REFERENCES
- Abebe, A.J., Guinot, V., and Solomatine, D.P., 2000. Fuzzy alpha-cut vs Monte Carlo techniques in assessing uncertainty in model parameters. In: Paper presented at Proceedings of the 4th international conference on hydroinformatics, 23–27 July, Iowa City, IA. Cedar Rapids: University of Iowa, College of Engineering. ISBN-10: 0874141249; ISBN-13: 978-0874141245.
- Alberta Environment Protection, 1997. Alberta water quality guideline for the protection of freshwater aquatic life: dissolved oxygen. Edmonton, Alberta, Canada: Standards and Guidelines Branch, Alberta Environment, Catalogue #: ENV-0.94–OP.
- Alberta Environment River Basins, 2012. Bow River at Calgary [online]. Available from: http://www.environment.alberta.ca/apps/basins/DisplayData.aspx?Type=Figure&BasinID=8&DataType=1&StationID=RBOWCALG [Accessed 5 April 2013].
- Altunkaynak, A., Özger, M., and Çakmakcı, M., 2005. Fuzzy logic modeling of the dissolved oxygen fluctuations in Golden Horn. Ecological Modelling, 189 (3–4), 436–446. doi:10.1016/j.ecolmodel.2005.03.007
- Alvisi, S., et al., 2006. Water level forecasting through fuzzy logic and artificial neural network approaches. Hydrology and Earth System Sciences, 10 (1), 1–17. doi:10.5194/hess-10-1-2006
- Alvisi, S. and Franchini, M., 2011. Fuzzy neural networks for water level and discharge forecasting with uncertainty. Environmental Modelling & Software, 26 (4), 523–537. doi:10.1016/j.envsoft.2010.10.016
- Bárdossy, A., 1990. Note on fuzzy regression. Fuzzy Sets and Systems, 37 (1), 65–75. doi:10.1016/0165-0114(90)90064-D
- Bardossy, A., Bogardi, I., and Duckstein, L., 1990. Fuzzy regression in hydrology. Water Resources Research, 26 (7), 1497–1508. doi:10.1029/WR026i007p01497
- Bargiela, A., Pedrycz, W., and Nakashima, T., 2007. Multiple regression with fuzzy data. Fuzzy Sets and Systems, 158 (19), 2169–2188. doi:10.1016/j.fss.2007.04.011
- Bisserier, A., Boukezzoula, R., and Galichet, S., 2009. An interval approach for fuzzy linear regression with imprecise data. In: J.P. Carvalho, et al., eds. Proceedings of the joint 2009 international fuzzy systems association world congress & 2009 European society of fuzzy logic and technology conference, 20–24 July, Lisbon. Lisbon: EUSFLAT, 1305–1310. ISBN 978-989-95079-6-8.
- Celmiņš, A., 1987. Least squares model fitting to fuzzy vector data. Fuzzy Sets and Systems, 22 (3), 245–269. doi:10.1016/0165-0114(87)90070-4
- Chachi, J., Taheri, S.M., and Pazhand, H.R., 2011. An interval-based approach to fuzzy regression for fuzzy input-output data. Paper presented at 2011 IEEE International Conference on Fuzzy Systems, Taipei. Taiwan: IEEE, 2859–2863. doi:10.1109/FUZZY.2011.6007457
- Chang, Y.-H.O. and Ayyub, B.M., 2001. Fuzzy regression methods—a comparative assessment. Fuzzy Sets and Systems, 119 (2), 187–203. doi:10.1016/S0165–0114(99)00091–3
- Chen, Z., Huang, G.H., and Chakma, A., 2003. Hybrid fuzzy-stochastic modeling approach for assessing environmental risks at contaminated groundwater systems. Journal of Environmental Engineering, 129 (1), 79–88. doi:10.1061/(ASCE)0733-9372(2003)129:1(79)
- Di Baldassarre, G. and Montanari, A., 2009. Uncertainty in river discharge observations: a quantitative analysis. Hydrology and Earth System Sciences, 13 (6), 913–921. doi:10.5194/hess-13-913-2009
- Diamond, P., 1988. Fuzzy least squares. Information Sciences, 46 (3), 141–157. doi:10.1016/0020-0255(88)90047-3
- Dou, C., et al., 1997. Numerical solute transport simulation using fuzzy sets approach. Journal of Contaminant Hydrology, 27 (1–2), 107–126. doi:10.1016/S0169-7722(96)00047-2
- Dubois, D., et al., 2004. Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Reliable Computing, 10, 273–297. doi:10.1023/B:REOM.0000032115.22510.b5
- Dubois, D. and Prade, H., 1980. Fuzzy sets and systems: theory and applications. New York, NY: Academic Press.
