Interval-parameter Fuzzy-stochastic Semi-infinite Mixed-integer Linear Programming for Waste Management under Uncertainty

An interval-parameter fuzzy-stochastic semi-infinite mixed-integer linear programming (IFSSIP) method is developed for waste management under uncertainties. The IFSSIP method integrates the fuzzy programming, chance-constrained programming, integer programming and interval semi-infinite programming within a general optimization framework. The model is applied to a waste management system with three disposal facilities, three municipalities, and three periods. Compared with the previous methods, IFSSIP have two major advantages. One is that it can help generate solutions for the stable ranges of the decision variables and objective function value under fuzzy satisfaction degree and different levels of probability of violating constraints, which are informative and flexible for solution users to interpret/justify. The other is that IFSSIP can not only handle uncertainties through constructing fuzzy and random parameter, but also reflect dynamic features of the system conditions through interval function of time over the planning horizon. By comparing IFSSIP with interval-parameter mixed-integer linear semi-infinite programming and parametric programming, the IFSSIP method is more reasonable than others.     

A Superiority-Inferiority-Based Inexact Fuzzy Stochastic Programming Approach for Solid Waste Management Under Uncertainty

A superiority–inferiority-based inexact fuzzy stochastic programming (SI-IFSP) model was developed for planning municipal solid waste management systems under uncertainty. The SI-IFSP approach represents a new attempt to tackle multiple uncertainties in objective function coefficients which are beyond the capabilities of existing inexact programming methods. Through introducing the concept of fuzzy random boundary interval, SI-IFSP is capable of reflecting multiple uncertainties (i.e., interval values, fuzzy sets, probability distributions, and their combinations) in both the objective function and constraints, leading to enhanced system robustness. The developed SI-IFSP method was applied to a case study of long-term municipal solid waste management. Useful solutions were generated. A number of decision alternatives could be generated based on projected applicable conditions, reflecting the compromise between system optimality and reliability as well as the tradeoffs between economic and environmental objectives. Moreover, the consequences of system violations could be quantified through introducing a set of economic penalties, reflecting the relationships between system costs and constraint violation risks. The results suggest that the proposed SI-IFSP method can explicitly address complexities in municipal solid waste management systems and is applicable to practical waste management problems.     

A fuzzy multi-stakeholder multi-criteria methodology for water allocation and reuse in metropolitan areas

In this paper, a fuzzy decision making methodology is proposed to find a socially optimal scenario for allocating effluent of wastewater treatment plants and urban and suburban runoffs to agricultural regions and recharging aquifers. The presented methodology named modified fuzzy social choice (MFSC) considers multi-stakeholder multi-criteria problems under uncertainties inherent in a decision making process utilizing a fuzzy ranking method and the fuzzy social choice (FSC) theory. A set of water and wastewater allocation scenarios are proposed for water quantity and quality management of the study area, while six main stakeholders with conflicting utilities and different negotiation powers are involved. The proposed methodology is applied to Tehran metropolitan area, the capital city of Iran with the population of about 8 million people, to examine its applicability and effectiveness. The results shows that using fuzzy multi-stakeholder multi-criteria decision making method considering equal and different negotiation powers can lead to different outcomes. Based on the results, the MFSC method, which considers a number of decision makers having different negotiation powers, degrees of importance of decision making criteria, and some important uncertainties, performs more promising in real water resources management problems.     

Inexact Fuzzy-Stochastic Programming for Water Resources Management Under Multiple Uncertainties

In this study, an interval-parameter fuzzy-stochastic two-stage programming (IFSTP) approach is developed for irrigation planning within an agriculture system under multiple uncertainties. A concept of the distribution with fuzzy-interval probability (DFIP) is defined to address multiple uncertainties expressed as integration of intervals, fuzzy sets, and probability distributions. IFSTP integrates the interval programming, two-stage stochastic programming, and fuzzy-stochastic programming within a general optimization framework. IFSTP incorporates the pre-regulated water resources management policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised amounts are not delivered. IFSTP is applied to an irrigation planning in a water resources management system. Solutions from IFSTP provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable solutions are generated for objective function values and decision variables; thus, a number of decision alternatives can be generated under different levels of stream flows.     

