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Some Maclaurin Symmetric Mean Operators for Single-Valued Trapezoidal Neutrosophic Numbers and Their Applications to Group Decision Making

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Abstract

The Maclaurin symmetric mean (MSM) operator has a desirable property that it can capture the interrelationships among multi-input arguments and it is a generalization of some existing aggregation operators by changing the value of parameter k. The single-valued trapezoidal neutrosophic number (SVTNNs) can more conveniently depict uncertain information in the decision-making process. In order to combine the advantages of MSM operator and the SVTNNs, in this paper, we extend the MSM operator to SVTNNs. Firstly, we reviewed some basic concepts about the MSM operator and the SVTNNs and defined some single-valued trapezoidal neutrosophic MSM operators; then, we studied some properties of them and discussed some special cases of the proposed operators by changing the value of parameter k. Moreover, we developed a method to deal with multi-attributes group decision-making problem based on SVTNWMSM operator. Finally, we verified the validity and reliability of the proposed method by an illustrative example and analyzed its advantages by comparing with other existing methods.

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References

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

    Article  MATH  Google Scholar 

  2. Atanassov, K.T.: More on intuitionistic fuzzy sets. Fuzzy Sets Syst. 33, 37–46 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  3. Biswas, P., Pramanik, S., Giri, B.C.: Value and ambiguity index based ranking method of single-valued trapezoidal neutrosophic numbers and its application to multi-attribute decision making. Neutr. Sets Syst. 12, 127–138 (2016)

    Google Scholar 

  4. Chen, Z., Liu, P., Pei, Z.: An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. Int. J. Comput. Intell. Syst. 8(4), 747–760 (2015)

    Article  Google Scholar 

  5. Deli, I., Subas, Y.: Single valued neutrosophic numbers and their applications to multi-criteria decision making problem. Neutrosophic Sets Syst. 2(1), 1–13 (2014)

    Google Scholar 

  6. Deli, I., Subas, Y.: A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems. Int. J. Mach. Learn. Cybernet. (2016). doi:10.1007/s13042-016-0505-3

    Google Scholar 

  7. Ju, Y.B., Liu, X.Y., Ju, D.W.: Some new intuitionistic linguistic aggregation operators based on Maclaurin symmetric mean and their applications to multiple attribute group decision making. Soft Comput. 20(11), 4521–4548 (2016)

    Article  MATH  Google Scholar 

  8. Li, D.F., Yang, J.: A difference-index based ranking method of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute decision making. Math. Comput. Appl. 25, 25–38 (2015)

    Google Scholar 

  9. Li, W., Zhou, X., Guo, G.: Hesitant fuzzy Maclaurin symmetric mean operators and their application in multiple attribute decision making. J. Comput. Anal. Appl. 20(3), 459–469 (2016)

    MathSciNet  MATH  Google Scholar 

  10. Liang, R.X., Wang, J.Q., Lin, L.: Multi-criteria group decision-making method based on interdependent inputs of single-valued trapezoidal neutrosophic information. Neural Comput. Appl. (2016). doi:10.1007/s00521-016-2672-2

    Google Scholar 

  11. Liu, C., Luo, Y.S.: Correlated aggregation operators for simplified neutrosophic set and their application in multi-attribute group decision making. J. Intell. Fuzzy Syst. 30(3), 1755–1761 (2016)

    Article  MATH  Google Scholar 

  12. Liu, P.D., Li, H.G.: Multiple attribute decision making method based on some normal neutrosophic Bonferroni mean operators. Neural Comput. Appl. 25(7), 1–16 (2015)

    Google Scholar 

  13. Liu, P.D., Shi, L.L.: Some neutrosophic uncertain linguistic number heronian mean operators and their application to multi-attribute group decision making. Neural Comput. Appl. 28(5), 1079–1093 (2017)

    Article  Google Scholar 

  14. Liu, P.D., Tang, G.L.: Some power generalized aggregation operators based on the interval neutrosophic numbers and their application to decision making. J. Intell. Fuzzy Syst. 30, 2517–2528 (2016)

    Article  MATH  Google Scholar 

  15. 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 

  16. Maclaurin, B.C.: A second letter to Martin Foulkes, Esq.; concerning the roots of equations with the demonstrations of other rules in algebra, pp. 59–96 (1729)

