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Uncertainty Analysis of Retardation Factor Using Monte Carlo, Fuzzy Set and Hybrid Approach

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 125))

Abstract

Uncertainty analysis of physical parameters present in the groundwater model is important from the point of safety measures in the field of nuclear science and technology. Researchers have carried out this uncertainty analysis using traditional Monte Carlo simulations. However, in practice, Monte Carlo simulation may not be possible because of lack of data obtained from field experiments. Therefore, the demand is to investigate uncertainty using imprecise-based method. In order to fulfill this demand, we have carried out uncertainty analysis of groundwater model parameter using fuzzy set and hybrid methods. Monte Carlo-based uncertainty is also presented in this paper. Overall, this paper highlights the various methodologies of uncertainty analysis. In the hybrid approach, the concept of fuzzy random variable and its computational details have been explored. Retardation factor is our representative groundwater model parameter on which illustration of the said methodologies of uncertainty modeling is presented.

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References

  1. Vose, D.: Quantitative Risk Analysis—A Guide to Monte Carlo Simulation Modeling. Wiley, New York (1996)

    MATH  Google Scholar 

  2. Helton, J.C.: Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal. Reliab. Eng. Syst. Saf. 42, 327–367 (1993)

    Article  Google Scholar 

  3. Ross, T.J.: Fuzzy Logic with Engineering Applications, 2nd edn. Wiley, New York (2004)

    MATH  Google Scholar 

  4. Dubois, D., Prade, H.: Fuzzy Sets and Systems. Academic Press, New York (1980)

    MATH  Google Scholar 

  5. Dong, W., Shah, H.: Vertex method for computing functions of fuzzy variables. Fuzzy Sets Syst. 24(1), 65–78 (1987)

    Article  MathSciNet  Google Scholar 

  6. Kwakernaak, H.: Fuzzy random variables—I, definitions and theorems. Inf. Sci. 15(1), 1–29 (1978)

    Article  MathSciNet  Google Scholar 

  7. Kwakernaak, H.: Fuzzy random variables—II, Algorithms and examples for the discrete case. Inf. Sci. 17(3), 253–278 (1979)

    Article  MathSciNet  Google Scholar 

  8. Puri, M.L., Ralescu, D.A.: Fuzzy random variables. J. Math. Anal. Appl. 114, 409–422 (1986)

    Article  MathSciNet  Google Scholar 

  9. Ferson, S., Tucker, W.T.: Sensitivity analysis using probability bounding. Reliab. Eng. Syst. Saf. 91, 1435–1442 (2006)

    Article  Google Scholar 

  10. Van Genuchten, M.Th., Alves, W.J.: Analytical solutions of the one-dimensional convective dispersive solute transport equation. United States Department of Agriculture, Agricultural Research Service, Technical Bulletin 1661 (1982)

    Google Scholar 

  11. Liu, B.: Uncertainty Theory: An Introduction to Its Axiomatic Foundations. Springer, Berlin (2004)

    Book  Google Scholar 

  12. Klir, G.J.: The many faces of uncertainty. In: Ayyub, B.M., Gupta, M.M (eds.) Uncertainty Modeling and Analysis: Theory and Applications, pp. 3–19. Elsevier, Amsterdam (1994)

    Google Scholar 

  13. Zadeh, L.: Fuzzy Sets. Inf. Control 8, 338–353 (1965)

    Google Scholar 

  14. Baudrit, C., Couso, I., Dubois, D.: Joint propagation of probability and possibility in risk analysis: towards a formal framework. Int. J. Approx. Reason. 45, 82–105 (2007)

    Article  MathSciNet  Google Scholar 

  15. Guyonnet, D., Bourgine, B., Dubois, D., Fargier, H., Come, B., Chiles, J.P.: Hybrid approach for addressing uncertainty in risk assessments. J. Environ. Eng. (ASCE) 129, 68–78 (2003)

    Article  Google Scholar 

  16. Givens, J., Tahani, H.: An improved method of performing fuzzy arithmetic for computer vision, In: Proceedings of North American Information Processing Society (NAFIPS), pp. 275–280. Purdue University, West Lafayette (1987)

    Google Scholar 

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Correspondence to T. K. Pal .

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Pal, T.K., Arumugam, V., Datta, D. (2015). Uncertainty Analysis of Retardation Factor Using Monte Carlo, Fuzzy Set and Hybrid Approach. In: Chakraborty, M.K., Skowron, A., Maiti, M., Kar, S. (eds) Facets of Uncertainties and Applications. Springer Proceedings in Mathematics & Statistics, vol 125. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2301-6_12

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