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A New MADA Methodology Based on D Numbers

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Abstract

Multiple attribute decision analysis (MADA) is still a hot issue. In order to represent information of attribute more flexibly and intuitively, quantitative and qualitative data are involved in real-world applications. In this paper, a new methodology to deal with MADA problem based on D numbers is proposed. Different with other existing methods, the new proposed method is more simply and straightforward, due to the integration property of D numbers. A numerical example of car assessment is used to demonstrate the effectiveness of proposed method.

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References

  1. Rikhtegar, N., Mansouri, N., Ahadi Oroumieh, A., Yazdani-Chamzini, A., Kazimieras Zavadskas, E.,  Kildienė, S.: Environmental impact assessment based on group decision-making methods in mining projects, Economic Research-Ekonomska Istraživanja 27 (2014) 378–392

    Article  Google Scholar 

  2. Wei, G.: Picture 2-tuple linguistic bonferroni mean operators and their application to multiple attribute decision making. Int. J. Fuzzy Syst. 19, 997–1010 (2017)

    Article  MathSciNet  Google Scholar 

  3. Yuan, J., Li, C.: A new method for multi-attribute decision making with intuitionistic trapezoidal fuzzy random variable. Int. J. Fuzzy Syst. 19, 15–26 (2017)

    Article  MathSciNet  Google Scholar 

  4. Zavadskas, E.K., Podvezko, V.: Integrated determination of objective criteria weights in MCDM. Int. J. Inf. Technol. Decis. Mak. 15, 267–283 (2016)

    Article  Google Scholar 

  5. Merigó, J.M., Casanovas, M.: Decision-making with distance measures and induced aggregation operators. Comput. Ind. Eng. 60, 66–76 (2011)

    Article  Google Scholar 

  6. Xiao, F.: A hybrid fuzzy soft sets decision making method in medical diagnosis. IEEE Access (2018). https://doi.org/10.1109/ACCESS.2018.2820099

    Article  Google Scholar 

  7. Liu, H., You, J., You, X., Shan, M.: A novel approach for failure mode and effects analysis using combination weighting and fuzzy VIKOR method. Appl. Soft Comput. 28, 579–588 (2015)

    Article  Google Scholar 

  8. Bian, T., Zheng, H., Yin, L., Deng, Y.: Failure mode and effects analysis based on D numbers and TOPSIS. Qual. Reliab. Eng. Int. 34, 501–515 (2018)

    Article  Google Scholar 

  9. Büyüközkan, G., Güleryüz, S.: Multi criteria group decision making approach for smart phone selection using intuitionistic fuzzy TOPSIS. Int. J. Comput. Intell. Syst. 9, 709–725 (2016)

    Article  Google Scholar 

  10. Tsai, S.-B., Chien, M.-F., Xue, Y., Li, L., Jiang, X., Chen, Q., Zhou, J., Wang, L.: Using the fuzzy DEMATEL to determine environmental performance: a case of printed circuit board industry in Taiwan. PLoS ONE 10, e0129153 (2015)

    Article  Google Scholar 

  11. Han, Y., Deng, Y.: A hybrid intelligent model for assessment of critical success factors in high risk emergency system. J. Ambient Intell. Humaniz. Comput. (2018). https://doi.org/10.1007/s12652-018-0882-4

    Article  Google Scholar 

  12. Liu, T., Deng, Y., Chan, F.: Evidential supplier selection based on DEMATEL and game theory. Int. J. Fuzzy Syst. 20, 1321–1333 (2018)

    Article  Google Scholar 

  13. Zhou, X., Hu, Y., Deng, Y., Chan, F.T.S., Ishizaka, A.: A DEMATEL-based completion method for incomplete pairwise comparison matrix in AHP. Ann. Oper. Res. (2018). https://doi.org/10.1007/s10479-018-2769-3

    Article  Google Scholar 

  14. Bausys, R., Zavadskas, E.K., Kaklauskas, A.: Application of neutrosophic set to multicriteria decision making by COPRAS. Econ. Comput. Econ. Cybern. Stud. Res. 49, 91–105 (2015)