- Dubois, D. and Prade, H., 1988. Possibility theory: an approach to computerized processing of uncertainty. New York, NY: Plenum Press.
- Dubois, D., Prade, H., and Sandri, S., 1993. On possibility/probability transformations. In: R. Lowen and M. Roubens, eds. Fuzzy logic. Dordrecht, Netherlands: Kluwer Academic Publishers, 103–112.
- Duch, W., 2005. Uncertainty of data, fuzzy membership functions, and multilayer perceptrons. IEEE Transactions on Neural Networks, 16 (1), 10–23. doi:10.1109/TNN.2004.836200
- Environment Canada Water Office, 2013. Bow River at Calgary [online]. Available from: http://www.wateroffice.ec.gc.ca/graph/graph_e.html?stn=05BH004 [Accessed 5 April 2013].
- Freissinet, C., Vauclin, M., and Erlich, M., 1999. Comparison of first-order analysis and fuzzy set approach for the evaluation of imprecision in a pesticide groundwater pollution screening model. Journal of Contaminant Hydrology, 37 (1–2), 21–43. doi:10.1016/S0169-7722(98)00163-6
- Giusti, E. and Marsili-Libelli, S., 2009. Spatio-temporal dissolved oxygen dynamics in the Orbetello Lagoon by fuzzy pattern recognition. Ecological Modelling, 220 (19), 2415–2426. doi:10.1016/j.ecolmodel.2009.06.007
- Guan, J. and Aral, M.M., 2004. Optimal design of groundwater remediation systems using fuzzy set theory. Water Resources Research, 40, W01518. doi:10.1029/2003WR002121
- Guyonnet, D., et al., 2003. Hybrid approach for addressing uncertainty in risk assessments. Journal of Environmental Engineering, 129 (1), 68–78. doi:10.1061/(ASCE)0733-9372(2003)129:1(68)
- Han, J.C., et al., 2013. Optimal land use management for soil erosion control by using an interval-parameter fuzzy two-stage stochastic programming approach. Environmental Management, 52, 621–638. doi:10.1007/s00267-013-0122-9.
- Hauer, F.R. and Hill, W.R., 2007. Temperature, light and oxygen. In: F.R. Hauer and G.A. Lamberti, eds. Methods in stream ecology. San Diego, CA: Academic Press, 103–117.
- He, J., et al., 2011. Abiotic influences on dissolved oxygen in a riverine environment. Ecological Engineering, 37 (11), 1804–1814. doi:10.1016/j.ecoleng.2011.06.022
- Hermann, G., 2011. Various approaches to measurement uncertainty: a comparison. Paper presented at 2011 IEEE 9th international symposium on intelligent systems and informatics, Subotica. Serbia: IEEE, 377–380. doi:10.1109/SISY.2011.6034356.
- Hojati, M., Bector, C.R., and Smimou, K., 2005. A simple method for computation of fuzzy linear regression. European Journal of Operational Research, 166 (1), 172–184. doi:10.1016/j.ejor.2004.01.039
- Huang, Y., et al., 2010. A fuzzy-based simulation method for modelling hydrological processes under uncertainty. Hydrological Processes, 24 (25), 3718–3732. doi:10.1002/hyp.7790
- Kahraman, C., Beşkese, A., and Bozbura, F.T., 2006. Fuzzy regression approaches and applications. In: C. Kahraman, ed. Fuzzy applications in industrial engineering. Berlin, Germany: Springer, 589–615.
