Optimisation of Treatment Scheme for Water Inrush Disaster in Tunnels Based on Fuzzy Multi-criteria Decision-Making in an Uncertain Environment

  • Zhu Wen
  • Ziming Xiong
  • Hao Lu
  • Yuanpu XiaEmail author
Research Article - Civil Engineering


Water inrush is a common geological hazard encountered during tunnel construction. According to the characteristics of water inrush risk, a triangular intuitive fuzzy multi-criteria decision-making model based on prospect theory and evidential reasoning is proposed to optimise the necessary disaster treatment scheme. Firstly, since the attribute information is difficult to be quantified in tunnel engineering works, this study proposes a method based on a combination of linguistic descriptions and triangular fuzzy numbers, and then, triangular intuitive fuzzy numbers are constructed to quantify attribute information. Secondly, a method for dynamic reference points under a triangular intuitive information environment is proposed, and then, a prospective value decision matrix can be constructed. Thirdly, based on the existing research results related to fuzzy information entropy and cross-entropy, the new formulae for cross-entropy and entropy of triangular intuitive fuzzy information are proposed, and the attribute weights are determined by using the proposed method of cross-entropy and entropy. Fourthly, since evidence theory has significant advantages in information aggregation, multi-source decision information is aggregated by evidential reasoning. Finally, the proposed decision-making model is applied to the Yuelongmen tunnel project, and the expected effect is achieved: this also provides a reference for other risk decision-making problems in underground engineering.


Fuzzy multi-criteria decision-making Tunnel Water inrush Prospect theory Evidential reasoning 


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We thank the anonymous peer reviewers for providing valuable suggestions leading to improvements in the written manuscript. This work was supported by the National Key Basic Research Programme (Grant No. 2013CB036005) and the National Natural Science Fund Youth Project (51608529).

Compliance with Ethical Standards

Author Contributions

YX conceived, designed, and performed the study. ZX and ZW collected and analysed the example used in the paper. YX and HL wrote and revised the paper together. The authors have read, and approved, the final published manuscript.

Conflict of interest

The authors declare no conflict of interest.

Data Availability

This theoretical paper does not rely on empirical data. All of the plots can be generated by following the equations and instructions provided in the paper.


