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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 731568, 14 pages
Research Article

Mathematical Modeling for Water Quality Management under Interval and Fuzzy Uncertainties

MOE Key Laboratory of Regional Energy Systems Optimization, Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206, China

Received 4 October 2013; Accepted 29 November 2013

Academic Editor: X. S. Qin

Copyright © 2013 J. Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this study, an interval fuzzy credibility-constrained programming (IFCP) method is developed for river water quality management. IFCP is derived from incorporating techniques of fuzzy credibility-constrained programming (FCP) and interval-parameter programming (IPP) within a general optimization framework. IFCP is capable of tackling uncertainties presented as interval numbers and possibility distributions as well as analyzing the reliability of satisfying (or the risk of violating) system’s constraints. A real-world case for water quality management planning of the Xiangxi River in the Three Gorges Reservoir Region (which faces severe water quality problems due to pollution from point and nonpoint sources) is then conducted for demonstrating the applicability of the developed method. The results demonstrate that high biological oxygen demand (BOD) discharge is observed at the Baishahe chemical plant and Gufu wastewater treatment plant. For nonpoint sources, crop farming generates large amounts of total phosphorus (TP) and total nitrogen (TN). The results are helpful for managers in not only making decisions of effluent discharges from point and nonpoint sources but also gaining insight into the tradeoff between system benefit and environmental requirement.