A Recourse-Based Type-2 Fuzzy Programming Method for Water Pollution Control under Uncertainty

Jing Liu,Lianrong Chen,Guohe Huang,Yongping Li

doi:10.3390/sym9110265

Jing Liu, Lianrong Chen + Show 2 more

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https://doi.org/10.3390/sym9110265

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Abstract

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.

Highlights

The trade-off between water pollution control and economic development is of great concern in many basins since it is essential to local sustainable development [1,2]
A recourse-based type-2 fuzzy programming (RTFP) approach is developed for water pollution control planning
A recourse-based type-2 fuzzyhas programming approach isofdeveloped for water programming and two-stage stochastic programming with recourse (TSP)

Summary

Introduction

The trade-off between water pollution control and economic development is of great concern in many basins since it is essential to local sustainable development [1,2]. It is difficult to keep the economy growing under the utilization of water resources and the deterioration of environmental conditions [3,4]. It is hard to promote human society improvement if the authorities excessively restrict economic development. Under such a contradictory situation, optimization techniques are proper to detect the economic and environmental impacts of alternative pollution control actions from a system point of view, and aid the authorities in formulating and adopting cost-effective water pollution plans and policies. Water pollution control planning is governed by significant sources of uncertainty associated with different variables, and uncertainty is a non-negligible constituent of such a procedure [5]. There are significant uncertainties in how the system might develop, and in how the system is expected to adjust when many system components are altered (e.g., pollutant discharge amount, cost/benefit coefficient and economic activity scale)

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Results

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