An inexact optimization approach for river water-quality management

A previously developed fuzzy waste load allocation model (FWLAM) for a river system is extended to address uncertainty involved in fixing the membership functions for the fuzzy goals of the pollution control agency (PCA) and the dischargers using the concept of grey systems. The model provides flexibility for the PCA and the dischargers to specify their goals independently, as the parameters for membership functions are considered as interval grey numbers instead of deterministic real numbers. An inexact or a grey fuzzy optimization model is developed in a multiobjective framework, to maximize the width of the interval valued fractional removal levels for providing latitude in decision-making and to minimize the width of the goal fulfillment level for reducing the system uncertainty. The concept of an acceptability index for order relation between two partially or fully overlapping intervals is used to get a deterministic equivalent of the grey fuzzy optimization model developed. The improvement of the optimal solutions over a previously developed grey fuzzy waste load allocation model (GFWLAM) is shown through an application to a hypothetical river system. The fuzzy multiobjective optimization and fuzzy goal programming techniques are used to solve the deterministic equivalent of the GFWLAM.     

Identification of river water quality using the fuzzy synthetic evaluation approach.

Proper identification of water quality conditions in a river system based on limited observations is an essential task for meeting the goals of environmental management. Various classification methods have been used for estimating the changing status and usability of surface water in river basins. However, a discrepancy frequently arises from the lack of a clear distinction between each water utilisation mode, 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 water quality conditions with respect to various chemical constituents, biological aspects, nutrients, and aesthetic qualities. This paper presents a comparative study using three fuzzy synthetic evaluation techniques to assess water quality conditions in comparison to the outputs generated by conventional procedures such as the Water Quality Index (WQI). Based on a set of data collected at seven sampling stations, a case study for the Tseng-Wen River system in Taiwan was used to demonstrate their application potential. The findings clearly indicate that the techniques may successfully harmonise inherent discrepancies and interpret complex conditions. A further, newly developed fuzzy synthetic evaluation approach described in this paper might also be useful for verifying water quality conditions for the Total Maximum Daily Load (TMDL) program and be helpful for constructing an effective water quality management strategy.     

ANALYSIS OF A KARSTIC AQUIFER MANAGEMENT PROBLEM BY FUZZY COMPOSITE PROGRAMMING1

ABSTRACT: A multiple objective framework for water resources problems possessing uncertain or imprecise elements is provided using distance-based concepts, fuzzy set theory, and fuzzy arithmetic. The case of regional management of a karstic aquifer in Hungary in which six conflicting objectives and six alternatives have been identified illustrates the methodology The objectives are classified into three groups of two objectives each, namely: (1) environmental (aesthetics, thermal springs temperature), (2) economic (mining, tourism), and (3) water quality (nitrates, phosphates). Both environmental objectives are formulated under fuzziness, and all objectives are scaled using the extension principle. Fuzzy compromise programming (FCP-I) is then applied; here, all six objectives are entered in a single l_p norm measuring the distance between each alternative and an ideal point. Next, fuzzy composite programming (FCP-II) is developed; here, a trade off is first made within each group of objectives, and then an upper level trade-off takes place between the three groups. The fuzzy numbers describing each alternative as a result from applying these techniques are ranked to yield an ordering of the alternatives. The results of applying FCP.I, FCP-II, and two different ordering techniques are compared. The FCP-II technique appears to provide a relatively simple approach at hierarchical or multilevel multiple objective decision-making, where uncertainty is described by fuzziness. (KEY TERMS: compromise programming; fuzzy arithmetic; fuzzy sets; hierarchical criteria; karstic aquifer; l_p, norms; mining; multiple objectives; thermal springs.)     