  1. 1.
    Kim, Y.G.: Application of risk analysis and assessment in tunnel design. Int. J. JCRM 5, 11–18 (2014)Google Scholar
  2. 2.
    Siang, L.Y.; Ghazali, F.E.M.; Zainun, N.Y.; et al.: General risks for tunnelling projects: an overview. In: International Conference of Global Network for Innovative Technology and Awam International Conference in Civil Engineering, p. 080004 (2017)Google Scholar
  3. 3.
    Parker, H.: Security of Tunnels and Underground Space: Challenges and Opportunities SP Sveriges provnings- och forskningsinstitut, Sweden (2008)Google Scholar
  4. 4.
    Beard, A.N.: Tunnel safety, risk assessment and decision-making. Tunn. Undergr. Space Technol. 25(1), 91–94 (2010)Google Scholar
  5. 5.
    Li, S.C.; Wu, J.; Xu, Z.H.; et al.: Unascertained measure model of water and mud inrush risk evaluation in karst tunnels and its engineering application. KSCE J. Civ. Eng. 21(4), 1170–1182 (2017)Google Scholar
  6. 6.
    Huang, R.; Huang, J.; Li, Y.; et al.: Automated tunnel rock classification using rock engineering systems. Eng. Geol. 156(2), 20–27 (2013)Google Scholar
  7. 7.
    Li, L.; Tu, W.; Shi, S.; et al.: Mechanism of water inrush in tunnel construction in karst area. Geomat. Nat. Hazards Risk 7, 1–12 (2016)Google Scholar
  8. 8.
    Wang, Y.; Jing, H.; Yu, L.; et al.: Set pair analysis for risk assessment of water inrush in karst tunnels. Bull. Eng. Geol. Environ. 76(3), 1199–1207 (2017)Google Scholar
  9. 9.
    Hao, Y.; Rong, X.; Ma, L.; et al.: Uncertainty analysis on risk assessment of water inrush in karst tunnels. Math. Probl. Eng. 2, 1–11 (2016)Google Scholar
  10. 10.
    Liang, D.X.; Jiang, Z.Q.; Zhu, S.Y.; et al.: Experimental research on water inrush in tunnel construction. Nat. Hazards 81(1), 467–480 (2016)Google Scholar
  11. 11.
    Einstein, H.: Risk assessment in rock engineering. In: New Generation Design Codes For Geotechnical Engineering Practice—-Taipei 2006 (with CD-ROM) (2015)Google Scholar
  12. 12.
    Cárdenas, I.C.; Al-Jibouri, S.S.H.; Halman, J.I.M.; et al.: Capturing and integrating knowledge for managing risks in tunnel works. Risk Anal. 33(1), 92–108 (2013)Google Scholar
  13. 13.
    Brown, E.T.: Risk assessment and management in underground rock engineering—an overview. J. Rock Mech. Geotech. Eng. 4(3), 193–204 (2012)Google Scholar
  14. 14.
    Olga, Š.: Risk management of tunnel construction projects: modelling uncertainty of construction time (cost) estimates for risk assessment and decision-making. PhD Thesis, Czech Technical University, Prague, Czechoslovakia (2012)Google Scholar
  15. 15.
    Li, X.; Li, Y.: Research on risk assessment system for water inrush in the karst tunnel construction based on GIS: case study on the diversion tunnel groups of the Jinping II hydropower station. Tunn. Undergr. Space Technol. 40(2), 182–191 (2014)Google Scholar
  16. 16.
    Li, S.C.; Zhou, Z.Q.; Li, L.P.; et al.: Risk assessment of water inrush in karst tunnels based on attribute synthetic evaluation system. Tunn. Undergr. Space Technol. Inc. Trenchless Technol. Res. 38, 50–58 (2013)Google Scholar
  17. 17.
    Chu, H.; Xu, G.; Yasufuku, N.; et al.: Risk assessment of water inrush in karst tunnels based on two-class fuzzy comprehensive evaluation method. Arab. J. Geosci. 10(7), 179 (2017)Google Scholar
  18. 18.
    Li, B.; Wu, Q.; Duan, X.Q.; et al.: Risk analysis model of water inrush through the seam floor based on set pair analysis. Mine Water Environ. 4, 1–7 (2017)Google Scholar
  19. 19.
    Wang, Y.; Yin, X.; Geng, F.; et al.: Risk assessment of water inrush in karst tunnels based on the efficacy coefficient method. Pol. J. Environ. Stud. 26(4), 1765–1775 (2017)Google Scholar
  20. 20.
    Wang, Y.; Yin, X.; Jing, H.; et al.: A novel cloud model for risk analysis of water inrush in karst tunnels. Environ. Earth Sci. 75(22), 1450 (2016)Google Scholar
  21. 21.
    Li, L.; Lei, T.; Li, S.; et al.: Risk assessment of water inrush in karst tunnels and software development. Arab. J. Geosci. 8(4), 1843–1854 (2015)Google Scholar
  22. 22.