IFTCIP: An Integrated Optimization Model for Environmental Management under Uncertainty

In this study, an interval-fuzzy two-stage chance-constrained integer programming (IFTCIP) method is developed for supporting environmental management under uncertainty. The IFTCIP improves upon the existing interval, fuzzy, and two-stage programming approaches by allowing uncertainties expressed as probability distributions, fuzzy sets, and discrete intervals to be directly incorporated within a general mixed integer linear programming framework. It has advantages in uncertainty reflection, policy investigation, risk assessment, and capacity-expansion analysis in comparison to the other optimization methods. Moreover, it can help examine the risk of violating system constraints and the associated consequences. The developed method is applied to the planning for facility expansion and waste-flow allocation within a municipal solid waste management system. Violations of capacity constraints are allowed under a range of significance levels, which reflects tradeoffs between the system cost and the constraint-violation risk. The results indicate that reasonable solutions for both binary and continuous variables have been generated under different risk levels. They are useful for generating desired decision alternatives with minimized system cost and constraint-violation risk under various environmental, economic, and system-reliability conditions. Generally, willingness to take a higher risk of constraint violation will guarantee a lower system cost; a strong desire to acquire a lower risk will run into a higher system cost.     

Development of fuzzy air quality index using soft computing approach

Proper assessment of air quality status in an atmosphere based on limited observations is an essential task for meeting the goals of environmental management. A number of classification methods are available for estimating the changing status of air quality. However, a discrepancy frequently arises from the quality criteria of air employed and vagueness or fuzziness embedded in the decision making output values. Owing to inherent imprecision, difficulties always exist in some conventional methodologies like air quality index when describing integrated air quality conditions with respect to various pollutants parameters and time of exposure. In recent years, the fuzzy logic-based methods have demonstrated to be appropriated to address uncertainty and subjectivity in environmental issues. In the present study, a methodology based on fuzzy inference systems (FIS) to assess air quality is proposed. This paper presents a comparative study to assess status of air quality using fuzzy logic technique and that of conventional technique. The findings clearly indicate that the FIS may successfully harmonize inherent discrepancies and interpret complex conditions.     

Fragmentary provisions for uncertainty disclosure and consideration in EA legislation,regulations and guidelines and the need for improvement

The consideration and disclosure of uncertainties is fundamental to a credible EA process, but little is known about the nature and type of requirements and guidance available to proponents, practitioners and decision makers about how to deal with uncertainties. This paper examines the provisions for considering and disclosing uncertainties in EA. Methods are based on a comparative review of uncertainty provisions in EA legislation, regulations and guidance documents under Canadian federal, provincial and territorial jurisdictions. Results show 10 types of provisions applied at different stages of the EA process with considerable jurisdictional variability and incoherence. The most common provision was that decision makers can request that project proponents provide more information, followed by the preparation of contingency plans, and that practitioners document their assumptions about data reliability. Most of these provisions were found in guidelines, versus legislation or regulations; and most addressed impact management, with very few provisions for addressing uncertainty during EA review and decision making. Current practices of uncertainty (non)disclosure and (non)consideration in EA can be explained, in part, by the superficial nature and limited extent of the requirements and guidance made available to EA practitioners, proponents, and decision makers. The existing requirements placed on proponents and practitioners to disclose and consider uncertainties are necessary, but insufficient. Stronger, more coherent and transparent requirements for those tasked with EA review and decision making to consider uncertainty information when disclosed, and the development of practical guidance on how to do so, are needed.     

Construction of fuzzy membership functions for urban vehicular exhaust emissions modeling

This paper presents a method for constructing a membership function (MF) for the fuzzy sets that expert systems deal with. This paper introduces a Bezier curve-based mechanism for constructing MFs of convex normal fuzzy sets. The mechanism can fit any given data set with a minimum level of discrepancy. In the absence of data, the mechanism can be intuitively manipulated by the user to construct MFs with the desired shape. MFs have been developed using the proposed mechanism for urban vehicular exhaust emission modeling. It has been observed that all meteorological and vehicular parameters have either S-shaped MFs or Z-shaped MFs. Gaussian MF has been mostly applied for modeling air quality. The present study explored the application of fuzzy MF to analyze air pollution data from vehicular emission. The study reveals that S-shaped and Z-shaped MF can be used in addition to Gaussian MF.     