WATER QUALITY ALLOCATED COST FOR MULTIPURPOSE RESERVOIRS1

ABSTRACT: Low flow augmentation from multipurpose reservoirs may yield significant water quality benefits. Cost allocation assigns a portion of reservoir expense to water quality consumers, waste water dischargers who benefit from increased receiving flow. Whereas such allocation currently is not authorized for Federal projects, the procedure is increasingly appropriate for efficient multiobjective management. Waste water treatment costs, multipurpose reservoir costs, and water quality are modeled for Oregon's Willamette River. Water quality is expressed as a function of treatment and augmentation levels. Treatment cost necessary to achieve a given water quality without augmentation less treatment cost with augmentation is an alternative cost of water quality maintenance. With a cost allocation procedure, this alternative cost is used to determine water quality's share of reservoir cost. Under current conditions, water quality beneficiaries could be charged approximately seven percent of annualized reservoir expense. This charge is one-fourth the expense of additional treatment facilities required were augmentation not provided.     

Waste management with recourse: An inexact dynamic programming model containing fuzzy boundary intervals in objectives and constraints

The existing inexact optimization methods based on interval-parameter linear programming can hardly address problems where coefficients in objective functions are subject to dual uncertainties. In this study, a superiority–inferiority-based inexact fuzzy two-stage mixed-integer linear programming (SI-IFTMILP) model was developed for supporting municipal solid waste management under uncertainty. The developed SI-IFTMILP approach is capable of tackling dual uncertainties presented as fuzzy boundary intervals (FuBIs) in not only constraints, but also objective functions. Uncertainties expressed as a combination of intervals and random variables could also be explicitly reflected. An algorithm with high computational efficiency was provided to solve SI-IFTMILP. SI-IFTMILP was then applied to a long-term waste management case to demonstrate its applicability. Useful interval solutions were obtained. SI-IFTMILP could help generate dynamic facility-expansion and waste-allocation plans, as well as provide corrective actions when anticipated waste management plans are violated. It could also greatly reduce system-violation risk and enhance system robustness through examining two sets of penalties resulting from variations in fuzziness and randomness. Moreover, four possible alternative models were formulated to solve the same problem; solutions from them were then compared with those from SI-IFTMILP. The results indicate that SI-IFTMILP could provide more reliable solutions than the alternatives.     

用模糊数学对大连湾水质的评价研究

由于海域水环境系统的不确定性、随机性以及海域水质分级的模糊性，传统的海域水质评价方法如单因子评价法、综合污染指数法往往不能客观地反映海域水资源的质量状况。用模糊数学的方法对大连湾的水质环境质量进行评价，能够客观地分析出大连湾的污染状况，为合理规划、控制大连湾沿岸污染企业的污水排放提供科学依据，从而达到有计划地控制和治理海域污染，改善海域环境质量的目的。     

A COMPLEMENTARY TOOL TO WATER QUALITY INDEX: FUZZY CLUSTERING ANALYSIS1

ABSTRACT: A general methodology for fuzzy clustering analysis is developed and illustrated with a case study of water quality evaluation for Dianshan Lake, Shanghai, China. Fuzzy clustering analysis may be used whenever a composite classification of water quality 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 is worked out. The methodology is relatively simple, and the results can be interpreted to provide valuable information to support decision making and to aid water quality management.     

ANALYSIS OF WASTE LOAD ALLOCATION PROCEDURES1

A study was made to analyze and modify procedures used for stream assimilation capacity and point source wasteload allocation calculations. This paper describes the sources and types of information collected and the analysis of alternative computation methods developed during the study. The calculation of stream assimilation capacity or Total Maximum Daily Load (TMDL), will depend upon assumed stream flows, quality standards, reaction rates, and modeling procedures. The “critical conditions” selected for TMDL calculations usually are low flows and warm temperatures. The complexity of water quality models used for TMDL and allocation calculations can range from simple, complete mixing to calibrated and verified mathematical models. A list of 20 wasteload allocation (WLA) methods was developed. Five of these WLA's were applied to an example stream to permit comparisons based on cost, equity, efficient use of stream assimilation capacity, and sensitivity to fundamental stream quality data. Based on insensitivity to data errors and current use by several states, the WLA method of “equal percent treatment” was preferable in the example stream.     

