Interactive two-stage stochastic fuzzy programming for water resources management

In this study, an interactive two-stage stochastic fuzzy programming (ITSFP) approach has been developed through incorporating an interactive fuzzy resolution (IFR) method within an inexact two-stage stochastic programming (ITSP) framework. ITSFP can not only tackle dual uncertainties presented as fuzzy boundary intervals that exist in the objective function and the left- and right-hand sides of constraints, but also permit in-depth analyses of various policy scenarios that are associated with different levels of economic penalties when the promised policy targets are violated. A management problem in terms of water resources allocation has been studied to illustrate applicability of the proposed approach. The results indicate that a set of solutions under different feasibility degrees has been generated for planning the water resources allocation. They can help the decision makers (DMs) to conduct in-depth analyses of tradeoffs between economic efficiency and constraint-violation risk, as well as enable them to identify, in an interactive way, a desired compromise between satisfaction degree of the goal and feasibility of the constraints (i.e., risk of constraint violation).     

An interval-based regret-analysis method for identifying long-term municipal solid waste management policy under uncertainty

In this study, an interval-based regret-analysis (IBRA) model is developed for supporting long-term planning of municipal solid waste (MSW) management activities in the City of Changchun, the capital of Jilin Province, China. The developed IBRA model incorporates approaches of interval–parameter programming (IPP) and minimax–regret (MMR) analysis within an integer programming framework, such that uncertainties expressed as both interval values and random variables can be reflected. The IBRA can account for economic consequences under all possible scenarios associated with different system costs and risk levels without making assumptions on probabilistic distributions for random variables. A regret matrix with interval elements is generated based on a matrix of interval system costs, such that desired decision alternatives can be identified according to the interval minimax regret (IMMR) criterion. The results indicate that reasonable solutions have been generated. They can help decision makers identify the desired alternatives regarding long-term MSW management with a compromise between minimized system cost and minimized system-failure risk.     

Inexact credibility constrained programming for environmental system management

This study proposed an inexact credibility constrained programming (ICCP) to deal with multi-formats of uncertainties in parameters and variables for an agricultural water planning system. The study system includes three subareas with different crop distributions. The redundant water in the wet season can be stored in the reservoir and utilized in the dry season. The ICCP method can reflect not only inexact uncertainties in the objective function, variables and parameters, but also fuzzy uncertainties in the right-hand side. Interval credibility levels which represent satisfaction degrees of the constraints can be analyzed. Scenario analysis is conducted to analyze possible events in wet and dry years. The resulting solutions can provide stable intervals for the objective function and decision variables with different levels of risk when violating the constraints.     

A two-stage support-vector-regression optimization model for municipal solid waste management - a case study of Beijing, China

In this study, a two-stage support-vector-regression optimization model (TSOM) is developed for the planning of municipal solid waste (MSW) management in the urban districts of Beijing, China. It represents a new effort to enhance the analysis accuracy in optimizing the MSW management system through coupling the support-vector-regression (SVR) model with an interval-parameter mixed integer linear programming (IMILP). The developed TSOM can not only predict the city's future waste generation amount, but also reflect dynamic, interactive, and uncertain characteristics of the MSW management system. Four kernel functions such as linear kernel, polynomial kernel, radial basis function, and multi-layer perception kernel are chosen based on three quantitative simulation performance criteria [i.e. prediction accuracy (PA), fitting accuracy (FA) and over all accuracy (OA)]. The SVR with polynomial kernel has accurate prediction performance for MSW generation rate, with all of the three quantitative simulation performance criteria being over 96%. Two cases are considered based on different waste management policies. The results are valuable for supporting the adjustment of the existing waste-allocation patterns to raise the city's waste diversion rate, as well as the capacity planning of waste management system to satisfy the city's increasing waste treatment/disposal demands.     

Using biological data from field studies with multiple reference sites as a basis for environmental management: the risks for false positives and false negatives

Field surveys of biological responses can provide valuable information about environmental status and anthropogenic stress. However, it is quite usual for biological variables to differ between sites or change between two periods of time also in the absence of an impact. This means that there is an obvious risk that natural variation will be interpreted as environmental impact, or that relevant effects will be missed due to insufficient statistical power. Furthermore, statistical methods tend to focus on the risks for Type-I error, i.e. false positives. For environmental management, the risk for false negatives is (at least) equally important. The aim of the present study was to investigate how the probabilities for false positives and negatives are affected by experimental set up (number of reference sites and samples per site), decision criteria (statistical method and α-level) and effect size. A model was constructed to simulate data from multiple reference sites, a negative control and a positive control. The negative control was taken from the same distribution as the reference sites and the positive control was just outside the normal range. Using the model, the probabilities to get false positives and false negatives were calculated when a conventional statistical test, based on a null hypothesis of no difference, was used along with alternative tests that were based on the normal range of natural variation. Here, it is tested if an investigated site is significantly inside (equivalence test) and significantly outside (interval test) the normal range. Furthermore, it was tested how the risks for false positives and false negatives are affected by changes in α-level and effect size. The results of the present study show that the strategy that best balances the risks between false positives and false negatives is to use the equivalence test. Besides tests with tabulated p-values, estimates generated using a bootstrap routine were included in the present study. The simulations showed that the probability for management errors was smaller for the bootstrap compared to the traditional test and the interval test.     