    Wang, S.; Tang, Z.; Luo, W.; et al.: Risk evaluation of water inrush in karst tunnels based on multilevel fuzzy synthetic evaluation model. C E Ca 42(5), 1850–1855 (2017)Google Scholar
  23. 23.
    Hao, Y.; Rong, X.; Lu, H.; et al.: Quantification of margins and uncertainties for the risk of water inrush in a karst tunnel: representations of epistemic uncertainty with probability. Arab. J. Sci. Eng. 1–3, 1–14 (2017)Google Scholar
  24. 24.
    Li, L.P.; Lei, T.; Li, S.C.; et al.: Dynamic risk assessment of water inrush in tunnelling and software development. Geomech. Eng. 9(1), 57–81 (2015)Google Scholar
  25. 25.
    Li, T.; Yang, X.: Risk assessment model for water and mud inrush in deep and long tunnels based on normal grey cloud clustering method. KSCE J. Civ. Eng. 22(5), 1991–2001 (2018)Google Scholar
  26. 26.
    Li, S.C.; Wu, J.: A multi-factor comprehensive risk assessment method of karst tunnels and its engineering application. Bull. Eng. Geol. Environ. 6, 1–16 (2017)MathSciNetGoogle Scholar
  27. 27.
    Ying-Hua, T.; Qing-Song, Z.; Li-Ping, L.; et al.: Water inrush and mud bursting scale prediction and risk assessment of tunnel in water-rich fault. Electron. J. Geotech. Eng. 21(26), 10401–10413 (2016)Google Scholar
  28. 28.
    Shi, S.; Xie, X.; Bu, L.; et al.: Hazard-based evaluation model of water inrush disaster sources in karst tunnels and its engineering application. Environ. Earth Sci. 77(4), 141 (2018)Google Scholar
  29. 29.
    Shi, S.; Bu, L.; Li, S.; et al.: Application of comprehensive prediction method of water inrush hazards induced by unfavourable geological body in high risk karst tunnel: a case study. Geomat. Nat. Hazards Risk 8(2), 1407–1423 (2017)Google Scholar
  30. 30.
    Xue, Y.; Wang, D.; Li, S.; et al.: A risk prediction method for water or mud inrush from water-bearing faults in subsea tunnel based on cusp catastrophe model. KSCE J. Civ. Eng. 21(7), 1–8 (2017)Google Scholar
  31. 31.
    Rundmo, T.; Nordfjærn, T.; Iversen, H.H.; et al.: The role of risk perception and other risk-related judgements in transportation mode use. Saf. Sci. 49(2), 226–235 (2011)Google Scholar
  32. 32.
    Karagoz, S.; Aydin, N.; Isikli, E.: Decision making in solid waste management under fuzzy environment. In: Intelligence Systems in Environmental Management: Theory and Applications. Springer International Publishing, pp. 91–115 (2017)Google Scholar
  33. 33.
    Dong, X.; Lu, H.; Xia, Y.; et al.: Decision-making model under risk assessment based on entropy. Entropy 18(11), 404 (2016)Google Scholar
  34. 34.
    Xia, Y.; Xiong, Z.; Dong, X.; et al.: Risk assessment and decision-making under uncertainty in tunnel and underground engineering. Entropy 19(10), 549 (2017)Google Scholar
  35. 35.
    Zavadskas, E.K.; Antucheviciene, J.; Turskis, Z.; et al.: Hybrid multiple-criteria decision-making methods: a review of applications in engineering. Sci. Iran. 23(1), 1–20 (2016)Google Scholar
  36. 36.
    Marle, F.; Gidel, T.: A multi-criteria decision-making process for project risk management method selection. Int. J. Multicriteria Decis. Mak. 2(2), 189–223 (2017)Google Scholar
  37. 37.
    Krohling, R.A.; Souza, T.T.M.D.: Combining prospect theory and fuzzy numbers to multi-criteria decision making. Expert Syst. Appl. 39(13), 11487–11493 (2012)Google Scholar
  38. 38.
    Chen, Z.S.; Chin, K.S.; Ding, H.; et al.: Triangular intuitionistic fuzzy random decision making based on combination of parametric estimation, score functions, and prospect theory. J. Intell. Fuzzy Syst. 30(6), 3567–3581 (2016)zbMATHGoogle Scholar
  39. 39.
    Zavadskas, E.K.; Antuchevičenė, J.; KaplińSki, O.: Multi-criteria decision making in civil engineering: part I a state-of-the-art survey. Statybinä—s Konstrukcijos Ir Technologijos 7(3), 103–113 (2015)Google Scholar
  40. 40.
    Zavadskas, E.K.; Antuchevičenė, J.; KaplińSki, O.: Multi-criteria decision making in civil engineering. Part II—applications. Statybinä—s Konstrukcijos Ir Technologijos 7(4), 151–167 (2015)Google Scholar
  41. 41.
