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A novel approach to multi-criteria group decision-making problems based on linguistic D numbers

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Abstract

The theory of D numbers (DNs) is an extension of Dempster–Shafer (D–S) evidence theory. Linguistic DNs (LDNs) combine the advantages of the linguistic terms (LTs) and DNs, and can express the uncertain and incomplete information more easily and precisely in decision-making. In addition, the Bonferroni mean (BM) operator and the TOPSIS method are both useful tools to address multiple-attribute group decision-making (MAGDM) problems. Then, in this paper, we extend the BM operator based on the new defined operational rules of LDNs to propose the linguistic D number arithmetic Bonferroni mean (LDABM) operator and the linguistic D number weighted arithmetic Bonferroni mean (LDWABM) operator. We also integrate the proposed LDWABM operator and the TOPSIS method, and further establish a novel method to address MAGDM problems. Finally, we use the proposed method to solve the practical problems of investment decision-making and materials supplier selection and then we prove the feasibility and the superiority of the proposed method by comparing with other methods.

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References

  • Bhatt D, Babu SR, Chudgar HS (2017) A novel approach towards utilizing Dempster Shafer fusion theory to enhance WiFi positioning system accuracy. Pervasive Mob Comput 37:115–123

    Google Scholar 

  • Bonferroni C (1950) Sulle medie multiple di potenze. Bolletino Matematica Italiana 5:267–270

    MathSciNet  MATH  Google Scholar 

  • Dempster AP (1967) Upper and lower probabilities induced by a multi-valued mapping. Ann Math Stat 38(2):325–339

    MATH  Google Scholar 

  • Deng Y (2012) D numbers: theory and applications. J Inf Comput Sci 9(9):2421–2428

    Google Scholar 

  • Deng X, Deng Y (2019) D-AHP method with different credibility of information. Soft Comput 23(2):683–691

    Google Scholar 

  • Dutta B, Guha D (2015) Partitioned Bonferroni mean based on linguistic 2-tuple for dealing with multi-attribute group decision making. Appl Soft Comput 37:166–179

    Google Scholar 

  • Fan GC, Zhong DH, Yan FG, Yue P (2016) A hybrid fuzzy evaluation method for curtain grouting efficiency assessment based on an AHP method extended by D numbers. Expert Syst Appl 44:289–303

    Google Scholar 

  • Fei L, Hu Y, Xiao F, Chen L, Deng Y (2016) A modified TOPSIS method based on D numbers and its application in human resource selection. Math Probl Eng 3:1–14

    MathSciNet  MATH  Google Scholar 

  • Han X, Chen X (2014) A D-VIKOR method for medicine provider selection. International Joint Conference on Computational Sciences and Optimization, pp 419–423, Beijing. https://doi.org/10.1109/CSO.2014.87

  • Huang SK (2015) Multi-criteria decision making method based on prioritized weighted average operator with linguistic D numbers. J Jiamusi Univ (Natural Science Edition) 33(3):464–469

    Google Scholar 

  • Hwang CL, Yoon KS (1981) Multiple attribute decision methods and applications. Springer, Berlin

    MATH  Google Scholar 

  • Jafari H, Li X, Qian L, Aved A, Kroecker T (2017) Multi-sensor change detection on the basis of big time-series data and Dempster–Shafer theory. Concurr Comput Pract Exp 29(17):e4026

    Google Scholar 

  • Jiao Z, Gong H, Wang Y (2018) A D–S evidence theory-based relay protection system hidden failures detection method in smart grid. IEEE Trans Smart Grid 9(3):2118–2126

    Google Scholar 

  • Jousselme AL, Grenier D, Bosse E (2001) A new distance between two bodies of evidence. Inf Fusion 2(2):91–101

    Google Scholar 

  • Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47(2):263–291

    MathSciNet  MATH  Google Scholar 

  • Leung Y, Li R, Ji N (2017) Application of extended Dempster–Shafer theory of evidence in accident probability estimation for dangerous goods transportation. J Geogr Syst 19(3):249–271

    Google Scholar 

  • Li Z, Wen G, Xie N (2015) An approach to fuzzy soft sets in decision making based on grey relational analysis and Dempster–Shafer theory of evidence: an application in medical diagnosis. Artif Intell Med 64(3):161–171

    Google Scholar 

  • Li M, Hu Y, Zhang Q, Deng Y (2016a) A novel distance function of D numbers and its application in product engineering. Eng Appl Artif Intell 47:61–67

    Google Scholar 

  • Li XH, Wang FQ, Li XZ (2016b) Intuitionistic trapezoidal fuzzy IOWA operator based on Dempster–Shafer theory and its application. Syst Eng-Theory Pract 36(11):2915–2923

    Google Scholar 

  • Liang D, Xu Z (2017) The new extension of TOPSIS method for multiple criteria decision making with hesitant pythagorean fuzzy sets. Appl Soft Comput 60:167–179

    Google Scholar 

  • Liang D, Xu Z, Darko AP (2017) Projection model for fusing the information of pythagorean fuzzy multi-criteria group decision making based on geometric Bonferroni mean. Int J Intell Syst 32(9):966–987

