A Recourse-Based Type-2 Fuzzy Programming Method for Water Pollution Control under Uncertainty
1
Department of Environmental Engineering, Xiamen University of Technology, Xiamen 361024, China
2
Sino-Canada Energy and Environmental Research Center, North China Electric Power University, Beijing 102206, China
*
Author to whom correspondence should be addressed.
Symmetry 2017, 9(11), 265; https://doi.org/10.3390/sym9110265
Received: 29 September 2017 / Revised: 29 October 2017 / Accepted: 31 October 2017 / Published: 4 November 2017
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making)
In this study, a recourse-based type-2 fuzzy programming (RTFP) method is developed for supporting water pollution control of basin systems under uncertainty. The RTFP method incorporates type-2 fuzzy programming (TFP) within a two-stage stochastic programming with recourse (TSP) framework to handle uncertainties expressed as type-2 fuzzy sets (i.e., a fuzzy set in which the membership function is also fuzzy) and probability distributions, as well as to reflect the trade-offs between conflicting economic benefits and penalties due to violated policies. The RTFP method is then applied to a real case of water pollution control in the Heshui River Basin (a rural area of China), where chemical oxygen demand (COD), total nitrogen (TN), total phosphorus (TP), and soil loss are selected as major indicators to identify the water pollution control strategies. Solutions of optimal production plans of economic activities under each probabilistic pollutant discharge allowance level and membership grades are obtained. The results are helpful for the authorities in exploring the trade-off between economic objective and pollutant discharge decision-making based on river water pollution control.
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Keywords:
recourse; River Basin; stochastic; type-2 fuzzy; uncertainty; water pollution control
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MDPI and ACS Style
Liu, J.; Li, Y.; Huang, G.; Chen, L. A Recourse-Based Type-2 Fuzzy Programming Method for Water Pollution Control under Uncertainty. Symmetry 2017, 9, 265. https://doi.org/10.3390/sym9110265
AMA Style
Liu J, Li Y, Huang G, Chen L. A Recourse-Based Type-2 Fuzzy Programming Method for Water Pollution Control under Uncertainty. Symmetry. 2017; 9(11):265. https://doi.org/10.3390/sym9110265
Chicago/Turabian StyleLiu, Jing; Li, Yongping; Huang, Guohe; Chen, Lianrong. 2017. "A Recourse-Based Type-2 Fuzzy Programming Method for Water Pollution Control under Uncertainty" Symmetry 9, no. 11: 265. https://doi.org/10.3390/sym9110265
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