    Google Scholar 

  15. Ghorabaee, M.K., Amiri, M., Sadaghiani, J.S., Zavadskas, E.K.: Multi-criteria project selection using an extended VIKOR method with interval type-2 fuzzy sets. Int. J. Inf. Technol. Decis. Mak. 14, 993–1016 (2015)

    Article  Google Scholar 

  16. Fu, C., Xu, D.L., Xue, M.: Determining attribute weights for multiple attribute decision analysis with discriminating power in belief distributions. Knowl.-Based Syst. 143, 127–141 (2018)

    Article  Google Scholar 

  17. Fu, C., Xu, D.L.: Determining attribute weights to improve solution reliability and its application to selecting leading industries. Ann. Oper. Res. 245, 401–426 (2014)

    Article  MathSciNet  Google Scholar 

  18. Ghorabaee, M.K., Zavadskas, E.K., Amiri, M., Turskis, Z.: Extended EDAS method for fuzzy multi-criteria decision-making: an application to supplier selection. Int. J. Comput. Commun. Control 11, 358–371 (2016)

    Article  Google Scholar 

  19. Fu, C., Xu, D.L., Yang, S.L.: Distributed preference relations for multiple attribute decision analysis. J. Oper. Res. Soc. 67, 457–473 (2016)

    Article  Google Scholar 

  20. Hashemkhani Zolfani, S., Maknoon, R., Zavadskas, E.K.: An introduction to prospective multiple attribute decision making (PMADM). Technol. Econ. Dev. Econ. 22, 309–326 (2016)

    Article  Google Scholar 

  21. Zafar, F., Akram, M.: A novel decision-making method based on rough fuzzy information. Int. J. Fuzzy Syst. 20, 1–15 (2017)

    MathSciNet  Google Scholar 

  22. Jiang, W., Wei, B., Liu, X., Li, X., Zheng, H.: Intuitionistic fuzzy power aggregation operator based on entropy and its application in decision making. Int. J. Intell. Syst. 33, 49–67 (2018)

    Article  Google Scholar 

  23. Jiang, W., Wei, B.: Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making. Int. J. Syst. Sci. 49, 582–594 (2018)

    Article  MathSciNet  Google Scholar 

  24. Zavadskas, E.K., Kalibatas, D., Kalibatiene, D.: A multi-attribute assessment using WASPAS for choosing an optimal indoor environment. Arch. Civil Mech. Eng. 16, 76–85 (2016)

    Article  Google Scholar 

  25. Song, M., Jiang, W.,  Xie, C.,  Zhou, D.: A new interval numbers power average operator in multiple attribute decision making, Int. J. Intell. Syst. (2017) Published online, https://doi.org/10.1002/int.21861

    Article  Google Scholar 

  26. Bian, T., Deng, Y.: Identifying influential nodes in complex networks: a node information dimension approach. Chaos 28, 043109 (2018)

    Article  MathSciNet  Google Scholar 

  27. Kang, B., Chhipi-Shrestha, G., Deng, Y., Hewage, K., Sadiq, R.: Stable strategies analysis based on the utility of Z-number in the evolutionary games. Appl. Math. Comput. 324, 202–217 (2018)

    MathSciNet  Google Scholar 

  28. Zhang, Q., Li, M., Deng, Y.: Measure the structure similarity of nodes in complex networks based on relative entropy. Physica A 491, 749–763 (2018)

    Article  MathSciNet  Google Scholar 

  29. Yang, J.-B.,  Sen, P.: Evidential reasoning based hierarchical analysis for design selection of ship retro-fit options, in: Artificial Intelligence in Design, Springer, pp. 327–344

  30. Yang, J.-B., Xu, D.-L.: Evidential reasoning rule for evidence combination. Artif. Intell. 205, 1–29 (2013)

    Article  MathSciNet  Google Scholar 

  31. Fu, C., Yang, J.B., Yang, S.L.: A group evidential reasoning approach based on expert reliability. Eur. J. Oper. Res. 246, 886–893 (2015)

    Article  MathSciNet  Google Scholar 

  32. Dempster, A. P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38, 325–339 (1967)

    Article  MathSciNet  Google Scholar 

  33. Shafer, G.: A Mathematical Theory of Evidence, vol. 1. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  34. Yang, J.-B., Wang, Y., Xu, D., Chin, K.: The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties. Eur. J. Oper. Res. 171, 309–343 (2006)