Classification of air quality using fuzzy synthetic multiplication

Proper identification of environment's air quality based on limited observations is an essential task to meet the goals of environmental management. Various classification methods have been used to estimate the change of air quality status and health. However, discrepancies frequently arise from the lack of clear distinction between each air quality, the uncertainty in the quality criteria employed and the vagueness or fuzziness embedded in the decision-making output values. Owing to inherent imprecision, difficulties always exist in some conventional methodologies when describing integrated air quality conditions with respect to various pollutants. Therefore, this paper presents two fuzzy multiplication synthetic techniques to establish classification of air quality. The fuzzy multiplication technique empowers the max-min operations in "or" and "and" in executing the fuzzy arithmetic operations. Based on a set of air pollutants data carbon monoxide, sulfur dioxide, nitrogen dioxide, ozone, and particulate matter (PM(10)) collected from a network of 51 stations in Klang Valley, East Malaysia, Sabah, and Sarawak were utilized in this evaluation. The two fuzzy multiplication techniques consistently classified Malaysia's air quality as "good." The findings indicated that the techniques may have successfully harmonized inherent discrepancies and interpret complex conditions. It was demonstrated that fuzzy synthetic multiplication techniques are quite appropriate techniques for air quality management.     

Interval-Parameter Conditional Value-at-Risk Two-Stage Stochastic Programming Model for Management of End-of-Life Vehicles

The management of end-of-life vehicles conserves natural resources, provides economic benefits, and reduces water, air, and soil pollution. Sound management of end-of-life vehicles is vitally important worldwide thus requiring sophisticated decision-making tools for optimizing its efficiency and reducing system risk. This paper proposes an interval-parameter conditional value-at-risk two-stage stochastic programming model for management of end-of-life vehicles. A case study is conducted in order to demonstrate the usefulness of the developed model. The model is able to provide the trade-offs between the expected profit and system risk. It can effectively control risk at extremely disadvantageous availability levels of end-of-life vehicles. The formulated model can produce optimal solutions under predetermined decision-making risk preferences and confidence levels. It can simultaneously determine the optimal long-term allocation targets of end-of-life vehicles and reusable parts as well as capital investment, production planning, and logistics management decisions within a multi-period planning horizon. The proposed model can efficiently handle uncertainties expressed as interval values and probability distributions. It is able to provide valuable insights into the effects of uncertainties. Compared to the available models, the resulting solutions are far more robust.

     

Cokriging optimization of monitoring network configuration based on fuzzy and non-fuzzy variogram evaluation

A number of optimization approaches regarding monitoring networkdesign and sampling optimization procedures have been reported inthe literature. Cokriging Estimation Variance (CEV) is a usefuloptimization tool to determine the influence of the spatial configuration of monitoring networks on parameter estimations. Itwas used in order to derive a reduced configuration of a nitrateconcentration monitoring well network. The reliability of the reduced monitoring configuration suffers from the uncertainties caused by the variographer's choices and several inherent assumptions. These uncertainties can be described considering thevariogram parameters as fuzzy numbers and the uncertainties by means of membership functions.Fuzzy and non-fuzzy approaches were used to evaluate differencesamong well network configurations. Both approaches permitted estimates of acceptable levels of information loss for nitrate concentrations in the monitoring network of the aquifer of the Plain of Modena, Northern Italy. The fuzzy approach was found torequire considerably more computational time and numbers of wellsat comparable level of information loss.     

Multi-criteria group decision-making based sustainability measurement of wastewater treatment processes

There are various processes which can be used for wastewater treatment (WT), and the selection of the most sustainable one among different processes is a hard task. This study aims at helping the decision-makers (DM) to address this by developing an intuitionistic fuzzy set (IFS) theory based group multi-attribute decision analysis (MADA) method. Ten criteria in environment, economy, society-politic, and technology dimensions were employed to achieve sustainability measurement (SM) of WT processes. The multi-criteria sustainability assessment method developed in this study allow different experts to attend the SM, and enable the participants to employ the natural language/words to depict their intuitionistic opinions. Accordingly, the proposed method can achieve group SM under uncertainties. An illustrative case including four processes for wastewater treatment, namely Anaerobic-Anoxic-Oxic (AAO) process, Triple Oxidation Ditch (TOD) process, Anaerobic single-ditch oxidation (ASD) process, and Sequencing batch reactor activated sludge process (SBR), has been studied, and the results reveal that this method can determine sustainability sequence of different WT processes.     