    Antucheviciene, J.; Kala, Z.; Marzouk, M.; et al.: Solving civil engineering problems by means of fuzzy and stochastic MCDM methods: current state and future research. Math. Probl. Eng. 2015, 1–16 (2015)Google Scholar
  42. 42.
    Kabir, G.; Sadiq, R.; Tesfamariam, S.: A review of multi-criteria decision-making methods for infrastructure management. Struct. Infrastruct. Eng. 10(9), 1176–1210 (2014)Google Scholar
  43. 43.
    Kahraman, C.; Onar, S.C.; Oztaysi, B.: Fuzzy multicriteria decision-making: a literature review. Int. J. Comput. Intell. Syst. 8(4), 637–666 (2015)zbMATHGoogle Scholar
  44. 44.
    Fouladgar, M.M.; Yazdani-Chamzini, A.; Zavadskas, E.K.: Risk evaluation of tunneling projects. Arch. Civ. Mech. Eng. 12(1), 1–12 (2012)Google Scholar
  45. 45.
    Dubois, D.: Possibility theory and statistical reasoning. Comput. Stat. Data Anal. 51, 47–69 (2006)MathSciNetzbMATHGoogle Scholar
  46. 46.
    Helton, J.C.; Johnson, J.D.; Oberkampf, W.L.: An exploration of alternative approaches to the representation of uncertainty in model predictions. Reliab. Eng. Syst. Saf. 85(1–3), 39–71 (2004)Google Scholar
  47. 47.
    Shortridge, J.; Aven, T.; Guikema, S.: Risk assessment under deep uncertainty: a methodological comparison. Reliab. Eng. Syst. Saf. 159, 12–23 (2017)Google Scholar
  48. 48.
    Gupta, P.; Mehlawat, M.K.; Grover, N.: Intuitionistic fuzzy multi-attribute group decision-making with an application to plant location selection based on a new extended VIKOR method. Inf. Sci. 370–371, 184–203 (2016)Google Scholar
  49. 49.
    Zeng, J.; Huang, G.: Set pair analysis for karst waterlogging risk assessment based on AHP and entropy weight. Hydrol. Res. nh2017265 (2017)Google Scholar
  50. 50.
    Liu, F.; Zhao, S.; Weng, M.; et al.: Fire risk assessment for large-scale commercial buildings based on structure entropy weight method. Saf. Sci. 94, 26–40 (2017)Google Scholar
  51. 51.
    Chen, Z.; Yang, W.: A new multiple attribute group decision making method in intuitionistic fuzzy setting. Appl. Math. Model. 35(9), 4424–4437 (2011)MathSciNetzbMATHGoogle Scholar
  52. 52.
    Qi, X.; Liang, C.; Zhang, J.: Generalized cross-entropy based group decision making with unknown expert and attribute weights under interval-valued intuitionistic fuzzy environment. Comput. Ind. Eng. 79, 52–64 (2015)Google Scholar
  53. 53.
    Khaleie, S.; Fasanghari, M.: An intuitionistic fuzzy group decision making method using entropy and association coefficient. Soft Comput. 16(7), 1197–1211 (2012)Google Scholar
  54. 54.
    Xu, Z.: Intuitionistic fuzzy multiattribute decision making: an interactive method. IEEE Trans. Fuzzy Syst. 20(3), 514–525 (2012)Google Scholar
  55. 55.
    Gopal, P.M.; Prakash, K.S.: Minimization of cutting force, temperature and surface roughness through GRA, TOPSIS and Taguchi techniques in end milling of Mg hybrid MMC. Measurement 116, 178–192 (2018)Google Scholar
  56. 56.
    Liu, J.; Liao, X.; Yang, J.B.: A group decision-making approach based on evidential reasoning for multiple criteria sorting problem with uncertainty. Eur. J. Oper. Res. 246(3), 858–873 (2015)MathSciNetzbMATHGoogle Scholar
  57. 57.
    Yang, J.; Feng, Y.; Qiu, W.: Stock selection for portfolios using expected utility-entropy decision model. Entropy 19(10), 508 (2017)Google Scholar
  58. 58.
    Chen, Z.S.; Chin, K.S.; Ding, H.; et al.: Triangular intuitionistic fuzzy random decision making based on combination of parametric estimation, score functions, and prospect theory. J. Intell. Fuzzy Syst. 30(6), 3567–3581 (2016)zbMATHGoogle Scholar
  59. 59.
    Varghese, A.; Kuriakose, S.: More on Cartesian products over intuitionistic fuzzy sets. Int. Math. Forum 21–24, 1129–1133 (2012)MathSciNetzbMATHGoogle Scholar
  60. 60.
    Chen, S.M.; Han, W.H.: A new multiattribute decision making method based on multiplication operations of interval-valued intuitionistic fuzzy values and linear programming methodology. Inf. Sci. 429, 421–432 (2018)MathSciNetGoogle Scholar
  61. 61.
