Uncertainty assessment of hydrological models with fuzzy extension principle: Evaluation of a new arithmetic operator

Water Resources Research

Volumn 50, Issue 2, 2014, Pages 1095-1111

  Nasseri, M ^a   Ansari, A ^b   Zahraie, B ^a  

^a UNIVERSITY OF TEHRAN   (Iran)

^b INTERNATIONAL INSTITUTE OF EARTHQUAKE ENGINEERING AND SEISMOLOGY IIEES   (Iran)

Author keywords

Fuzzy Arithmetic Operator; Fuzzy Extension Principle; Fuzzy Reasoning; Standard fuzzy arithmetic; Uncertainty Assessment; Vertex Method

Indexed keywords

ARID REGIONS; COMPUTER SIMULATION; EFFICIENCY;

FUZZY ARITHMETICS; FUZZY EXTENSION PRINCIPLE; FUZZY REASONING; STANDARD FUZZY ARITHMETICS; UNCERTAINTY ASSESSMENT; VERTEX METHOD;

FUZZY SETS;

BASIN; ESTIMATION METHOD; FUZZY MATHEMATICS; HYDROLOGICAL MODELING; SEMIARID REGION; SIMULATION; STATISTICAL ANALYSIS; UNCERTAINTY ANALYSIS; WATER BUDGET;

FRANCE; IRAN;

EID: 84893663232     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/2012WR013382     Document Type: Article

References (38)

