A Fuzzy Robust Nonlinear Programming Model for Stream Water Quality Management

Beijing Normal University Chinese Research Academy of Environmental Science Beijing 100875 China
Water Resources Management (Impact Factor: 2.6). 11/2009; 23(14):2913-2940. DOI: 10.1007/s11269-009-9416-3

ABSTRACT An interval-parameter fuzzy robust nonlinear programming (IFRNP) approach was developed for stream water quality management
under uncertainty. The interval and fuzzy robust programming methods were incorporated within a general framework to address
uncertainties associated with the nonlinear objective and the left- and right-hand sides of the constraints. A piecewise linearization
approach was developed to deal with the nonlinear cost function. IFRNP could explicitly address complexities of various system
uncertainties, where parameters were represented as both interval numbers and fuzzy membership functions. Furthermore, the
dual uncertain information associated with the lower and upper bounds of each interval parameter could be effectively tackled
through the concept of fuzzy boundary interval. The proposed IFRNP method was applied to a case of water quality management
in the Guoyang section of the Guo River in Anhui province, China. A number of cost-effective schemes for water quality management
were generated, and allowable wastewater discharge amounts were recommended. The results indicated that IFRNP was applicable
to water quality management problems, where high nonlinearities and dual uncertainties exist.

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    • "Sasikumar & Mujumdar (1998, 2000) and Mujumdar & Sasikumar (2002) have addressed the uncertainty due to imprecision as well as randomness in a multiobjective framework. Fuzzy logic has been used for water quality management to model imprecision by Zhu et al. (2009) and Lermontov et al. (2009). Recently, uncertainty resulting from the inexactness of parameter values in water quality management models has been addressed in Karmakar & Mujumdar (2007) and Nie et al. (2008). "
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