COMPUTING THE RISKS ASSOCIATED WITH WASTELOAD) ALLOCATION MODELING1

ABSTRACT: The risks associated with a traditional wasteload allocation (WLA) analysis were quantified with data from a recent study of the Upper Trinity River (Texas). Risk is define here as the probability of failing to meet an established in-stream water quality standard. The QUAL-TX dissolved oxygen (DO) water quality model was modified to a Monte Carlo framework. Flow augmentation coding was also modified to allow an exact match to be computed between the predicted and an established DO concentration standard, thereby providing an avenue for linking input parameter uncertainty to the assignment of a wasteload permit (allowable mass loading rate). Monte Carlo simulation techniques were employed to propagate input parameter uncertainties, typically encountered during WLA analysis, to the computed effluent five-day carbonaceous biochemical oxygen demand requirements for a single major wastewater treatment plant (WWTP). The risk of failing to meet an established in-stream DO criterion may be as high as 96 percent. The uncertainty associated with estimation of the future total Kjeldahl nitrogen concentration for a single tributary was found to have the greatest impact on the determination of allowable WWTP loadings.     

DECISION SUPPORT FOR ALLOCATION OF WATERSHED POLLUTION LOAD USING GREY FUZZY MULTIOBJECTIVE PROGRAMMING1

ABSTRACT: This paper uses the grey fuzzy multiobjective programming to aid in decision making for the allocation of waste load in a river system under versatile uncertainties and risks. It differs from previous studies by considering a multicriteria objective function with combined grey and fuzzy messages under a cost benefit analysis framework. Such analysis technically integrates the prior information of water quality models, water quality standards, wastewater treatment costs, and potential benefits gained via in‐stream water quality improvement. While fuzzy sets are characterized based on semantic and cognitive vagueness in decision making, grey numbers can delineate measurement errors in data collection. By employing three distinct set theoretic fuzzy operators, the synergy of grey and fuzzy implications may smoothly characterize the prescribed management complexity. With the aid of genetic algorithm in the solution procedure, the modeling outputs contribute to the development of an effective waste load allocation and reduction scheme for tributaries in this subwatershed located in the lower Tseng‐Wen River Basin, South Taiwan. Research findings indicate that the inclusion of three fuzzy set theoretic operators in decision analysis may delineate different tradeoffs in decision making due to varying changes, transformations, and movements of waste load in association with land use pattern within the watershed.     

Resolution of an uncertain closed-loop logistics model: An application to fuzzy linear programs with risk analysis

With the urgency of global warming, green supply chain management, logistics in particular, has drawn the attention of researchers. Although there are closed-loop green logistics models in the literature, most of them do not consider the uncertain environment in general terms. In this study, a generalized model is proposed where the uncertainty is expressed by fuzzy numbers. An interval programming model is proposed by the defined means and mean square imprecision index obtained from the integrated information of all the level cuts of fuzzy numbers. The resolution for interval programming is based on the decision maker (DM)’s preference. The resulting solution provides useful information on the expected solutions under a confidence level containing a degree of risk. The results suggest that the more optimistic the DM is, the better is the resulting solution. However, a higher risk of violation of the resource constraints is also present. By defining this probable risk, a solution procedure was developed with numerical illustrations. This provides a DM trade-off mechanism between logistic cost and the risk.     

DECISION SUPPORT SYSTEM FOR RESERVOIR OPERATION1

ABSTRACT: A decision support system to determine reservoir releases in an uncertain environment during the dry season was developed. A key characteristic of the decision support system is its recursive procedure that processes observations to obtain the most feasible estimate. The system consists of three components: (1) a hydrologic model; (2) an optimization model, and (3) a fuzzy decision model. This methodology was applied to the operation of the Techi reservoir in central Taiwan. Three criteria (public water supply, irrigation, and hydropower) were taken into account within the operation process. Simulation results show that the decision support system can successfully assist government officials in determining operating policy for the Techi reservoir during the dry season. Also, the system is simple enough to lead to a rapid transfer of theoretical knowledge into practice.     

