RBNGM operator respectively under the RBNS environment. Finally, we provide a real-life numerical example to validate the proposed MADM strategy.

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References

  1. Broumi, S., Smarandache, F., Dhar, M.: Rough neutrosophic sets. Ital. J. Pure Appl. Math. 32, 493–502 (2014)

    MathSciNet  MATH  Google Scholar 

  2. Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)

    Article  MATH  Google Scholar 

  3. Smarandache, F.: A Unifying Field in Logics, Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth (1998)

    MATH  Google Scholar 

  4. Deli, I., Ali, M., Smarandache, F.: Bipolar neutrosophic sets and their application based on multi-criteria decision making problems. In: Proceedings of the 2015 International Conference on Advanced Mechatronic Systems, Beijing, China, 22–24 August 2015, pp. 249–254 (2015)

    Google Scholar 

  5. Lee, K.M.: Bipolar-valued fuzzy sets and their operations. In: Proceedings of International Conference on Intelligent Technologies, Bangkok, Thailand, pp. 307–312 (2000)

    Google Scholar 

  6. Salama, A.A., Broumi, S.: Roughness of neutrosophic sets. Elixir Appl. Math. 74, 26833–26837 (2014)

    Google Scholar 

  7. Broumi, S., Smarandache, F.: Interval neutrosophic rough set. Neutrosophic Sets Syst. 7, 23–31 (2015)

    Google Scholar 

  8. Broumi, S., Smarandache, F.: Interval-valued neutrosophic soft rough sets. Int. J. Comput. Math. 232919 (2015). https://doi.org/10.1155/2015/232919

  9. Mondal, K., Pramanik, S.: Rough neutrosophic multi-attribute decision-making based on rough accuracy score function. Neutrosophic Sets Syst. 8, 14–21 (2015)

    Google Scholar 

  10. Pramanik, S., Mondal, K.: Some rough neutrosophic similarity measure and their application to multi attribute decision making. Glob. J. Eng. Sci. Res. Manag. 2(7), 61–74 (2015)

    Google Scholar 

  11. Mondal, K., Pramanik, S.: Decision making based on some similarity measures under interval rough neutrosophic environment. Neutrosophic Sets Syst. 10, 46–57 (2015)

    Google Scholar 

  12. Pramanik, S., Mondal, K.: Cotangent similarity measure of rough neutrosophic sets and its application to medical diagnosis. J. New Theory 4, 90–102 (2015)

    Google Scholar 

  13. Mondal, K., Pramanik, S.: Tri-complex rough neutrosophic similarity measure and its application in multi-attribute decision making. Crit. Rev. 11, 26–40 (2015)

    Google Scholar 

  14. Mondal, K., Pramanik, S., Smarandache, F.: Several trigonometric hamming similarity measures of rough neutrosophic sets and their applications in decision making. In: Smarandache, F., Pramanik, S. (eds) New Trends in Neutrosophic Theory and Application, pp. 93–103. Pons Editions, Brussels, Belgium (2016)

    Google Scholar 

  15. Mondal, K., Pramanik, S., Smarandache, F.: Multi-attribute decision making based on rough neutrosophic variational coefficient similarity measure. Neutrosophic Sets Syst. 13, 3–17 (2016)

    Google Scholar 

  16. Mondal, K., Pramanik, S., Smarandache, F.: Rough neutrosophic hyper-complex set and its application to multi-attribute decision making. Crit. Rev. 13, 111–126 (2016)

    Google Scholar 

  17. Mondal, K., Pramanik, S., Smarandache, F.: Rough neutrosophic TOPSIS for multi-attribute group decision making. Neutrosophic Sets Syst. 13, 105–117 (2016)

    Google Scholar 

  18. Zhang, C., Zhai, Y., Li, D., Mu, Y.: Steam turbine fault diagnosis based on single-valued neutrosophic multigranulation rough sets over two universes. J. Intell. Fuzzy Syst. 31(6), 2829–2837 (2016). https://doi.org/10.3233/jifs-169165

    Article  MATH  Google Scholar 

  19. Pramanik, S., Roy, R., Roy, T.K., Smarandache, F.: Multi criteria decision making using correlation coefficient under rough neutrosophic environment. Neutrosophic Sets Syst. 17, 29–36 (2017)

    Google Scholar 

  20. Yang, H.L., Zhang, C.L., Guo, Z.L., Liu, Y.L., Liao, X.: A hybrid model of single valued neutrosophic sets and rough sets: single valued neutrosophic rough set model. Soft. Comput. 21, 6253–6267 (2017)

    Article  MATH  Google Scholar 

  21. Pramanik, S., Roy, R., Roy, T.K.: Multi criteria decision making based on projection and bidirectional projection measures of rough neutrosophic sets. In: Smarandache, F., Pramanik, S. (eds.) New Trends in Neutrosophic Theory and Applications, vol. 2, pp. 175–187. Pons Editions, Brussels (2018)

