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

Abstract

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.

Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty

“…Tang et al [185,186] Heihe River Basin Li and Guo [107], Li et al [109,111] and Zhang et al [231] Heshui River Basin Li et al [117], Liu et al [128,132] and Xu et al [212] Huai River Basin Gu et al [73] and Li et al [112] Hun River Xu et al [215,216] Kaidu-Kongque River Basin Huang et al [88,90], Li et al [125], Zeng et al [222,224,[226][227][228][229] and Zhou et al [242] Lake Tai Watershed Liu et al [134] and Xu and Huang [217] Miyun Reservoir Han et al [81] and Rong et al [175] Nansihu Lake Basin Xie et al [207,209] Tarim River Basin Huang et al [88][89][90] Three Gorges Reservoir Feng et al [58], Han et al [79], Han et al [87], Huang et al [91], Li et al [126], Xu et al [211], Yuan et al [220] and Zhang et al [236] Xiangxi River Basin Han et al [79], Hu et al [86,87], Huang et al …”

“…where the solution is constrained by and must adhere to quality targets [17,42,91]). The mathematical programming techniques applied in this research include linear programming [80,103,178,197], nonlinear programming [17,91,121,150,155,206], dynamic programming [138,174,241], stochastic programming [33,42,70,99,128,139,141,187,207,208,224,225,240], and quadratic programming [86,113].…”

“…A traditional approach for modelling parameter uncertainty within a model is to use probability distributions [102]; however, the complexity of hydrological models can make estimation of these distributions difficult [201,213]. The computational burden of stochasticity and the difficulty of parameter estimation have been addressed in a number of ways including, interval programming [86,99,150,217], inexact programming [86,113,126,208], possibilistic and fuzzy methodologies [99,128,224,225,235,237], and constraint flexibility [206]. Some authors have used a combination of these techniques.…”

A Heuristic Projection Pursuit Method Based on a Connection Cloud Model and Set Pair Analysis for Evaluation of Slope Stability

“…The foraging behavior of individuals is different from each other when flying compared to the optimal individual. Such deviations can lead to fuzziness being inherent in the real-world optimization problems, neglect of which can cause the solutions of the issues to deviate significantly from their actual situation [32]. Thus, the MSFOA and IFFO may inevitably affect the capability of showing the structure of high-dimensional problems.…”

Fuzzy Techniques for Decision Making

“…Applications to project delivery systems [6], maintenance performance in industry [8], group emergencies [10], pedestrians flows [11], valuation of assets [13], water pollution control [17], or aquaculture enterprise sustainability [19].…”