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Cognitive Computation

, Volume 11, Issue 5, pp 735–747 | Cite as

A Novel Decision-Making Method Based on Probabilistic Linguistic Information

  • Peide LiuEmail author
  • Ying Li
Article

Abstract

The Maclaurin symmetric mean (MSM) operator has the characteristic of capturing the interrelationship among multi-input arguments, the probabilistic linguistic terms set (PLTS) can reflect the different degrees of importance or weights of all possible evaluation values, and the improved operational laws of probabilistic linguistic information (PLI) can not only avoid the operational values out of bounds for the linguistic terms set (LTS) but also keep the probability information complete after operations; hence, it is very meaningful to extend the MSM operator to PLTS based on the operational laws. To fully take advantage of the MSM operator and the improved operational laws of PLI, the MSM operator is extended to PLI. At the same time, two new aggregated operators are proposed, including the probabilistic linguistic MSM (PLMSM) operator and the weighted probabilistic linguistic MSM (WPLMSM) operator. Simultaneously, the properties and the special cases of these operators are discussed. Further, based on the proposed WPLMSM operator, a novel approach for multiple attribute decision-making (MADM) problems with PLI is proposed. With a given numerical example, the feasibility of the proposed method is proven, and a comparison with the existing methods can show the advantages of the new method in this paper. The developed method adopts the new operational rules with the accurate operations, and it can overcome some existing weaknesses and capture the interrelationship among the multi-input PLTSs, which easily express the qualitative information given by the decision-makers’ cognition.

Keywords

Probabilistic linguistic Maclaurin symmetric mean Multiple attribute decision-making 

Notes

Acknowledgments

This paper is supported by the National Natural Science Foundation of China (Nos. 71771140 and 71471172), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045), the Humanities and Social Sciences Research Project of Ministry of Education of China (No. 19YJC630023).

