Advertisement

A Multicriteria Decision-Making Approach with Linguistic D Numbers Based on the Choquet Integral

  • Peide LiuEmail author
  • Xiaohong Zhang
Article
  • 36 Downloads

Abstract

Linguistic D numbers (LDNs) provide a reliable expression of cognitive information. By inheriting the advantages of linguistic terms (LTs) and D numbers (DNs), LDNs can express uncertain and incomplete cognitive information in multicriteria decision-making (MCDM), and they do so better than existing methods. The TODIM (an acronym in Portuguese of interactive and multicriteria decision-making) method can consider decision experts’ (DEs’) bounded rationality, such as cognition toward loss, which is caused by the DEs’ cognitive limitations during the decision process. Additionally, the Choquet integral can process the interrelationship among criteria or cognitive preferences, which helps to reflect the complex cognition of DEs. Therefore, it is necessary to propose a novel cognitive MCDM approach by extending the TODIM method and Choquet integral to handle MCDM problems in which the cognitive information is expressed by LDNs. In this paper, we introduced LDNs to represent uncertain and hesitant cognitive information. The definition and comparison approach of LDNs were also recommended. Then, we proposed the distance function and modified the score function of LDNs. Later, considering the limitations of the DEs’ cognitive abilities in real decision-making and the phenomenon where attributes or cognitive preferences in MCDM problems are not independent, we developed a novel cognitive MCDM approach with LDNs by extending the TODIM method and the Choquet integral to deal with these cases. The proposed approach can not only take the influence of the limited cognitive abilities of DEs on the decision-making results into account but can also deal with the correlation between the cognitive preferences. A novel cognitive MCDM approach with LDNs based on the TODIM method and Choquet integral was proposed. Moreover, the validity and superiority of the presented approach were verified by dealing with practical problems and comparing them to other approaches. The proposed approach can consider cases where the DEs are rationally bounded in their cognitive decision-making and the criteria or cognitive preferences in MCDM problems have an interrelationship. Therefore, this approach can produce more reliable decision-making results than some existing MCDM approaches.

Keywords

Multicriteria decision-making (MCDM) Linguistic D numbers (LDNs) Choquet integral TODIM 

Notes

Funding Information

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).