An interval type-2 fuzzy stochastic approach for regional-scale electric power system under parameter uncertainty

In this study, an interval type-2 fuzzy stochastic linear programming method (IT2FSLP) is developed to support regional-scale electric power system (REM) planning. The IT2FSLP-REM model is based on an integration of interval type-2 fuzzy sets boundary programming and stochastic linear programming techniques enable it to have robust abilities to the deal with uncertainties expressed as type-2 fuzzy intervals and probabilistic distributions within a general optimization framework. Moreover, it can reflect dynamic decisions for energy supply and energy conversion processes, as well as provide capacity expansion options with multiple periods. The developed model is applied to a case of planning regional-scale energy and environmental systems to demonstrate its applicability. Based on a two-step solution algorithm, reasonable solutions have been obtained, which reflect tradeoffs among economic cost, environmental requirements, and energy-supply security. Thus, the lower and upper solutions of IT2FSLP-REM would then help energy authorities adjust or justify allocation patterns of regional energy resources and services.     

基于χ~2优化方法的铸钢侧架原始裂纹尺寸分布研究

将铸钢侧架清砂后未经修复的原始裂纹尺寸进行了统计 ,综合运用参数的点估计方法和区间估计方法 ,以置信区间作为优化的约束条件 ,提出了对检验值进行最优化处理的方法 ,并运用二参数约束非线性优化方法的直接解法 ,搜索出最佳点估计值。经过对裂纹尺寸分布参数的计算证明 ,其结果符合对数正态分布     

Statistical Methods and Pitfalls in Environmental Data Analysis

This paper reviews four commonly used statistical methods for environmental data analysis and discusses potential pitfalls associated with application of these methods through real case study data. The four statistical methods are percentile and confidence interval, correlation coefficient, regression analysis, and analysis of variance (ANOVA). The potential pitfall for estimation of percentile and confidence interval includes the automatic assumption of a normal distribution to environmental data, which so often show a log-normal distribution. The potential pitfall for correlation coefficient includes the use of a wide range of data points in which the maximum in value may trivialize other smaller data points and consequently skew the correlation coefficient. The potential pitfall for regression analysis includes the propagation of uncertainties of input variables to the regression model prediction, which may be even more uncertain. The potential pitfall for ANOVA includes the acceptance of a hypothesis as a weak argument to imply a strong conclusion. As demonstrated in this paper, we may draw very different conclusions based on statistical analysis if the pitfalls are not identified. Reminder and enlightenment obtained from the pitfalls are given at the end of this article.     

区间模糊优化在电厂动力配煤技术中的应用

电厂配煤是一项通过混合多种不同品质的原煤来最终达到锅炉燃烧要求的一项技术,动力配煤往往是世界上很多电厂运行过程中一个复杂的优化问题,而优化过程中的模糊性与不确定性往往困扰着电厂的运营者,这篇文章中建立了一种区间模糊模型来解决配煤中的模糊不确定性问题,同时也解决了不同脱硫效率对煤质要求的影响的问题。这种方法可以有效的使电厂充分利用多种煤资源尤其是高硫煤资源,高硫煤不仅价格便宜．而且在很多煤矿中储量很大,在满足环境要求的同时,既降低成本,又充分利用了国家有限的自然资源。     

集对分析在湖泊富营养化评价中的应用研究——区间数与三角模糊数组合的集对分析

针对湖泊富营养化评价的不确定性型多属性决策问题,提出了基于区间数与三角模糊数组合的集对分析模型,引入简单关联函数来确定指标的权重,详细介绍了湖泊富营养化评价的基本原理和关于区间数、三角模糊数转化为集对分析联系数的表示方法。通过计算联系数的模以及属性等级模与属性值模的同一度,再利用这些同一度并参照属性等级数n建立n元联系数,再建立等级与联系数的映射关系确定评价等级。应用该模型对我国9个湖泊的富营养化程度进行了评价,该方法的评价结果与实际情况相符,为湖泊富营养化的治理和保护提供了技术支持。