EVALUATION OF THE WORTH OF ADDITIONAL DATA1

ABSTRACT .Inherent in every decision process is a certain amount of uncertainty, which is reduced with information. Perfect knowledge yields no uncertainty for a process, but perfect knowledge for hydrologic and water resource systems would require a highly excessive investment. Therefore, it is the aim of this paper to delineate a procedure that places a value on this uncertainty so that it may be compared to a cost of further investment, which would provide a basis for deciding the time at which the value of additional data does not exceed the cost of that data. A decision theory approach is employed on a hydrologic problem to formalize the steps in making a decision. Examples are given.     

COST-EFFECTIVE REGULATORY OPTIONS FOR WATER QUALITY LIMITED STREAMS1

With the pressure from industries and municipalities to reduce the waste water treatment costs associated with the permit limits needed to attain the goals of the Clean Water Act, attention has turned ways of introducing flexibility into the regulations without sacrificing the water quality goals. Wisconsin is the first state to have adopted a variety of options from which dischargers may choose when meeting their water quality requirements. These options were developed for the express purpose of minimizing the costs and maximizing the flexibility of the point source water quality regulations while ensuring that permitted discharge would not violate the water quality standards. This paper presents five options that the state has made available to dischargers, as well as one the state did not adopt. The conclusion is that a mix of options can substantially increase the flexibility and reduce the costs of meeting water quality standards on effluent limited streams.     

模糊神经网络模型在拟建项目环境质量评价中的应用

由于评价因子与环境质量标准之间的模糊关系,导致传统的评价模型结果的不确定性。本文将模糊理论和神经网络模型相结合,利用模糊理论的隶属度反映各因子的质量相对状态,从而更精确地识别模糊性。通过模糊神经网络模型对环境质量标准样本的学习和测试,得出评价等级,并与模糊综合评价方法进行对比,实验结果表明,模糊神经网络模型用于环境质量评价是可行的,且比模糊综合评价方法更为客观、合理。     

THE IMPACT OF ENERGY DEVELOPMENT JN THE TONGUE RIVER BASIN,SOUTHEASTERN MONTANA1

ABSTRACT: Southeastern Montana's Tongue River basin is experiencing rapid development of its extensive coal deposits. This development has a significant impact on the basin's hydrologic systems. Ground water flow is disrupted by mining and its quality degraded. Mine mouth conversion of the coal involves consumption of large amounts of water at the expense of downstream UBCTS, creating several water conflicts. Allocation of Tongue River water has favored agricultural users, and re-allocation is difficult.     

Fuzzy assessment of land suitability for scientific research reserves

Evaluating the characteristics of a set of sites as potential scientific research reserves is an example of land suitability assessment. Suitability in this case is based upon multiple criteria, many of which can be linguistically imprecise and often incompatible. Fuzzy logic is a useful method for characterizing imprecise suitability criteria and for combining criteria into an overall suitability rating. The Ecosystem Management Decision Support software combined a fuzzy logic knowledge base we developed to represent the assessment problem with a GIS database providing site-specific data for the assessment. Assessment of sites as a potential natural reserve for the new University of California campus at Merced demonstrates the benefits of fuzzy suitability assessment. The study was conducted in three stages of successively smaller assessment regions with increasingly fine spatial resolution and specificity of criteria. Several sites were identified that best satisfy the suitability criteria for a reserve to represent vernal pool habitat.     