- Kao, C. and Chyu, C.-L., 2003. Least-squares estimates in fuzzy regression analysis. European Journal of Operational Research, 148 (2), 426–435. doi:10.1016/S0377-2217(02)00423-X
- Kaufmann, A. and Gupta, M.M., 1984. Introduction to fuzzy arithmetic: theory and applications. New York, NY: VanNostrand Reinhold.
- Kentel, E. and Aral, M.M., 2004. Probabilistic-fuzzy health risk modeling. Stochastic Environmental Research and Risk Assessment, 18 (5), 324–338. doi:10.1007/s00477-004-0187-3
- Khan, U.T., Valeo, C., and He, J., 2013. Non-linear fuzzy-set based uncertainty propagation for improved DO prediction using multiple-linear regression. Stochastic Environmental Research and Risk Assessment, 27 (3), 599–616. doi:10.1007/s00477-012-0626-5
- Kim, K.J., Moskowitz, H., and Koksalan, M., 1996. Fuzzy versus statistical linear regression. European Journal of Operational Research, 92 (2), 417–434. doi:10.1016/0377-2217(94)00352-1
- Kumar, V., Schuhmacher, M., and García, M., 2006. Integrated fuzzy approach for system modeling and risk assessment. In: V. Torra, Y. Narukawa, A. Valls and J. Domingo-Ferrer, eds. Modeling decisions for artificial intelligence. Berlin, Germany: Springer, 227–238. doi:10.1007/11681960_23
- Lee, H.T. and Chen, S.H., 2001. Fuzzy regression model with fuzzy input and output data for manpower forecasting. Fuzzy Sets and Systems, 119 (2), 205–213. doi:10.1016/S0165-0114(98)00382-0
- Maskey, S., Guinot, V., and Price, R.K., 2004. Treatment of precipitation uncertainty in rainfall–runoff modelling: a fuzzy set approach. Advances in Water Resources, 27 (9), 889–898. doi:10.1016/j.advwatres.2004.07.001
- McMillan, H., et al., 2010. Impacts of uncertain river flow data on rainfall‐runoff model calibration and discharge predictions. Hydrological Processes, 24 (10), 1270–1284. doi:10.1002/hyp.7587
- Mujumdar, P.P. and Sasikumar, K., 2002. A fuzzy risk approach for seasonal water quality management of a river system. Water Resources Research, 38 (1), 5.1–5.9. doi:10.1029/2000WR000126
- Nasrabadi, M.M. and Nasrabadi, E., 2004. A mathematical-programming approach to fuzzy linear regression analysis. Applied Mathematics and Computation, 155 (3), 873–881. doi:10.1016/j.amc.2003.07.031
- Novák, V., 1989. Fuzzy sets and their applications. Bristol, UK: Adam Hilger.
- Peters, G., 1994. Fuzzy linear regression with fuzzy intervals. Fuzzy Sets and Systems, 63 (1), 45–55. doi:10.1016/0165-0114(94)90144-9
- Pogue, T.R. and Anderson, C.W., 1995. Factors controlling dissolved oxygen and pH in the upper Willamette River and major tributaries. Oregon, USA: US Geological Survey Water Resources Investigations Report 95–4205.