    Article  MathSciNet  Google Scholar 

  35. Liu, Z., Pan, Q., Dezert, J.: A belief classification rule for imprecise data. Appl. Intell. 40, 214–228 (2014)

    Article  Google Scholar 

  36. Liu, H., Liu, L., Lin, Q.: Fuzzy failure mode and effects analysis using fuzzy evidential reasoning and belief rule-based methodology. IEEE Trans. Reliab. 62, 23–36 (2013b)

    Article  Google Scholar 

  37. Liu, Z., Pan, Q., Dezert, J., Mercier, G.: Credal C-means clustering method based on belief functions. Knowl.-Based Syst. 74, 119–132 (2015)

    Article  Google Scholar 

  38. Xiao, F.: Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy. Information Fusion (2018). https://doi.org/10.1016/j.inffus.2018.04.003

    Article  Google Scholar 

  39. Mo, H., Gao, C., Deng, Y.: Evidential method to identify influential nodes in complex networks. J. Syst. Eng. Electron. 26, 381–387 (2015)

    Article  Google Scholar 

  40. Song, M., Jiang, W.: Engine fault diagnosis based on sensor data fusion using evidence theory. Adv. Mech. Eng. 8, 1–9 (2016)

    Google Scholar 

  41. Xiao, F.: A novel evidence theory and fuzzy preference approach-based multi-sensor data fusion technique for fault diagnosis. Sensors 17, 2504 (2017)

    Article  Google Scholar 

  42. Zheng, X., Deng, Y.: Dependence assessment in human reliability analysis based on evidence credibility decay model and iowa operator. Ann. Nucl. Energy 112, 673–684 (2018)

    Article  Google Scholar 

  43. Deng, X., Jiang, W.: Dependence assessment in human reliability analysis using an evidential network approach extended by belief rules and uncertainty measures. Ann. Nucl. Energy 117, 183–193 (2018a)

    Article  Google Scholar 

  44. Deng, X., Jiang, W.: An evidential axiomatic design approach for decision making using the evaluation of belief structure satisfaction to uncertain target values. Int. J. Intell. Syst. 33, 15–32 (2018b)

    Article  Google Scholar 

  45. Deng, W., Lu, X., Deng, Y.: Evidential Model Validation under Epistemic Uncertainty. Math. Probl. Eng. 2018, 6789635 (2018)

    MathSciNet  Google Scholar 

  46. Xiao, F.: An improved method for combining conflicting evidences based on the similarity measure and belief function entropy. Int. J. Fuzzy Syst. (2017). https://doi.org/10.1007/s40815-017-0436-5

    Article  Google Scholar 

  47. Zheng, H., Deng, Y.: Evaluation method based on fuzzy relations between dempster-shafer belief structure. Int. J. Intell. Syst. 33, 1343–1363 (2018)

    Article  Google Scholar 

  48. Xu, H., Deng, Y.: Dependent evidence combination based on shearman coefficient and pearson coefficient. IEEE Access 6, 11634–11640 (2018)

    Article  Google Scholar 

  49. Kang, B.,  Deng, Y.: Generating Z-number based on OWA weights using maximum entropy, Int. J. Intell. Syst. (2018) accepted

  50. Yin, L., Deng, Y.: Measuring transferring similarity via local information. Physica A Stat. Mech. Appl. 498, 102–115 (2018)

    Article  MathSciNet  Google Scholar 

  51. Zhang, R., Ashuri, B., Deng, Y.: A novel method for forecasting time series based on fuzzy logic and visibility graph. Adv. Data Anal. Classif. 11, 759–783 (2017)

    Article  MathSciNet  Google Scholar 

  52. Deng, X.: Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory, International Journal of Intelligent Systems (2018) Published online, https://doi.org/10.1002/int.21999

    Article  Google Scholar 

  53. Jiang, W., Wang, S.: An uncertainty measure for interval-valued evidences. Int. J. Comput. Commun. Control 12, 631–644 (2017)

