Dempster-Shafer theory applied to uncertainty surrounding permeability

Mathematical Geosciences

Volumn 42, Issue 3, 2010, Pages 293-307

  Mathon, Bree R ^a   Ozbek, Metin M ^b   Pinder, George F ^a  

^a University of Vermont   (United States)

^b ENVIRON INTERNATIONAL CORPORATION   (United States)

Author keywords

Dempster's rule of combination; Evidence theory; Groundwater modeling; Permeability; Yager's rule

Indexed keywords

DATA SET; GROUNDWATER; HYDROGEOLOGY; MODELING; PERMEABILITY; PROBABILITY; THEORETICAL STUDY;

EID: 77952888603     PISSN: 18748961     EISSN: 18748953     Source Type: Journal    
DOI: 10.1007/s11004-009-9246-0     Document Type: Article

References (27)

1. Agarwal H, Renaud JE, Preston EL, Padmanabhan D (2004) Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliab Eng Syst Saf 85: 281-294.
2. Belitz K, Bredehoeft JD (1988) Hydrodynamics of Denver basin-explanation of subnormal fluid pressures. Am Assoc Petroleum Geol Bull 72(11): 1334-1359.
3. Binaghi E, Luzi L, Madella P, Pergalani F, Rampini A (1998) Slope instability Zonation: a comparison between certainty factor and fuzzy Dempster-Shafer approaches. Nat Hazards 17: 77-97.
4. Cayuela L, Golicher JD, Salas Rey J, Rey Benayas JM (2006) Classification of a complex landscape using Dempster-Shafer theory of evidence. Int J Remote Sens 27(10): 1951-1971.
5. Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 38: 325-339.
6. Dubois D, Prade H (1986) A set-theoretic view on belief functions: logical operations and approximations by fuzzy sets. Int J Gen Syst 12: 193-226.
7. Dubois D, Prade H (1992) On the combination of evidence in various mathematical frameworks. In: Flamm J, Luisi T (eds) Reliability data collection and analysis. Kluwer Academic, Brussels, pp 213-241.
8. Ferson S, Kreinovich V (2002) Representation, propagation, and aggregation of uncertainty: Sandia National Laboratories. Technical report, Albuquerque, New Mexico.
9. Ferson S, Kreinovich V, Ginzburg L, Myers DS, Sentz K (2002) Constructing probability boxes and Dempster-Shafer structures: Sandia National Laboratories. Technical report SAND2002-4015, Albuquerque, New Mexico. Available at: http://www. sandia. gov/epistemic/Reports/SAND2002-4015. pdf.
10. Hau HY, Kashyap RL (1990) Belief combination and propagation in a lattice-structured inference network. IEEE Trans Syst Man Cybern 20(1): 45-57.
11. Inagaki T (1991) Interdependence between safety-control policy and multiple-sensor schemes via Dempster-Shafer theory. IEEE Trans Reliab 40(2): 182-188.
12. Joslyn C, Booker JM (2004) Generalized information theory for engineering modeling and simulation. In: Nikolaidid E, Ghiocel D, Singhal S (eds) Engineering design reliability handbook. CRC Press, Boca Raton, pp 9-1-9-40.
13. Joslyn C, Ferson S (2004) Approximate representations of random intervals for hybrid uncertainty quantification in engineering modeling. In: Hanson KM, Hemez FM (eds), Sensitivity analysis of model output (SAMO04), LANL, Los Alamos, pp 453-469. http://library. lanl. gov/cgi-bin/getdoc?event=SAMO2004& document=samo04-83. pdf.
14. Klir GJ (2003) Uncertainty. Encycl Inf Syst 4: 511-521.
15. Kriegler E, Held H (2005) Utilizing belief functions for the estimation of future climate change. Int J Approx Reason 39: 185-209.
16. Ricciardi KL (2002) Optimal groundwater remediation design subject to uncertainty. PhD dissertation, University of Vermont, USA, pp 50-66.
17. Ross J, Ozbek M, Pinder GF (2008) Kalman filter updating of possibilistic hydraulic conductivity. J Hydrol 354: 149-159.
18. Sentz K, Ferson S (2002) Combination of evidence in Dempster-Shafer theory: Sandia National Laboratories. Technical report SAND2002-0835, Albuquerque, New Mexico. Available at: http://www. sandia. gov/epistemic/Reports/SAND2002-0835. pdf.
19. Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton. 312 p.
20. Smarandache F (2004) An in-depth look at information fusion rules and the unification of fusion theories: arXiv electronic archives. Available at: http://xxx. lanl. gov/ftp/cs/papers/0410/0410033. pdf.
21. Smarandache F, Dezert J (eds) (2004) Applications and advances of DSmT for information fusion. American Research Press, Rehoboth. http://www. gallup. unm. edu/~smarandache/DSmT-book1. pdf.
22. Smets P (2005) Analyzing the combination of conflicting belief functions. Available at: http://iridia. ulb. ac. be/%7epsmets/Combi_Confl. pdf.
23. Smets P, Kennes R (1994) The transferable belief model. Artif Intell 66: 191-234.
24. Yager RR (1987) On the Dempster-Shafer framework and new combination rules. Inf Sci 41: 93-138.
25. Zadeh LA (1984) Review of books: a mathematical theory of evidence. AI Mag 5(3): 81-83.
26. Zadeh LA (1986) A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination. AI Mag 7: 85-90.
27. Zhang L (1994) Representation, independence, and combination of evidence in the Dempster-Shafer theory. In: Yager RR, Kacprzyk J, Fedrizzi M (eds) Advances in the Dempster-Shafer theory of evidence. Wiley, New York, pp 51-69.