Fuzzy-stochastic characterization of site uncertainty and variability in groundwater flow and contaminant transport through a heterogeneous aquifer

Journal of Contaminant Hydrology

Volumn 106, Issue 1-2, 2009, Pages 73-82

  Zhang, Kejiang ^a   Li, Hua ^a   Achari, Gopal ^a  

^a UNIVERSITY OF CALGARY   (Canada)

Author keywords

Fuzzy set theory; Groundwater flow; Possibility probability transformation; Solute transport; Uncertainty; Variability

Indexed keywords

COMPLEX ENVIRONMENTS; COMPUTATIONAL ALGORITHMS; CONTAMINANT TRANSPORTS; DATA AND INFORMATIONS; FUZZY NUMBERS; FUZZY SET THEORY; GEO-STATISTICS; GOVERNING EQUATIONS; HETEROGENEOUS AQUIFERS; POSSIBILITY-PROBABILITY TRANSFORMATION; PROBABILITY THEORIES; RANDOM UNCERTAINTIES; UNCERTAINTY; UNCERTAINTY AND VARIABILITIES; VARIABILITY;

AQUIFERS; FUZZY SETS; GROUNDWATER FLOW; GROUNDWATER POLLUTION; GROUNDWATER RESOURCES; HYDROGEOLOGY; LEAD; SOLUTE TRANSPORT; UNDERGROUND RESERVOIRS;

PROBABILITY DISTRIBUTIONS;

AQUIFER POLLUTION; FUZZY MATHEMATICS; GROUNDWATER FLOW; HETEROGENEITY; POLLUTANT TRANSPORT; SOLUTE TRANSPORT; STOCHASTICITY; UNCERTAINTY ANALYSIS;

ENVIRONMENTAL MONITORING; FRESH WATER; FUZZY LOGIC; MODELS, THEORETICAL; OBSERVER VARIATION; STOCHASTIC PROCESSES; UNCERTAINTY; WATER MOVEMENTS; WATER POLLUTANTS, CHEMICAL;

EID: 62649083128     PISSN: 01697722     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jconhyd.2009.01.003     Document Type: Article

References (52)