    Article  Google Scholar 

  54. Jiang, W., Yang, T., Shou, Y., Tang, Y., Hu, W.: Improved evidential fuzzy c-means method. J. Syst. Eng. Electron. 29, 187–195 (2018)

    Google Scholar 

  55. Zadeh, L.A.: Review of a mathematical theory of evidence. AI Mag. 5, 81 (1984)

    Google Scholar 

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

    Google Scholar 

  57. Sepahvand, L.: Application of D numbers to the environmental impact assessment of highway. Nat. Environ. Pollut. Technol. 14, 973 (2015)

    Google Scholar 

  58. Zhou, X., Deng, X., Deng, Y., Mahadevan, S.: Dependence assessment in human reliability analysis based on D numbers and AHP. Nucl. Eng. Des. 313, 243–252 (2017)

    Article  Google Scholar 

  59. Mo, H., Deng, Y.: A new aggregating operator for linguistic information based on D numbers. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 24, 831–846 (2016)

    Article  MathSciNet  Google Scholar 

  60. Sun, L., Liu, Y., Zhang, B., Shang, Y., Yuan, H., Ma, Z.: An integrated decision-making model for transformer condition assessment using game theory and modified evidence combination extended by D numbers. Energies 9, 697 (2016)

    Article  Google Scholar 

  61. Fan, G., Zhong, D., Yan, F., Yue, P.: 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 (2016)

    Article  Google Scholar 

  62. Xiao, F.: An intelligent complex event processing with D numbers under fuzzy environment. Math. Problems Eng. 2016, 1–10 (2016)

    Google Scholar 

  63. Xiao, F.: A novel multi-criteria decision making method for assessing health-care waste treatment technologies based on D numbers. Eng. Appl. Artif. Intell. 71, 216–225 (2018)

    Article  Google Scholar 

  64. Deng, X.,  Deng, Y.: D-AHP method with different credibility of information, Soft Computing (2018) Published online, https://doi.org/10.1007/s00500-017-2993-9

  65. Chen, L., Deng, X.: A modified method for evaluating sustainable transport solutions based on ahp and dempster shafer evidence theory. Appl. Sci. 8, 563 (2018)

    Article  Google Scholar 

  66. Smets, P., Kennes, R.: The transferable belief model. Artif. Intell. 66, 191–234 (1994)

    Article  MathSciNet  Google Scholar 

  67. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

  68. Yin, L., Deng, Y.: Toward uncertainty of weighted networks: an entropy-based model. Physica A (2018). https://doi.org/10.1016/j.physa.2018.05.067

    Article  Google Scholar 

  69. Yang, J.-B.: Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties. Eur. J. Oper. Res. 131, 31–61 (2001)

    Article  MathSciNet  Google Scholar 

  70. Winston, W. L.: Operations research applications and algorithms, vol. 3. Wadsworth Press, California (1994)

    MATH  Google Scholar 

  71. Saaty, T. L.: Decision making with the analytic hierarchy process. Int. J. Serv. Sci. 1, 83–98 (2005)

    Google Scholar 

  72. Belton, V., Gear, T.: On a short-coming of saaty’s method of analytic hierarchies. Omega 11, 228–230 (1983)

    Article  Google Scholar 

  73. Johnson, C.R., Beine, W.B., Wang, T.J.: Right-left asymmetry in an eigenvector ranking procedure. J. Math. Psychol. 19, 61–64 (1979)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors greatly appreciate the reviews’ suggestions and the editor’s encouragement. This work is partly supported by National Natural Science Foundation of China (Grant Nos. 61573290, 61503237) and General Research Program of Sichuan Educational Department (Grant No. 17ZB0328).

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Authors and Affiliations

  1. Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054, Sichuan, China

    Hongming Mo & Yong Deng

  2. Library, Sichuan Minzu College, Kangding, 626001, Sichuan, China

    Hongming Mo

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  1. Hongming Mo
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Correspondence to Yong Deng.

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Mo, H., Deng, Y. A New MADA Methodology Based on D Numbers. Int. J. Fuzzy Syst. 20, 2458–2469 (2018). https://doi.org/10.1007/s40815-018-0514-3

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