    Google Scholar 

  • Liu P, Gao H (2019) Some intuitionistic fuzzy power bonferroni mean operators in the framework of Dempster–Shafer theory and their application to multicriteria decision making. Appl Soft Comput 85:105790

    Google Scholar 

  • Liu P, Li H (2017) Multiple attribute decision making method based on some normal neutrosophic Bonferroni mean operators. Neural Comput Appl 28(1):179–194

    Google Scholar 

  • Liu P, Liu J (2019a) Partitioned Bonferroni mean based on two-dimensional uncertain linguistic variables for multiattribute group decision making. Int J Intell Syst 34(2):155–187

    Google Scholar 

  • Liu P, Liu W (2019b) Multiple-attribute group decision-making based on power Bonferroni operators of linguistic q-rung orthopair fuzzy numbers. Int J Intell Syst 34(4):652–689

    Google Scholar 

  • Liu P, Wang P (2019) Multiple-attribute decision-making based on Archimedean Bonferroni operators of q-Rung orthopair fuzzy numbers. IEEE Trans Fuzzy Syst 27(5):834–848

    Google Scholar 

  • Liu P, Zhang X (2019) A multicriteria decision-making approach with linguistic D numbers based on the Choquet integral. Cogn Comput 11(4):560–575

    Google Scholar 

  • Liu P, Chen SM, Liu J (2017) Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators. Inf Sci 411:98–121

    MathSciNet  MATH  Google Scholar 

  • Liu P, Gao H, Ma J (2019) Novel green supplier selection method by combining quality function deployment with partitioned Bonferroni mean operator in interval type-2 fuzzy environment. Inf Sci 490:292–316

    Google Scholar 

  • Sahin A, Yapici PN (2017) Evaluation of life quality by integrated method of AHP and TOPSIS based on interval type-2 fuzzy sets. Hacettepe J Math Stat 46(3):511–523

    MATH  Google Scholar 

  • Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Wang CY, Chen SM (2017) Multiple attribute decision making based on interval-valued intuitionistic fuzzy sets, linear programming methodology, and the extended TOPSIS method. Inf Sci 397:155–167

    Google Scholar 

  • Wang J, Huang S (2016) Multi-criteria decision making method based on fuzzy entropy and evidential reasoning with linguistic D numbers. Control Decis 31(4):673–677

    MATH  Google Scholar 

  • Wang N, Wei D (2016) Uncertain multi-attribute decision making method based on D numbers. J Hubei Univ Natl 34(1):35–39

    MathSciNet  Google Scholar 

  • Wang J, Wu J, Zhang H, Chen X (2016a) Multi-criteria decision-making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers. Soft Comput 20(4):1621–1633

    Google Scholar 

  • Wang NK, Liu XM, Wei DJ (2016b) A modified combination rule for D numbers theory. Math Probl Eng 2:1–10

    MathSciNet  MATH  Google Scholar 

  • Wang NK, Liu XM, Wei DJ (2018) A modified D numbers’ integration for multiple attributes decision making. Int J Fuzzy Syst 20(5):104–115

    MathSciNet  Google Scholar 

  • Wei G (2016) Picture 2-Tuple linguistic Bonferroni mean operators and their application to multiple attribute decision making. Int J Fuzzy Syst 19(4):201–214

    MathSciNet  Google Scholar 

  • Xia J, Feng Y, Liu L et al (2019) On entropy function and reliability indicator for D numbers. Appl Intell 49(4):3248–3266

    Google Scholar 

  • Xiao F (2019) A multiple-criteria decision-making method based on D numbers and belief entropy. Int J Fuzzy Syst 21(4):1144–1153

    MathSciNet  Google Scholar 

  • Yager RR (2009) On generalized Bonferroni mean operators for multi-criteria aggregation. Int J Approx Reason 50:1279–1286

    MathSciNet  MATH  Google Scholar 

  • Yan JL (2015) Emergency Materials supplier evaluation method research based on D number and LINMAP, Dissertation, Beijing Institute of Technology

  • Yang C, Pu J, Deng Y, Liu Z, Liang L (2017) Salient object detection in complex scenes via D-S evidence theory based region classification. Vis Comput 33(11):1415–1428

    Google Scholar 

  • Zhu B, Xu Z, Xia M (2010) Hesitant fuzzy geometric Bonferroni means. Inf Sci 205(1):72–85

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This paper is supported by the National Natural Science Foundation of China (No. 71771140), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045), and Major bidding projects of National Social Science Fund of China (19ZDA080), (Project of cultural masters and “the four kinds of a batch” talents).

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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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We declare that we do have no commercial or associative interests that represent a conflict of interests in connection with this manuscript. There are no professional or other personal interest that can inappropriately influence our submitted work.

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Communicated by Rosana Sueli da Motta Jafelice.

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Liu, P., Zhang, X. A novel approach to multi-criteria group decision-making problems based on linguistic D numbers. Comp. Appl. Math. 39, 132 (2020). https://doi.org/10.1007/s40314-020-1132-x

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