    Rani, P.; Jain, D.; Hooda, D.S.: Shapley function based interval-valued intuitionistic fuzzy VIKOR technique for correlative multi-criteria decision making problems. Iran. J. Fuzzy Syst. 15(1), 25–54 (2018)MathSciNetzbMATHGoogle Scholar
  62. 62.
    Chen, J.: An approach to multiple attribute decision making with triangular intuitionistic fuzzy information. J. Comput. Theor. Nanosci. 13(10), 7258–8288 (2016)Google Scholar
  63. 63.
    Ye, J.: Improved method of multicriteria fuzzy decision-making based on vague sets. Comput. Aided Des. 39(2), 164–169 (2007)Google Scholar
  64. 64.
    Muralidhar, A.: Modern prospect theory: the missing link between modern portfolio theory and prospect theory. Soc. Sci. Electron. Publ. 9, 1–36 (2014)Google Scholar
  65. 65.
    Liu, Y.; et al.: A theoretical development on the entropy of interval-valued intuitionistic fuzzy soft sets based on the distance measure. Int. J. Comput. Intell. Syst. 10(1), 569 (2017)Google Scholar
  66. 66.
    Deng,; et al.: Decision-making method with bounded rationality under intuitionistic fuzzy information environment. J. Comput. Appl. 37(5), 1376–1381 (2017)Google Scholar
  67. 67.
    Lin, J.: Divergence Measures Based on the Shannon Entropy. IEEE Press, New York (1991)zbMATHGoogle Scholar
  68. 68.
    Shang, X.G.; Jiang, W.S.: A Note on Fuzzy Information Measures. Elsevier, Amsterdam (1997)Google Scholar
  69. 69.
    Bao, T.; et al.: MADM method based on prospect theory and evidential reasoning approach with unknown attribute weights under intuitionistic fuzzy environment. Expert Syst. Appl. 88, 305–317 (2017)Google Scholar
  70. 70.
    Parkash, O.; Sharma, P.K.; Mahajan, R.: New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle. Inf. Sci. 178(11), 2389–2395 (2008)MathSciNetzbMATHGoogle Scholar
  71. 71.
    Khaleie, S.; Fasanghari, M.: An intuitionistic fuzzy group decision making method using entropy and association coefficient. Soft Comput. 16(7), 1197–1211 (2012)Google Scholar
  72. 72.
    Atanassov, K.T.; Gargov, G.: Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31, 343–349 (1981)MathSciNetzbMATHGoogle Scholar
  73. 73.
    Zhang, Q.S.; Jiang, S.; Jia, B.; et al.: Some information measures for interval-valued intuitionistic fuzzy sets. Inf. Sci. Int. J. 180(24), 5130–5145 (2010)MathSciNetzbMATHGoogle Scholar
  74. 74.
    Ye, J.: Fuzzy cross entropy of interval-valued intuitionistic fuzzy sets and its optimal decision-making method based on the weights of alternatives. Expert Syst. Appl. 38(5), 6179–6183 (2011)Google Scholar
  75. 75.
    Meng, F.; Tang, J.: Interval-valued intuitionistic fuzzy multiattribute group decision making based on cross entropy measure and choquet integral. Int. J. Intell. Syst. 28(12), 1172–1195 (2013)Google Scholar
  76. 76.
    Meng, F.; Chen, X.: Interval-valued intuitionistic fuzzy multi-criteria group decision making based on cross entropy and 2-additive measures. Soft Comput. 19(7), 2071–2082 (2015)zbMATHGoogle Scholar
  77. 77.
    Rassafi, A.A.; Ganji, S.S.; Pourkhani, H.: Road safety assessment under uncertainty using a multi attribute decision analysis based on Dempster–Shafer theory. KSCE J. Civ. Eng. 1, 1–16 (2017)Google Scholar
  78. 78.
    Kong, G.; Jiang, L.; Yin, X.; et al.: Combining principal component analysis and the evidential reasoning approach for healthcare quality assessment. Ann. Oper. Res. 271(2), 679–699 (2018)Google Scholar
  79. 79.
    Zhang, M.J.; Wang, Y.M.; Li, L.H.; et al.: A general evidential reasoning algorithm for multi-attribute decision analysis under interval uncertainty. Eur. J. Oper. Res. 257(3), 1005–1015 (2017)MathSciNetzbMATHGoogle Scholar
  80. 80.
    Potocki, T.: Cumulative prospect theory as a model of economic rationality. Ekonomia J. 31, 71–95 (2015)Google Scholar

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© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringNanjing University of Science and TechnologyNanjingChina
  2. 2.State Key Laboratory of Disaster Prevention and Mitigation of Explosion and ImpactThe Army Engineering University of PLANanjingChina

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