Pragmatic Approaches for Water Management Under Climate Change Uncertainty1

Stakhiv, Eugene Z., 2011. Pragmatic Approaches for Water Management Under Climate Change Uncertainty. Journal of the American Water Resources Association (JAWRA) 47(6):1183–1196. DOI: 10.1111/j.1752‐1688.2011.00589.x Abstract: Water resources management is in a difficult transition phase, trying to accommodate large uncertainties associated with climate change while struggling to implement a difficult set of principles and institutional changes associated with integrated water resources management. Water management is the principal medium through which projected impacts of global warming will be felt and ameliorated. Many standard hydrological practices, based on assumptions of a stationary climate, can be extended to accommodate numerous aspects of climate uncertainty. Classical engineering risk and reliability strategies developed by the water management profession to cope with contemporary climate uncertainties can also be effectively employed during this transition period, while a new family of hydrological tools and better climate change models are developed. An expansion of the concept of “robust decision making,” coupled with existing analytical tools and techniques, is the basis for a new approach advocated for planning and designing water resources infrastructure under climate uncertainty. Ultimately, it is not the tools and methods that need to be revamped as much as the suite of decision rules and evaluation principles used for project justification. They need to be aligned to be more compatible with the implications of a highly uncertain future climate trajectory, so that the hydrologic effects of that uncertainty are correctly reflected in the design of water infrastructure.     

Fuzzy adaptive management of social and ecological carrying capacities for protected areas

Commonly used methods of evaluating the degree of consistency of protected area ecosystems with social and ecological carrying capacities are likely to result in decision errors. This occurs because such methods do not account for imprecision and uncertainty in inferring the degree of ecosystem consistency from an observed ecosystem indicator. This paper proposes a fuzzy adaptive management approach to determine whether a protected area ecosystem is consistent with ecological and social carrying capacities and, if not, to identify management actions that are most likely to achieve consistency when there is uncertainty about the current degree of consistency and how alternative management actions are likely to influence that consistency. The proposed approach is illustrated using a hypothetical example that uses an ecosystem indicator that reflects combinations of different levels of user satisfaction and conservation of threatened and endangered species. Application of the proposed fuzzy adaptive management approach requires a protected area manager to: (1) identify alternative management actions for achieving ecosystem consistency with social and ecological carrying capacities in each of several management zones in a protected area; (2) randomly assign alternative management actions to management zones; (3) define fuzzy sets for the ecosystem indicator and degree of ecosystem consistency, and fuzzy relations between the ecosystem indicator and the degree of ecosystem consistency; (4) monitor the indicator in each management zone; (5) define fuzzy sets based on the observed indicator in each management zone; and (6) combine the fuzzy sets defined on the observed indicator and the fuzzy relations between the indicator and the degree of ecosystem consistency to reach conclusions about the most likely degree of consistency for alternative management actions in each management zone. The fuzzy adaptive management approach proposed here is advantageous when the benefits of avoiding the decision errors inherent with crisp and stochastic decision rules outweigh the added cost of implementing the approach.     

A fuzzy analytic network process for multi-criteria evaluation of contaminated site remedial countermeasures

The Analytic Network Process (ANP) has been proposed to incorporate interdependence and feedback effect in the prioritization of remedial countermeasures using a hierarchical network decision model, but this approach seems to be incapable of capturing the vagueness and fuzziness during value judgment elicitation. The aim of this paper is to present an evaluation method using a fuzzy ANP (FANP) approach to address this shortcoming. Triangular fuzzy numbers (TFN) and their degree of fuzziness are used in the semantic scale as human judgment expressed in natural language is most often vague and fuzzy. The method employs the alpha-cuts, interval arithmetic and optimism index to transform the fuzzy comparative judgment matrix into set of crisp matrices, and then calculates the desired priorities using the eigenvector method. A numerical example, which was drawn from a real-life case study of an uncontrolled landfill in Japan, is presented to demonstrate the process. Results from the sensitivity analysis describe how the fuzziness in judgment could affect the solution robustness of the prioritization method. The proposed FANP approach therefore could effectively deal with the uncertain judgment inherent in the decision making process and derive the meaningful priorities explicitly from a complex decision structure in the evaluation of contaminated site remedial countermeasures.