  17. Pecaric, J., Wen, J.J., Wang, W.L., Lu, T.: A generalization of Maclaurin’s inequalities and its applications. Math. Inequal. Appl. 8, 583–598 (2005)

    MathSciNet  MATH  Google Scholar 

  18. Peng, J.J., Wang, J.Q., Zhang, H.Y., Chen, X.H.: An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl. Soft Comput. 25(25), 336–346 (2015)

    Google Scholar 

  19. Qin, J., Liu, X.: Approaches to uncertain linguistic multiple attribute decision making based on dual Maclaurin symmetric mean. J. Intell. Fuzzy Syst. 29(1), 171–186 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  20. Qin, J., Liu, X., Pedrycz, W.: Hesitant fuzzy Maclaurin symmetric mean operators and its application to multiple-attribute decision making. Int. J. Fuzzy Syst. 17(4), 509–520 (2015)

    Article  MathSciNet  Google Scholar 

  21. Qin, J.D., Liu, X.W.: An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J. Intell. Fuzzy Syst. Appl. Eng. Technol. 27(5), 2177–2190 (2014)

    MathSciNet  MATH  Google Scholar 

  22. Smarandache, F.: Neutrosophic probability, set, and logic, Bull.transilv.univ.braov Ser.b, pp. 41–48 (2000)

  23. Smarandache, F.: Neutrosophic logic: generalization of the Intuitionistic fuzzy logic. Extr. Metal. Nickel Cobalt Platin. Group Metals 269(51), 49–53 (2016)

    Google Scholar 

  24. Wang, H.B., Smarandache, F., Zhang, Y.Q., Sunderraman, R.: Interval neutrosophic sets and logic: theory and applications in computing. Comput. Sci. 65(4), 87 (2005)

    MathSciNet  MATH  Google Scholar 

  25. Wang, H.B., Smarandache, F., Zhang, Y.Q., Sunderraman, R.: Single valued neutrosophic sets. Rev. Air Force Acad. 10, 33–39 (2009)

    MATH  Google Scholar 

  26. Wang, J.Q., Zhang, Z.: Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems. Syst. Eng. Electron. 20(2), 321–326 (2007)

    MathSciNet  Google Scholar 

  27. Xu, Z.S.: On consistency of the weighted geometric mean complex judgement matrix in AHP. Eur. J. Oper. Res. 126, 683–687 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  28. Ye, J.: A multi-criteria decision-making method using aggregation operators for simplified neutrosophic sets. J. Intell. Fuzzy Syst. 26(5), 2459–2466 (2014)

    MATH  Google Scholar 

  29. Ye, J.: Similarity measures between interval neutrosophic sets and their applications in multi-criteria decision-making. J. Intell. Fuzzy Syst. 26, 165–172 (2014)

    MATH  Google Scholar 

  30. Ye, J.: Some weighted aggregation operators of trapezoidal neutrosophic numbers and their multiple attribute decision making method. Neutrosophic Sets Syst. 3(1), 1–14 (2015)

    MathSciNet  Google Scholar 

  31. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–356 (1965)

    Article  MATH  Google Scholar 

  32. Zhang, H.Y., Ji, P., Wang, J.Q.: A method considering the risk preference with single valued trapezoidal neutrosophic numbers and its application to medical treatment options selection. J. Intell. Fuzzy Syst. 32, 1–33 (2016)

    Google Scholar 

Download references

Acknowledgements

This paper is supported by the National Natural Science Foundation of China (Nos. 71471172 and 71271124), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045), Shandong Provincial Social Science Planning Project (Nos. 15BGLJ06,16CGLJ31 and 16CKJJ27), the Teaching Reform Research Project of Undergraduate Colleges and Universities in Shandong Province (No. 2015Z057), and Key research and development program of Shandong Province (No. 2016GNC110016). The authors also would like to express appreciation to the anonymous reviewers and Editors for their very helpful comments that improved the paper.

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  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, Shandong, China

    Peide Liu & Xiaohong Zhang

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  1. Peide Liu
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  2. Xiaohong Zhang
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Correspondence to Peide Liu.

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Liu, P., Zhang, X. Some Maclaurin Symmetric Mean Operators for Single-Valued Trapezoidal Neutrosophic Numbers and Their Applications to Group Decision Making. Int. J. Fuzzy Syst. 20, 45–61 (2018). https://doi.org/10.1007/s40815-017-0335-9

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  • DOI: https://doi.org/10.1007/s40815-017-0335-9

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