1. Baudrit C., and Dubois D. Practical representations of incomplete probabilistic knowledge. Computational Statistics and Data Analysis 51 1 (2006) 86-108
2. Bellin A., and Rubin Y. HYDRO-GEN: a spatially distributed random filed generator for correlated properties. Stochastic Hydrology and Hydraulics 10 (1996) 253-278
3. Charbeneau R.J. Groundwater Hydraulic and Pollutant Transport (2000), Prentice Hall, New Jersey
4. Chen Z., Huang G.H., and Chakma A. Hybrid fuzzy-stochastic modeling approach for assessing environmental risk at contaminated groundwater systems. Journal of Environmental Engineering 129 1 (2003) 79-88
5. In: Dagan G., and Neuman S.P. (Eds). Subsurface Flow and Transport: A Stochastic Approach (1997), Cambridge Press, Cambridge
6. Delhomme J.P. Spatial variability and uncertainty in. groundwater flow parameters: a geostatistical approach. Water Resource Research 15 2 (1979) 269-280
7. Dempster A.P. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38 (1967) 325-339
8. Dou C., Woldt W., Bogardi I., and Dahab M. Numerical solute transport simulation using fuzzy sets approach. Journal of Contaminant Hydrology 27 (1997) 107-126
9. Dubois D., and Prade H. Fuzzy sets and systems: Theory and applications (1980), Academic Press, New York
10. Dubois D., and Prade H. Possibility Theory (1988), Pleanum Press, New York
11. Dubois D., and Prade H. The three semantics of fuzzy sets. Fuzzy Sets and Systems 90 (1997) 141-150
12. Dubois D., and Prade H. Possibility theory in information fusion. Proc. of the third international conference on information fusion, July 10-13, Paris, France 1, PS 6-19 (2000)
13. Dubois D., and Prade H. On the use of aggregation operations in information fusion process. Fuzzy Sets and Systems 142 (2004) 143-161
14. Dubois D., Prade H., and Sandri S. On possibility/probability transformations. In: Lowen R., and Roubens M. (Eds). Fuzzy logic (1993), Kluwer Academic Publishers, Netherlands 103-112
15. Dubois D., Nguyen H.T., and Prade H. Possibility theory, probability and fuzzy sets: misunderstandings, bridges and gaps. In: Dubois D., and Prade H. (Eds). Fundamentals of fuzzy sets, The Handbooks of Fuzzy Sets Series (2000), Kluwer Academic Publishers, Boston, USA
16. Dubois D., Foulloy L., Mauris G., and Prade H. Probability-possibility transformations, triangular fuzzy sets and probabilistic inequalities. Reliable Computing 10 (2004) 273-297
17. Evans K.L., and Bedient P.B. A transient methodology for assessing risk: development and comparison with the conventional approach. Proceedings of the 1995 Petroleum Hydrocarbons and Organic Chemicals in Ground Water: Prevention, Detection, and Remediation Conference (1995) 111-125
18. Ferson, S., Kreinovich, V., Ginzburg, L., Myers, D.M. and Sentz, K., 2003. Construction of probability boxes and Dempster-Shafer structures. SAND report, SANDD2002-4015.
19. Gomez-Hernandez J.J., and Srivastava R.M. ISIM3D: and ANSI-C three-dimensional multiple indicator conditional simulation program. Computers & Geosciences 16 4 (1990) 395-440
20. Guan J., and Aral M.M. Optimal design of groundwater remediation systems using fuzzy set theory. Water Resource Research 40 (2004) w01518 10.1029/2003WR002121
21. Gutjahr, A.L., 1989. Fast Fourier Transforms for random field generation. New Mexio Tech Report 4-R58-2690R.
22. Guyonnet D., Bourgine B., Dubois D., Fargier H., Come B., and Chiles J.-P. Hybrid approach for addressing uncertainty in risk assessments. ASCE Journal of Environmental Engineering 129 1 (2003) 68-78
23. Kentel E., and Aral M.M. Probabilistic-fuzzy health risk modeling. Stochastic Environmental Research and Risk Assessment 18 (2004) 324-338
24. Khadam I., and Kaluarachchi J.J. Applicability of risk-based management and the need for risk-based economic decision analysis at hazardous waste contaminated sites. Environmental International 29 (2003) 503-519
25. Klimke A., Willner K., and Wohlmuth B. Uncertainty modeling using fuzzy arithmetic based on sparse grids: application to dynamic systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12 6 (2004) 745-759
26. Klimke A., and Wohlmuth B. Computing expensive multivariate functions of fuzzy numbers using sparse grids. Fuzzy Sets and Systems 153 (2005) 432-453
27. Kwakernaak H. Fuzzy random variables-I. Definitions and theorems. Information Sciences 15 (1978) 1-29
28. Lahkim M.B., and Garcia L.A. Stochastic modeling of exposure and risk in a contaminated heterogeneous aquifer. 1: Monte Carlo uncertainty analysis. Environmental Engineering Science 16 5 (1999) 315-328
29. Mantoglou A., and Wilson J.L. The turning bands method for simulation of random fields using line generation by a spectral method. Water Resource Research 18 5 (1982) 1379-1394
30. Matheron G. The intrinsic random functions and their applications. Advances in Applied Probability 5 (1973) 439-468
31. Matheron G. Random Sets and Integral Geometry (1975), John Wiley &Sons, New York
32. Maxwell R.M., Pelmulder S.D., Tompson A.F.B., and Kastenberg W.E. On the development of a new methodology for groundwater-driven health risk assessment. Water Resource Research 34 4 (1998) 833-847
33. Maxwell R.M., Kastenberg W.E., and Rubin Y. A methodology to investigate site characterization information into groundwater-driven health risk assessment. Water Resource Research 35 9 (1999) 2841-2855
34. Molchanov I.S. Theory of Random Sets (2005), Springer-Verlag, Berlin
35. Moller B., and Beer M. Fuzzy randomness-uncertainty in civil engineering and computational mechanics (2004), Springer, Berlin
36. Nguyen H.T. An Introduction to Random Sets (2006), Chapman & Hall/CRC, Boca Raton
37. Novak E., and Ritter K. High-dimensional integration of smooth functions over cubes. Numerical Mathematics 37 (1996) 79-97
38. O'Hagan A., Buck C.E., Daneshkhah A., Eiser J.R., Garthwaite P.H., Jenkinson D.J., Oakley J.E., and Rakow T. Uncertainty judgement: eliciting experts' probabilities (2006), John Wiley &Sons, Ltd, England
39. Porter D.W., Gibbs B.P., Jones W.F., Huyakorn P.S., Hamm L.L., and Flach G.P. Data fusion modeling for groundwater systems. Journal of Contaminant Hydrology 42 (2000) 303-335
40. Ross T.J. Fuzzy logic with engineering applications (2004), John Wiley&Sons, Ltd, England (2nd)
41. Ruan F., and McLaughlin D. An efficient multivariate random filed generator using the fast Fourier transform. Advances in Water Resources 21 (1998) 385-399
42. Rubin Y., and Bellin A. Conditional simulation of geologic media with evolving scales of heterogeneity. In: Sposito G. (Ed). Scale dependence and scale invariance in hydrology (1997), Cambridge University Press
43. Rubin Y., Berlin A., and Lawrence A.E. On the use of block-effective macrodispersion for numerical simulation of transport in heterogeneous formations. Water Resource Research 39 9 (2003) 1242-1251
44. Sentz, K. and Ferson, S., 2002. Combination of evidence in Dempster-Shafer theory. AANDIA Report, SAND2002-0835, Sandia National Lab. USA.
45. Shafer G. A mathematical theory of evidence (1976), Princeton University Press, Princeton
46. Smets P., and Kennes R. The transferable belief model. Artificial Intelligence 66 (1994) 191-234
47. Smoljak S.A. Quadrature and interpolation formulas for tensor products of certain classes of functions. Soviet Mathematics. Doklady 4 (1963) 240-243
48. Terano T., Asai K., and Sugeno M. Fuzzy systems theory and its applications (1991), Academic Press Inc., San Diego, CA
49. Tompson A.F.B., Ababou R., and Gelhar L.W. Implementation of the three-dimensional turning bands random field generator. Water Resource Research 25 10 (1989) 2227-2243
50. Vick S.G. Degree of belief: subjective probability and engineering judgment (2002), ASCE Press, Reston, Virginia
51. Zadeh L.A. Fuzzy sets. Information and Control 8 (1965) 338-353
52. Zadeh L.A. Fuzzy sets as a base for a theory of possibility. Fuzzy Sets and Systems 1 (1978) 3-28