1. Abebe, A. J., V. Guinot, and, D. P. Solomatine, (2000), Fuzzy alpha-cut vs. Monte Carlo techniques in assessing uncertainty in model parameters, paper presented at Fourth International Conference on Hydroinformatics, Iowa Institute of Hydraulic Research, Cedar-Rapids, Iowa
2. Beven, K. J., and, A. Binley, (1992), The future of distributed models: Model calibration and uncertainty prediction, Hydrol. Processes, 6 (3), 279-298, doi: 10.1002/hyp.3360060305.
3. Civanlar, M. R., and, H. J. Trussell, (1986), Constructing membership functions using statistical data, Fuzzy Sets Syst., 18 (1), 1-13, doi: 10.1016/0165-0114(86)90024-2.
4. Davis, T. J., and, C. P. Keller, (1997), Modelling uncertainty in natural resource analysis using fuzzy sets and Monte Carlo simulation: Slope stability prediction, Int. J. Geogr. Inform. Sci., 11 (5), 409-434, doi: 10.1080/136588197242239.
5. Dong, W. M., and, H. C. Shah, (1987), Vertex method for computing functions of fuzzy variables, Fuzzy Sets Syst., 21 (1), 65-78, doi: 10.1016/0165-0114(87)90114-X. (Pubitemid 18544508)
6. Dong, W. M., and, F. S. Wong, (1987), Fuzzy weighted averages and implementation of the extension principle, Fuzzy Sets Syst., 21 (2), 183-199, doi: 10.1016/0165-0114(87)90163-1.
7. Dou, C., W. Woldt, I. Bogardi, and, M. Dahab, (1997), Numerical solute transport simulation using fuzzy sets approach, J. Contam. Hydrol., 27, 107-126, doi: 10.1016/S0169-7722(96)00047-2. (Pubitemid 27288192)
8. Eder, G., Nachtnebel, H.-P., and, M. Sivapalan, (2006), Water balance modeling with fuzzy parameterizations: Application to an Alpine catchment, in Climate and Hydrology in Mountain Areas, edited by, C. de Jong, D. Collins, and, R. Ranzi, John Wiley, Chichester, U. K., p. 185-214, doi: 10.1002/0470858249. ch10.
9. Faybishenko, B., (2010), Fuzzy-probabilistic calculations of water-balance uncertainty, Stochastic Environ. Res. Risk Assess., 24 (6), 939-952, doi: 10.1007/s00477-010-0379-y.
10. Filev, D. P., and, R. R. Yager, (1997), Operations on fuzzy numbers via fuzzy reasoning, Fuzzy Sets and Systems, 91, 137-142. (Pubitemid 127683708)
11. Freissinet, C., M. Erlich, and, M. Vauclin, (1998), A fuzzy logic-based approach to assess imprecisions of soil water contamination modeling, Soil Till. Res., 47, 11-17, doi: 10.1016/S0167-1987(98)00067-1. (Pubitemid 28324634)
12. Gerla, G., and, L. Scarpati, (1998), Extension principles for fuzzy set theory, J. Inform. Sci., 106, 49-69, doi: 10.1016/S0020-0255(97)10003-2. (Pubitemid 128383789)
13. Guo, S., J. Wang, L. Xiong, A. Ying, and, D. Li, (2002), A macro-scale and semi-distributed monthly water balance model to predict climate change impacts in China, J. Hydrol., 268 (1-4), 1-15, doi: 10.1016/S0022-1694(02)00075- 6. (Pubitemid 35307220)
14. Guo, S., H. Chen, H. Zhang, L. Xiong, P. Liu, B. Pang, G. Wang, and, Y. Wang, (2005), A semi-distributed monthly water balance model and its application in a climate change impact study in the middle and lower yellow river basin, Water Int., 30 (2), 250-260, doi: 10.1080/02508060508691864. (Pubitemid 40856551)
15. Hanss, M., (2002), The transformation method for the simulation and analysis of systems with uncertain parameters, Fuzzy Sets Syst., 130 (3), 277-289, doi: 10.1016/S0165-0114(02)00045-3. (Pubitemid 34862873)
16. Hanss, M., (2004), Applied Fuzzy Arithmetic: An Introduction with Engineering Applications, 256 pp., Springer, Berlin.
17. Huang, Y., X. Chen, Y. P. Li, G. H. Huang, and, T. Liu, (2010), A fuzzy-based simulation method for modelling hydrological processes under uncertainty, Hydrol. Processes, 24 (25), 3718-3732, doi: 10.1002/hyp.7790.
18. Jang, J. S. R., C. T. Sun, and, E. Mizutani, (1996), Neuro-Fuzzy and Soft Computing, Prentice Hall, Englewood Cliffs, N. J.
19. Jiang, T., Y. D. Chen, C. Y. Xu, X. Chen, X. Chen, and, V. P. Singh, (2007), Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongxiang Basin, South China, J. Hydrol., 336 (3-4), 316-333, doi: 10.1016/j.jhydrol.2007.01.010. (Pubitemid 46420331)
20. Jin, X., C. Y. Xu, Q. Zhang, and, V. P. Singh, (2010), Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model, J. Hydrol., 383 (3-4), 147-155, doi: 10.1016/j.jhydrol.2009.12.028.
21. Juang, C. H., X. H. Huang, and, D. J. Elton, (1991), Fuzzy information processing by the Monte Carlo simulation technique, Civ. Eng. Syst., 8 (1), 19-25, doi: 10.1080/02630259108970602. (Pubitemid 21680682)
22. Klimke, A., K. Willner, and, B. I. Wohlmuth, (2004), Uncertainty modeling using fuzzy arithmetic based on sparse grids: Applications to dynamic systems, Int. J. Uncertain. Fuzz., 12 (6), 745-760, doi: 10.1142/S0218488504003181. (Pubitemid 40493394)
23. Kosko, B. A., (1990), Fuzziness vs. probability, Int. J. Gen. Syst., 17 (2-3), 211-240, doi: 10.1080/03081079008935108.
24. Lu, L., J. Xia, C. Y. Xu, and, V. P. Singh, (2010), Evaluation of subjective factors of the GLUE and comparison with the formal Bayesian method in uncertainty assessment of hydrological models, J. Hydrol., 390 (3-4), 210-221, doi: 10.1016/j.jhydrol.2010.06.044.
25. Maskey, S., V. Guinot, and, R. K. Price, (2004), Treatment of precipitation uncertainty in rainfall runoff modeling: A fuzzy set approach, Adv. Water Resour., 27, 889-898, doi: 10.1016/j.advwatres.2004.07.001. (Pubitemid 39437057)
26. Mantovan, P., and, E. Todini, (2006), Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology, J. Hydrol., 330 (1-2), 368-361, doi: 10.1016/j.jhydrol.2006.04.046. (Pubitemid 44528546)
27. Montanari, A., (2005), Large sample behaviors of the generalized likelihood uncertainty estimation (GLUE) in assessing the uncertainty of rainfall-runoff simulations, Water Resour. Res., 41, W08406, doi: 10.1029/2004WR003826. (Pubitemid 41393335)
28. Montanari, A., (2007), What do we mean by 'uncertainty'? The need for a consistent wording about uncertainty assessment in hydrology, Hydrol. Processes, 21 (6), 841-845, doi: 10.1002/hyp.6623. (Pubitemid 46470747)
29. Perrin, C., C. Michel, and, V. Andréassian, (2001), Does a large number of parameters enhance model performance? Comparative assessment of common catchment model structures on 429 catchments, J. Hydrol., 242 (3-4), 275-301, doi: 10.1016/S0022-1694(00)00393-0. (Pubitemid 32169968)
30. Schulz, K., and, B. Huwe, (1997), Water flow modeling in the unsaturatedzone with imprecise parameters using a fuzzy approach, J. Hydrol., 201, 211-229, doi: 10.1016/S0022-1694(97)00038-3. (Pubitemid 28037761)
31. Schulz, K., and, B. Huwe, (1999), Uncertainty and sensitivity analysis of water transportmodeling in a layered soil profile using fuzzy set theory, J. Hydroinform., 1 (2), 127-138.
32. Stedinger, J. R., R. M. Vogel, S. U. Lee, and, R. Batchelder, (2008), Appraisal of the generalized likelihhod uncertainty estimation (GLUE), Water Resour. Res., 44, W00B06, doi: 10.1029/2008WR006822.
33. Wang, W. J., and, C. H. Chiu, (1999), Entropy variation on the fuzzy numbers with arithmetic operations, Fuzzy Sets Syst., 103 (3), 443-455.
34. Xu, C., and, V. P. Singh, (1998), A review on monthly water balance models for water resources investigations, Water Resour. Manage., 12 (1), 31-50, doi: 10.1023/A:1007916816469.
35. Zadeh, L. A., (1965), Fuzzy sets, Inf. Control, 8, 338-353.
36. Zadeh, L. A., (1975), The concept of a linguistic variable and its application to approximate reasoning, Inf. Sci., 8 (3), 199-249,doi: 10.1016/0020-0255(75)90036-5.
37. Zhang, Y., G. Wang, and, F. Su, (1996), The general theory for response analysis of stochastic dynamic systems, Fuzzy Sets Syst., 83, 369-405, doi: 10.1016/0165-0114(95)00283-9. (Pubitemid 126667514)
38. Zimmermann, H. J., (1991), Fuzzy Set Theory: And Its Applications, 2nd ed., 399 pp., Kluwer Acad., Boston.