Accounting for Uncertainty in Value Judgements when Applying Multi-Attribute Value Theory

In environmental decisions, analysts commonly face substantial uncertainties around stakeholders’ values judgments. Multi-Attribute Value Theory (MAVT), a family of multi-criteria decision analysis techniques, is applied in participative settings to articulate stakeholders’ values in decision-making. In MAVT, value judgments represent the intensity of individuals’ preferences in a set of objectives, which are operationalized as scaling factors or weights. Different sets of weights may express variation in people’s preferences or value judgments. Unfortunately, there are still important methodological gaps regarding how to incorporate uncertainty and the substantial variation commonly encountered in stakeholders’ preferences. This article presents a model of uncertainty that encompasses the dispersion of value judgments in MAVT. To achieve this goal, we draw on info-gap theory, which provides a mathematically grounded method for exploring sensitivity to preference weights when there are relatively high levels of uncertainties. We experimentally tested the uncertainty model in an environmental decision problem. We found that MAVT can use info-gap analysis to deal with multiple value judgments, avoiding exclusive reliance on nominal expected values to inform decisions. We explored a mechanism to explicitly consider the trade-offs between the performance of alternatives and the level of uncertainty that in any specified context a decision maker is willing to accept. Findings emphasize the potential of MAVT to support environmental management decisions, particularly in situations where multiple stakeholders and their contested value judgments have to be considered simultaneously to explore uncertainties around value trade-offs.     

Optimal Expansion Strategy for a Sewer System under Uncertainty

Because of fast urban sprawl, land use competition, and the gap in available funds and needed funds, municipal decision makers and planners are looking for more cost-effective and sustainable ways to improve their sewer infrastructure systems. The dominant approaches have turned to planning the sanitary sewer systems within a regional context, while the decentralized and on-site/cluster wastewater systems have not overcome the application barriers. But regionalization policy confers uncertainties and risks upon cities while planning for future events. Following the philosophy of smart growth, this paper presents several optimal expansion schemes for a fast-growing city in the US/Mexico borderlands—the city of Pharr in Texas under uncertainty. The waste stream generated in Pharr is divided into three distinct sewer sheds within the city limit, including south region, central region, and north region. The options available include routing the wastewater to a neighboring municipality (i.e., McAllen) for treatment and reuse, expanding the existing wastewater treatment plant (WWTP) in the south sewer shed, and constructing a new WWTP in the north sewer shed. Traditional deterministic least-cost optimization applied in the first stage can provide a cost-effective and technology-based decision without respect to associated uncertainties system wide. As the model is primarily driven by the fees charged for wastewater transfer, sensitivity analysis was emphasized by the inclusion of varying flat-rate fees for adjustable transfer schemes before contracting process that may support the assessment of fiscal benefits to all parties involved. Yet uncertainties might arise from wastewater generation, wastewater reuse, and cost increase in constructing and operating the new wastewater treatment plant simultaneously. When dealing with multiple sources of uncertainty, the grey mixed integer programming (GIP) model, formulated in the second stage, can further allow all sources of uncertainties to propagate throughout the optimization context, simultaneously leading to determine a wealth of optimal decisions within a reasonable range. Both models ran for three 5-year periods beginning in 2005 and ending in 2020. The dynamic outputs of this analysis reflect the systematic concerns about integrative uncertainties within this decision analysis, which enable decision makers and stakeholders to make all-inclusive decisions for sanitary sewer system expansion in an economically growing region.     

Fuzzy clustering analysis in environmental impact assessment — A complement tool to environmental quality index

In spite of rapid progress achieved in the methodological research underlying environmental impact assessment (EIA), the problem of weighting various parameters has not yet been solved. This paper presents a new approach, fuzzy clustering analysis, which is illustrated with an EIA case study on Baoshan-Wusong District in Shanghai, China. Fuzzy clustering analysis may be used whenever a composite classification of environmental quality/impact incorporates multiple parameters. In such cases the technique may be used as a complement or an alternative to comprehensive assessment. In fuzzy clustering analysis, the classification is determined by a fuzzy relation. After a fuzzy similarity matrix has been established and the fuzzy relation stabilized, a dynamic clustering chart can be developed. Given a suitable threshold, the appropriate classification can be accomplished. The methodology is relatively simple and the results can be interpreted to provide valuable information to support decision making and improve management of the environment.     

