Mathematical Modeling for Water Quality Management under Interval and Fuzzy Uncertainties

Abstract

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.

An Interval Fuzzy-Stochastic Chance-Constrained Programming Based Energy-Water Nexus Model for Planning Electric Power Systems

“…c ± j is a trapezoidal or triangular fuzzy variable that can be expressed as c [35]. The expected values of c ± j can be calculated as EV( c…”

Different optimisation tasks used in water quality management

“…In the optimisation task (OT) where the objective function takes the form of a sum of CVs, the function is minimised against some constraints [11]. The task may have the following form:…”

“…level of pollution reduction coefficients and the same constrains for BODt and DO showed that different total BODt loads (∑Ł) would be introduced to the water in the hydrographic network ( Table 1). The largest BODt loads are associated with the tasks (5-7) and (9)(10)(11) and are 824.38 and 787.40g O 2 BODt/s, respectively (Table 1). These are tasks that attempt to maximise the pollution loads introduced to the network -they allow to utilise the transformation possibilities of the analysed pollutants through the aquatic environment to the highest extent.…”

“…Another approach for the management of water quality is fuzzy programming-this is not analysed in this paper [10][11][12].…”

A Comparative Assessment on Soil Environment Quality Based on Chemical Analyses of Heavy Metals

“…However, in all environmental quality assessments, owing to inconsistency and peculiarities of each soil pollutant, there is a vagueness or fuzziness in relation to environmental risk [14,15]. In classification schemes, fuzziness makes it difficult to justify the use of sharp boundaries.…”