- Porter, D.W., et al., 2000. Data fusion modeling for groundwater systems. Journal of Contaminant Hydrology, 42 (2–4), 303–335. doi:10.1016/S0169-7722(99)00081-9
- Savic, D.A. and Pedrycz, W., 1991. Evaluation of fuzzy linear regression models. Fuzzy Sets and Systems, 39 (1), 51–63. doi:10.1016/0165-0114(91)90065-X
- Shiklomanov, A.I., et al., 2006. Cold region river discharge uncertainty—Estimates from large Russian rivers. Journal of Hydrology, 326 (1–4), 231–256. doi:10.1016/j.jhydrol.2005.10.037
- Shrestha, R.R. and Nestmann, F., 2009. Physically based and data-driven models and propagation of input uncertainties in river flood prediction. Journal of Hydrologic Engineering, 14 (12), 1309–1319. doi:10.1061/(ASCE)HE.1943-5584.0000123
- Shrestha, R.R., Bárdossy, A., and Nestmann, F., 2007. Analysis and propagation of uncertainties due to the stage–discharge relationship: a fuzzy set approach. Hydrological Sciences Journal, 52 (4), 595–610. doi:10.1623/hysj.52.4.595
- Tanaka, H., Uejima, S., and Asai, K., 1982. Linear regression analysis with fuzzy model. IEEE Transactions on Systems, Man and Cybernetics, 12 (6), 903–907. doi:10.1109/TSMC.1982.4308925
- Wang, S., et al., 2011. An interval-valued fuzzy linear programming with infinite α-cuts method for environmental management under uncertainty. Stochastic Environmental Research and Risk Assessment, 25 (2), 211–222. doi: 10.1007/s00477-010-0432-x
- Wang, S. and Huang, G.H., 2012. Identifying optimal water resources allocation strategies through an interactive multi-stage stochastic fuzzy programming approach. Water Resources Management, 26 (7), 2015–2038. doi:10.1007/s11269-012-9996-1
- Wang, S. and Huang, G.H., 2013a. An interval-parameter two-stage stochastic fuzzy program with type-2 membership functions: an application to water resources management. Stochastic Environmental Research and Risk Assessment, 27, 1493–1506. doi:10.1007/s00477-013-0685-2.
- Wang, S. and Huang, G.H., 2013b. A two-stage mixed-integer fuzzy programming with interval-valued membership functions approach for flood-diversion planning. Journal of Environmental Management, 117, 208–218. doi:10.1016/j.jenvman.2012.12.037.
- Wang, S., Huang, G.H., and Yang, B.T., 2012. An interval-valued fuzzy-stochastic programming approach and its application to municipal solid waste management. Environmental Modelling & Software, 29 (1), 24–36. doi:10.1016/j.envsoft.2011.10.007
- Xia, X., Wang, Z., and Gao, Y., 2000. Estimation of non-statistical uncertainty using fuzzy-set theory. Measurement Science and Technology, 11 (4), 430–435. doi:10.1088/0957-0233/11/4/314
- Yang, M.S. and Lin, T.S., 2002. Fuzzy least-squares linear regression analysis for fuzzy input–output data. Fuzzy Sets and Systems, 126 (3), 389–399. doi:10.1016/S0165-0114(01)00066-5
- YSI Environmental, 2012. YSI 5200A continuous multiparameter RAS monitor [Online]. Available from: http://www.ysi.com/media/pdfs/W45-5200A-Continuous-Multiparameter-Monitor.pdf [Accessed 18 April 2013].
- Zadeh, L.A., 1965. Fuzzy sets. Information and Control, 8 (3), 338–353. doi:10.1016/S0019-9958(65)90241-X
- Zadeh, L.A., 1975. The concept of a linguistic variable and its application to approximate reasoning—I. Information Sciences, 8 (3), 199–249. doi:10.1016/0020-0255(75)90036-5
- Zadeh, L.A., 1978. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1 (1), 3–28. doi:10.1016/0165-0114(78)90029-5
- Zhang, K., 2009. Modeling uncertainty and variability in health risk assessment of contaminated sites. Thesis (Ph. D.), Department of Civil Engineering, University of Calgary, Calgary, AB, Canada.
- Zhang, K. and Achari, G., 2010a. Correlations between uncertainty theories and their applications in uncertainty propagation. In: H. Furuta, D.M. Frangopol and M. Shinozuka, eds. Safety, reliability and risk of structures, infrastructures and engineering systems. London, UK: Taylor & Francis Group, 1337–1344. doi:10.1201/9781439847657–c20
- Zhang, K. and Achari, G., 2010b. Uncertainty propagation in environmental decision making using random sets. Procedia Environmental Sciences, 2, 576–584. doi:10.1016/j.proenv.2010.10.063.
- Zhang, K., Li, H., and Achari, G., 2009. Fuzzy-stochastic characterization of site uncertainty and variability in groundwater flow and contaminant transport through a heterogeneous aquifer. Journal of Contaminant Hydrology, 106 (1–2), 73–82. doi:10.1016/j.jconhyd.2009.01.003