Multi-criteria decision analysis with probabilistic risk assessment for the management of contaminated ground water

Traditionally, environmental decision analysis in subsurface contamination scenarios is performed using cost–benefit analysis. In this paper, we discuss some of the limitations associated with cost–benefit analysis, especially its definition of risk, its definition of cost of risk, and its poor ability to communicate risk-related information. This paper presents an integrated approach for management of contaminated ground water resources using health risk assessment and economic analysis through a multi-criteria decision analysis framework. The methodology introduces several important concepts and definitions in decision analysis related to subsurface contamination. These are the trade-off between population risk and individual risk, the trade-off between the residual risk and the cost of risk reduction, and cost-effectiveness as a justification for remediation. The proposed decision analysis framework integrates probabilistic health risk assessment into a comprehensive, yet simple, cost-based multi-criteria decision analysis framework. The methodology focuses on developing decision criteria that provide insight into the common questions of the decision-maker that involve a number of remedial alternatives. The paper then explores three potential approaches for alternative ranking, a structured explicit decision analysis, a heuristic approach of importance of the order of criteria, and a fuzzy logic approach based on fuzzy dominance and similarity analysis. Using formal alternative ranking procedures, the methodology seeks to present a structured decision analysis framework that can be applied consistently across many different and complex remediation settings. A simple numerical example is presented to demonstrate the proposed methodology. The results showed the importance of using an integrated approach for decision-making considering both costs and risks. Future work should focus on the application of the methodology to a variety of complex field conditions to better evaluate the proposed methodology.     

Utility of fuzzy cross-impact simulation in environmental assessment

Fuzzy cross-impact simulation is a qualitative technique, where interactions within a system are represented by a cross-impact matrix that includes linguistic elements. It can be used effectively to visualize dynamic evolution of a system. The utility of the fuzzy cross-impact simulation approach is: (1) in dealing with uncertainties in environment-development systems; (2) scoping cumulative effect assessment; and (3) integrating societal response structure in environment impact assessment. Use of the method is illustrated in a case concerning the textile industry in Indore, India. Consequences of policy alternatives for cleanup and pollution abatement are predicted in terms of environmental quality and quality of life, using the simulation model. The consequence analysis is used to arrive at preferred policy options.     

典型高原山地城市环境空气质量预报预警平台设计

空气质量预报系统作为一种重要的工具用于为公众提供空气质量预报信息、评估城市空气质量,为污染控制战略、动态环境管理以及决策制定提供支持。研究对国内外环境空气质量预报现状进行了回顾,以云南省为例提出了高原山地城市环境空气质量预报预警体系建设的整体思路,针对系统建设现状,提出了环境空气质量预报预警系统建设所面临的问题以及对未来发展方向的建议。     

臭氧数值预报模型综述

光化学大气质量模型在研究臭氧(O_3)污染以及O_3预报方面具有核心作用,是O_3污染防治决策者的有力工具。文章结合目前中国及国际区域尺度光化学大气质量预报模型的研究与应用,重点论述与O_3有关的大气化学过程在数值预报模型中的数学表达和计算方法,阐述大气物理与大气化学过程在主流大气质量数值预报模型中的实现方法及其优势和缺陷,介绍用于数值预报模型的大气物理过程和湍流参数化方案的最新进展。就当前O_3数值模拟的主要输入资料进行讨论,强调那些易被忽视但又显著影响模型预报能力和效果的诸多因素以及模型效果评估的重要性。结合O_3与复合型大气污染的关系,强调区域大气质量数值预报模型的发展趋势与方向以及在大气环境管理方面的意义和作用。     

DMSP-IEES: A Stochastic Programming Model Based on Dual-Interval and Multi-Stage Scenarios Modeling Approaches for Energy Systems Management and GHG Emissions Control

Energy-related activities contribute a major portion of anthropogenic greenhouse gas (GHG) emissions into the atmosphere. In this study, a dual-interval multi-stage stochastic programming model for the planning of integrated energy-environment systems (DMSP-IEES) model is developed for integrated energy-environment systems management, in which issues of GHG-emission mitigation can be reflected throughout the process of energy systems planning. By integrating methodologies of interval linear programming (when numbers are described as interval values without distribution information), dual-interval programming (when lower and upper bounds of interval values are not available as deterministic values but as discrete intervals), and multi-stage stochastic programming, the DMSP-IEES model is capable of dealing with uncertainties expressed as discrete intervals, dual intervals, and probability distributions within a multi-stage context. Decision alternatives can also be generated through analysis of the single- and dual-interval solutions according to projected applicable conditions. A case study is provided for demonstrating the applicability of the developed methodology. The results indicate that the developed model can tackle the dual uncertainties and the dynamic complexities in the energy-environment management systems through a multi-layer scenario tree. In addition, it can reflect the interactions among multiple system components and the associated trade-offs.