Compliance with Ethical Standards

Conflicts 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.
    Atanassov KT, Rangasamy P. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986;20(1):87–96.Google Scholar
  2. 2.
    Dempster AP. Upper and lower probabilities induced by a multi-valued mapping. Ann Math Stat. 1967;38(2):325–39.Google Scholar
  3. 3.
    Deng Y, Numbers D. Theory and applications. J Inf Comput Sci. 2012;9(9):2421–8.Google Scholar
  4. 4.
    Deng XY, Wang J. Exploring the combination rules of D Numbers from a perspective of conflict redistribution, international conference on information fusion; 2017. p. 10–3.Google Scholar
  5. 5.
    Deng X, Hu Y, Deng Y, Mahadevan S. Supplier selection using AHP approachology extended by D numbers. Expert Syst Appl. 2014;41(1):156–67.Google Scholar
  6. 6.
    Fan G, Yan F, Yan F, Yue P. A hybrid fuzzy evaluation approach for curtain grouting efficiency assessment based on an AHP approach extended by D numbers. Expert Syst Appl. 2016;44:289–303.Google Scholar
  7. 7.
    Farhadinia B. A multiple criteria decision making model with entropy weight in an interval-transformed hesitant fuzzy environment. Cogn Comput. 2017;9(4):513–25.Google Scholar
  8. 8.
    Gomes L, Lima M. TODIM: basics and application to multicriteria ranking of projects with environmental impacts. Found Comput Decision Sci. 1992;16(4):113–27.Google Scholar
  9. 9.
    Grabisc M, Nguyen HT, Walker EA. Fuzzy measures and integrals. Netherlands: Springer; 1995. p. 563–604.Google Scholar
  10. 10.
    Han X, Chen X. A D-VIKOR approach for medicine provider selection, computational sciences and optimization 2014 seventh international joint conference on: IEEE; 2014. p. 419–23.Google Scholar
  11. 11.
    He Y, 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.Google Scholar
  12. 12.
    He Y, He Z, Chen H. Intuitionistic fuzzy interaction Bonferroni means and its application to multiple attribute decision making. IEEE Trans Cybern. 2015;45:116–28.Google Scholar
  13. 13.
    Herrera F, Herrera-Viedma E, Verdegay JL. A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst. 1996;79(1):73–87.Google Scholar
  14. 14.
    Huang SK. Multi-criteria decision making approach based on prioritized weighted average operator with linguistic D numbers. J Jiamusi Univ. 2015;33(3):464–9.Google Scholar
  15. 15.
    Kahneman D, Tversky A. Prospect theory: an analysis of decision under risk. Econometrica. 1979;47(2):263–91.Google Scholar
  16. 16.
    Kakati P, Borkotokey S, Mesiar R, et al. Interval neutrosophic hesitant fuzzy Choquet integral in multicriteria decision making. J Intell Fuzzy Syst (Preprint):1–19.Google Scholar
  17. 17.
    Li X, Chen X. D-intuitionistic hesitant fuzzy sets and their application in multiple attribute decision making. Cogn Comput. 2018;10(3):496–505.Google Scholar
  18. 18.
    Li M, Hu Y, Zhang Q, Deng Y. A novel distance function of D numbers and its application in product engineering. Eng Appl Artif Intell. 2016;47:61–7.Google Scholar
  19. 19.
    Liu P, Li H. Interval-valued intuitionistic fuzzy power Bonferroni aggregation operators and their application to group decision making. Cogn Comput. 2017;9(4):494–512.Google Scholar
  20. 20.
    Liu P, Tang G. Multi-criteria group decision-making based on interval neutrosophic uncertain linguistic variables and Choquet integral. Cogn Comput. 2016;8(6):1036–56.Google Scholar
  21. 21.
    Liu P, Teng F. An extended TODIM approach for multiple attribute group decision-making based on 2-dimension uncertain linguistic variable. Complexity. 2016;21(5):20–30.Google Scholar
  22. 22.
    Liu P, Zhang X. A novel picture fuzzy linguistic aggregation operator and its application to group decision making. Cogn Comput. 2018;10(2):242–59.Google Scholar
  23. 23.
    Lourenzutti R, Krohling RA, Reformat MZ. Choquet based TOPSIS and TODIM for dynamic and heterogeneous decision making with criteria interaction. Inf Sci. 2017;408:41–69.Google Scholar
  24. 24.
    Peng HG, Wang JQ. Hesitant uncertain linguistic Z -numbers and their application in multi-criteria group decision-making problems. Int J Fuzzy Syst. 2017;19(5):1300–16.Google Scholar
  25. 25.
    Peng XD, Yang Y. Pythagorean fuzzy Choquet integral based MABAC approach for multiple attribute group decision making. Int J Intell Syst. 2016;31(10):989–1020.Google Scholar
  26. 26.
    Peng XD, Yang Y. Algorithms for interval-valued fuzzy soft sets in stochastic multi- criteria decision making based on regret theory and prospect theory with combined weight. Appl Soft Comput. 2017;54:415–30.Google Scholar
  27. 27.
    Simon HA. Administrative behavior-a study of decision making processes in administrative organization. New York: Macmillan Publishing Co, lnc; 1971.Google Scholar
  28. 28.
    Sirbiladze G, Badagadze O. Intuitionistic fuzzy probabilistic aggregation operators based on the choquet integral: application in multicriteria decision-making. Int J Inf Technol Decis Mak. 2017;16(01):245–79.Google Scholar
  29. 29.
    Sun LJ, Liu YY, Zhang BY, Shang YW, Yuan HW, Ma Z. An integrated decision-making model for transformer condition assessment using game theory and modified evidence combination extended by D numbers. Energies. 2016;9(9):697.  https://doi.org/10.3390/en9090697.Google Scholar
  30. 30.
    Tan CQ, Jiang ZZ, Chen X. An extended TODIM approach for hesitant fuzzy interactive multi-criteria decision making based on generalized Choquet integral. J Intell Fuzzy Syst. 2015;29(1):293–305.Google Scholar
  31. 31.
    Tao Z, Han B, Chen H. On intuitionistic fuzzy copula aggregation operators in multiple- attribute decision making. Cogn Comput. 2018;10:1–15.  https://doi.org/10.1007/s12559-018-9545-1.Google Scholar
  32. 32.
    Wang X. Approach for multiple attribute decision-making with interval grey number based on Choquet integral. J Intell Fuzzy Syst. 2017;32(6):4205–11.Google Scholar
  33. 33.
    Wang JQ, Huang SK. Multi-criteria decision-making approach based on fuzzy entropy and evidential reasoning with linguistic D numbers. Control Decision. 2016;31(4):673–7.Google Scholar
  34. 34.
    Wang NK, Wei DJ. A modified D numbers approachology for environmental impact assessment. Technol Econ Dev Econ. 2018;24(2):653–69.Google Scholar
  35. 35.
    Wang NK, Wei DJ, Science SO. Uncertain multi-attribute decision making approach based on D numbers. Journal of Hubei University for Nationalities. 2016;34(1):35–9.Google Scholar
  36. 36.
    Wang JQ, Cao YX, Zhang HY. Multi-criteria decision-making approach based on distance measure and Choquet integral for linguistic Z-numbers. Cogn Comput. 2017;9(6):827–42.Google Scholar
  37. 37.
    Wang NK, Liu XM, Wei DJ. A modified D numbers’ integration for multiple attributes decision making. Int J Fuzzy Syst. 2018;20(1):104–15.Google Scholar
  38. 38.
    Xiao F. An intelligent complex event processing with D numbers under fuzzy environment. Math Probl Eng. 2016;2016:1–10.Google Scholar
  39. 39.
    Ye J. Multiple attribute decision-making approaches based on the expected value and the similarity measure of hesitant neutrosophic linguistic numbers. Cogn Comput. 2018;10(3):454–63.Google Scholar
  40. 40.
    Zhang MC, Liu P, Shi L. An extended multiple attribute group decision-making TODIM approach based on the neutrosophic numbers. J Intell Fuzzy Syst. 2016;30(3):1773–81.Google Scholar
  41. 41.
    Zhou X, Deng X, Deng Y, Mahadevan S. Dependence assessment in human reliability analysis based on D numbers and AHP. Nucl Eng Des. 2017;313:243–52.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

Personalised recommendations