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

Research Involving Human Participants and/or Animals

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

References

  1. 1.
    Abu-Saris R, Hajja M. On gauss compounding of symmetric weighted arithmetic means. J Math Anal Appl. 2006;322:729–34.CrossRefGoogle Scholar
  2. 2.
    Baležentis T, Baležentis A. Group decision making procedure based on trapezoidal intuitionistic fuzzy numbers: multimoora methodology. Econom Comput Econom Cybernet. Stud Res. 2016;50(1):103–22.Google Scholar
  3. 3.
    Bapat RB. Symmetrical function means and permanents. Linear Algebra Appl. 1993;182:101–8.CrossRefGoogle Scholar
  4. 4.
    Bai CZ, Zhang R, Qian LX, Wu YN. Comparisons of probabilistic linguistic term sets for multi-criteria decision making. Knowl-Based Syst. 2016.Google Scholar
  5. 5.
    Cuttler A, Greene C, Skandera M. Inequalities for symmetric means. Eur J Comb. 2011;32:745–61.CrossRefGoogle Scholar
  6. 6.
    Detemple D, Robertson J. On generalized symmetric means of two variables. Univ Beograd Publ Elektrotehn Fak Ser Mat Fiz. 1979;677(634):236–8.Google Scholar
  7. 7.
    Dong YC, Li CC, Herrera F. An optimization-based approach to adjusting unbalanced linguistic preference relations to obtain a required consistency level. Inf Sci. 2015;292:27–38.CrossRefGoogle Scholar
  8. 8.
    Gao P. On a conjecture on the symmetric means. J Math Anal Appl. 2008;337:416–24.CrossRefGoogle Scholar
  9. 9.
    Gou X, Xu Z. Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Inf Sci. 2016;372:407–27.CrossRefGoogle Scholar
  10. 10.
    Gou X, Xu Z, Liao H, Multiple criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information, Soft Comput (2016) 1–15.Google Scholar
  11. 11.
    He YD, He Z, Chen HY. Intuitionistic fuzzy interaction Bonferroni means and its application to multiple attribute decision making. IEEE Trans Cybernet. 2015;45:116–28.CrossRefGoogle Scholar
  12. 12.
    He YD, He Z. Extensions of Atanassov’s intuitionistic fuzzy interaction Bonferroni means and their application to multiple attribute decision making. IEEE Trans Fuzzy Syst. 2016;24(3):558–73.CrossRefGoogle Scholar
  13. 13.
    He YD, He Z, Lee D-H, Kim K-J, Zhang L, Yang X. Robust fuzzy programming method for MRO problems considering location effect, dispersion effect and model uncertainty. Comput Ind Eng. 2017;105:76–83.CrossRefGoogle Scholar
  14. 14.
    Liu PD. Some geometric aggregation operators based intervalvalued intuitionistic uncertain linguistic variables and their application to group decision making. Appl Math Model. 2013;37:2430–44.CrossRefGoogle Scholar
  15. 15.
    Liu P. Special issue: intuitionistic fuzzy theory and its application in economy, technology and management. Technol Econ Dev Econ. 2016;22(3):327–35.CrossRefGoogle Scholar
  16. 16.
    Liu PD. Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators. Comput Ind Eng. 2017;108:199–212.CrossRefGoogle Scholar
  17. 17.
    Liu P, Li Y, Antuchevičienė J. Multi-criteria decision-making method based on intuitionistic trapezoidal fuzzy prioritised OWA operator. Technol Econ Dev Econ. 2016;22(3):453–69.CrossRefGoogle Scholar
  18. 18.
    Liu PD, Chen SM, Liu JL. Some intuitionistic fuzzy interaction partitioned Bonferroni mean operators and their application to multi-attribute group decision making. Inf Sci. 2017;411:98–121.CrossRefGoogle Scholar
  19. 19.
    Liu PD, Jin F. Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making. Inf Sci. 2012;205:58–71.CrossRefGoogle Scholar
  20. 20.
    Liu PD, Li HG. Interval-valued intuitionistic fuzzy power Bonferroni aggregation operators and their application to group decision making. Cogn Comput. 2017;9(4):494–512.CrossRefGoogle Scholar
  21. 21.
    Liu PD, Liu ZM, Zhang X. Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making. Appl Math Comput. 2014;230:570–86.Google Scholar
  22. 22.
    Liu PD, Shi LL. Some neutrosophic uncertain linguistic number Heronian mean operators and their application to multi-attribute group decision making. Neural Comput & Applic. 2017;28(5):1079–93.CrossRefGoogle Scholar
  23. 23.
    Liu PD, Tang GL. Multi-criteria group decision-making based on interval neutrosophic uncertain linguistic variables and Choquet integral. Cogn Comput. 2016;8(6):1036–56.CrossRefGoogle Scholar
  24. 24.
    Maclaurin C. A second letter to Martin Folkes, Esq.; concerning the roots of equations, with demonstration of other rules of algebra. Philos Trans R Soc Lond. 1729;36:59–96.Google Scholar
  25. 25.
    Merigó JM. Decision-making under risk and uncertainty and its application in strategic management. J Bus Econ Manag. 2015;16(1):93–116.CrossRefGoogle Scholar
  26. 26.
    Pang Q, Xu ZS, Wang H. Probabilistic linguistic term sets in multi-attribute group decision making. Inf Sci. 2016;369:128–43.CrossRefGoogle Scholar
  27. 27.
    Peng JJ, Wang JQ, Wu XH. Novel multi-criteria decision-making approaches based on hesitant fuzzy sets and prospect theory. Int J Inf Technol Decis Mak. 2016;15(3):621–43.CrossRefGoogle Scholar
  28. 28.
    Qin JD, Liu XW. An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J Intell Fuzzy Syst. 2014;27(5):2177–90.Google Scholar
  29. 29.
    Rodriguez RM, Martinez L, Herrera F. Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst. 2012;20:109–19.CrossRefGoogle Scholar
  30. 30.
    Rong LL, Liu PD, Chu Y. Multiple attribute group decision making methods based on intuitionistic fuzzy generalized hamacher aggregation operator. Econom Comput Econom Cybernet Stud Res. 2016;50(2):211–30.Google Scholar
  31. 31.
    Stanujkic D, Zavadskas EK, Brauers WKM. An extension of the MULTIMOORA method for solving complex decision-making problems based on the use of interval-valued triangular fuzzy numbers. Transform Bus Econ. 2015;14(2B):355–77.Google Scholar
  32. 32.
    Wang JQ, Li JJ. The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Sci Technol Inform. 2009;33:8–9.Google Scholar
  33. 33.
    Wang JQ, Yang Y, Li L. Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators. Neural Comput & Applic. 2018;30(5):1529–47 (4)2016 1–19.CrossRefGoogle Scholar
  34. 34.
    Wu J, Chiclana F, Herrera-Viedma E. Trust based consensus model for social network in an incomplete linguistic information context. Appl Soft Comput. 2015;35:827–39.CrossRefGoogle Scholar
  35. 35.
    Xu ZS. Deviation measures of linguistic preference relations in group decision making. Omega. 2005;33:249–54.CrossRefGoogle Scholar
  36. 36.
    Xu ZS. Linguistic decision making: theory and methods. Berlin, Heidelberg: Springer-Verlag; 2012.CrossRefGoogle Scholar
  37. 37.
    Xu ZS, Yager RR. Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst Man and Cybernet Part B: Cybernet. 2011;41(2):568–78.CrossRefGoogle Scholar
  38. 38.
    Yu DJ, Wu YY. Interval-valued intuitionistic fuzzy Heronian mean operators and their application in multi-criteria decision making. Afr J Bus Manag. 2012;6(11):4158–68.Google Scholar
  39. 39.
    Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning—I. Inf Sci. 1975;8:199–249.CrossRefGoogle Scholar
  40. 40.
    Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning—II. Inf Sci. 1975;8:301–57.CrossRefGoogle Scholar
  41. 41.
    Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning—III. Inf Sci. 1975;9:43–80.CrossRefGoogle Scholar
  42. 42.
    Zavadskas EK, Antucheviciene J, Hajiagha SHR. Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF). Appl Soft Comput. 2014;24:1013–21.CrossRefGoogle Scholar
  43. 43.
    Zeng S, Su W, Zhang C. Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making. Technol Econ Dev Econ. 2016;22(2):177–93.CrossRefGoogle Scholar
  44. 44.
    Zhang XL, Xing XM. Probabilistic linguistic VIKOR method to evaluate green supply chain initiatives. Sustainability. 2017;9(7):1231.CrossRefGoogle Scholar
  45. 45.
    Zhang XM, Haining Z. S-geometric convexity of a function involving Maclaurin’s elementary symmetric mean. J Inequal Pure Appl Math. 2007;8:156–65.Google Scholar
  46. 46.
    Zhang YX, Xu ZS, Wang H, Liao HC. Consistency-based risk assessment with probabilistic linguistic preference relation. Appl Soft Comput J. 2016;49:817–33.CrossRefGoogle Scholar
  47. 47.
    Zhang ZH, Xiao ZG, Srivastava HM. A general family of weighted elementary symmetric means. Appl Math Lett. 2009;22:24–30.CrossRefGoogle Scholar
  48. 48.
    Zhu B, Xu ZS. Extended hesitant fuzzy sets. Technol Econ Dev Econ. 2016;22(1):1–22.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Management Science and EngineeringShandong University of Finance and EconomicsJinanChina

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