    Google Scholar 

  22. Zhao, X.R., Hu, B.Q.: Three-way decisions with decision theoretic rough sets in multiset-valued information tables. Inf. Sci. 507, 684–699 (2020). https://doi.org/10.1016/j.ins.2018.08.024

    Article  MathSciNet  MATH  Google Scholar 

  23. Jiao, L., Yang, H.-L., Li, S.-G.: Three-way decision based on decision-theoretic rough sets with single-valued neutrosophic information. Int. J. Mach. Learn. Cybern. 11(3), 657–665 (2019). https://doi.org/10.1007/s13042-019-01023-3

    Article  Google Scholar 

  24. Roy, R., Pramanik, S., Roy, T.K. Interval rough neutrosophic TOPSIS strategy for multi-attribute decision making. In: Abdel-Basset, M., Smarandache, F. (eds.) Neutrosophic Sets in Decision Analysis and Operations Research, pp. 98–118. IGI Global, Hershey (2020). https://doi.org/10.4018/978-1-7998-2555-5.ch005

  25. Pramanik, S., Dey, P.P., Giri, B.C., Smarandache, F.: Bipolar neutrosophic projection based models for solving multi-attribute decision making problems. Neutrosophic Sets Syst. 15, 70–79 (2017)

    Google Scholar 

  26. Pramanik, S., Dalapati, S., Alam, S., Roy, T.K.: TODIM method for group decision making under bipolar neutrosophic set environment. In: Smarandache, F., Pramanik, S. (eds.) New Trends in Neutrosophic Theory and Applications, vol. 2, pp. 140–155. Pons Editions, Brussels (2018)

    Google Scholar 

  27. Pramanik, S., Dalapati, S., Alam, S., Roy, T.K.: VIKOR based MAGDM strategy under bipolar neutrosophic set environment. Neutrosophic Sets Syst. 19, 57–69 (2018)

    Google Scholar 

  28. Fan, C., Ye, J., Fen, S., Fan, E., Hu, K.: Multi-criteria decision-making method using heronian mean operators under a bipolar neutrosophic environment. Mathematics 7, 97 (2019)

    Article  Google Scholar 

  29. Jamil, M., Abdullah, S., Yaqub Khan, M., Smarandache, F., Ghani, F.: Application of the bipolar neutrosophic hamacher averaging aggregation operators to group decision making: an illustrative example. Symmetry 11(5), 698 (2019). https://doi.org/10.3390/sym11050698

  30. Pramanik, S.: Rough neutrosophic set: an overview. In: Smarandache, F., Broumi, S. (eds.) Neutrosophic Theories in Communication, Management and Information Technology, pp. 275–311. Nova Science Publishers, New York (2020)

    Google Scholar 

  31. Pramanik, S., Mondal, K.: Rough bipolar neutrosophic set. Glob. J. Eng. Sci. Res. Manag. 3(6), 71–81 (2016)

    Google Scholar 

  32. Mondal, K., Pramanik, S., Giri, B.C.: Rough neutrosophic aggregation operators for multi-criteria decision-making. In: Kahraman, C., Otay, İ (eds.) Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. SFSC, vol. 369, pp. 79–105. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-00045-5_5

    Chapter  Google Scholar 

  33. Mondal, K., Pramanik, S.: Neutrosophic decision making of school choice. Neutrosophic Sets Syst. 7, 62–68 (2015)

    Google Scholar 

  34. Mondal, K., Pramanik, S.: Neutrosophic decision making model for clay-brick selection in construction field based on grey relational analysis. Neutrosophic Sets Syst. 9, 72–79 (2015)

    Google Scholar 

  35. Pramanik, S., Dalapati, S., Roy, T.K.: Logistics center location selection approach based on neutrosophic multicriteria decision making. In: Smarandache, F., Pramanik, S. (eds.) New Trends in Neutrosophic Theory and Application, pp. 161–174. Pons Editions, Brussels (2016)

    Google Scholar 

  36. Pramanik, S., Mukhopadhyaya, D.: Grey relational analysis based intuitionistic fuzzy multi criteria group decision-making approach for teacher selection in higher education. Int. J. Comput. Appl. 34(10), 21–29 (2011)

    Google Scholar 

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Correspondence to Surapati Pramanik .

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Pramanik, S., Das, S., Das, R., Tripathy, B.C. (2022). MADM Strategies Based on Arithmetic and Geometric Mean Operator Under Rough-Bipolar Neutrosophic Set Environment. In: Peters, J.F., Skowron, A., Bhaumik, R.N., Ramanna, S. (eds) Transactions on Rough Sets XXIII. Lecture Notes in Computer Science(), vol 13610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-66544-2_5

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  • DOI: https://doi.org/10.1007/978-3-662-66544-2_5

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