Risk-based environmental decision-making using fuzzy analytic hierarchy process (F-AHP)

Environmental risk management is an integral part of risk analyses. The selection of different mitigating or preventive alternatives often involve competing and conflicting criteria, which requires sophisticated multi-criteria decision-making (MCDM) methods. Analytic hierarchy process (AHP) is one of the most commonly used MCDM methods, which integrates subjective and personal preferences in performing analyses. AHP works on a premise that decision-making of complex problems can be handled by structuring the complex problem into a simple and comprehensible hierarchical structure. However, AHP involves human subjectivity, which introduces vagueness type uncertainty and necessitates the use of decision-making under uncertainty. In this paper, vagueness type uncertainty is considered using fuzzy-based techniques. The traditional AHP is modified to fuzzy AHP using fuzzy arithmetic operations. The concept of risk attitude and associated confidence of a decision maker on the estimates of pairwise comparisons are also discussed. The methodology of the proposed technique is built on a hypothetical example and its efficacy is demonstrated through an application dealing with the selection of drilling fluid/mud for offshore oil and gas operations.     

Risk tolerance measure for decision-making in fuzzy analysis: a health risk assessment perspective

In risk assessment studies it is important to determine how uncertain and imprecise knowledge should be included into the simulation and assessment models. Thus, proper evaluation of uncertainties has become a major concern in environmental and health risk assessment studies. Previously, researchers have used probability theory, more commonly Monte Carlo analysis, to incorporate uncertainty analysis in health risk assessment studies. However, in conducting probabilistic health risk assessment, risk analyst often suffers from lack of data or the presence of imperfect or incomplete knowledge about the process modeled and also the process parameters. Fuzzy set theory is a tool that has been used in propagating imperfect and incomplete information in health risk assessment studies. Such analysis result in fuzzy risks which are associated with membership functions. Since possibilistic health risk assessment studies are relatively new, standard procedures for decision-making about the acceptability of the resulting fuzzy risk with respect to a crisp standard set by the regulatory agency are not fully established. In this paper, we are providing a review of several available approaches which may be used in decision-making. These approaches involve defuzzification techniques, the possibility and the necessity measures. In this study, we also propose a new measure, the risk tolerance measure, which can be used in decision making. The risk tolerance measure provides an effective metric for evaluating the acceptability of a fuzzy risk with respect to a crisp compliance criterion. Fuzzy risks with different membership functions are evaluated with respect to a crisp compliance criterion by using the possibility, the necessity, and the risk tolerance measures and the results are discussed comparatively.     

An integrated fuzzy-stochastic modeling approach for assessing health-impact risk from air pollution

High concentrations of air pollutants in the ambient environment can result in breathing problems with human communities. Effective assessment of health-impact risk from air pollution is important for supporting decisions of the related detection, prevention, and correction efforts. However, the quality of information available for environmental/health risk assessment is often not satisfactory enough to be presented as deterministic numbers. Stochastic method is one of the methods for tackling those uncertainties, by which uncertain information can be presented as probability distributions. However, if the uncertainties can not be presented as probabilities, they can then be handled through fuzzy membership functions. In this study, an integrated fuzzy-stochastic modeling (IFSM) approach is developed for assessing air pollution impacts towards asthma susceptibility. This development is based on Monte Carlo simulation for the fate of SO₂ in the ambient environment, examination of SO₂ concentrations based on the simulation results, quantification of evaluation criteria using fuzzy membership functions, and risk assessment based on the combined fuzzy-stochastic information. The IFSM entails (a) simulation for the fate of pollutants in ambient environment, with the consideration of source/medium uncertainties, (b) formulation of fuzzy air quality management criteria under uncertain human-exposure pathways, exposure dynamics, and SPG-response variations, and (c) integrated risk assessment under complexities of the combined fuzzy/stochastic inputs of contamination level and health effect (i.e., asthma susceptibility). The developed IFSM is applied to a study of regional air quality management. Reasonable results have been generated, which are useful for evaluating health risks from air pollution. They also provide support for regional environmental management and urban planning.     

Modelling uncertainties in short-term reservoir operation using fuzzy sets and a genetic algorithm / Modélisation d’incertitudes dans la gestion de barrage à court terme grâce à des ensembles flous et à un algorithme génétique

Abstract

Abstract Various uncertainties are inherent in modelling any reservoir operation problem. Two of these are addressed in this study: uncertainty involved in the expression of reservoir penalty functions, and uncertainty in determining the target release value. Fuzzy set theory was used to model these uncertainties where the preferences of the decision maker for the fuzzified parameters are expressed as membership functions. Nonlinear penalty functions are used to determine the penalties due to deviations from targets. The optimization was performed using a genetic algorithm with the objectives to minimize the total penalty and to maximize the level of satisfaction of the decision maker with fuzzified input parameters. The proposed formulation was applied to the problem of finding the optimal release and storage values, taking Green reservoir in Kentucky, USA as a case study. The approach offers more flexibility to reservoir decision-making by demonstrating an efficient way to represent subjective uncertainties, and to deal with non-commensurate objectives under a fuzzy multi-objective environment.     

Comprehensive flood risk assessment based on set pair analysis-variable fuzzy sets model and fuzzy AHP

On the basis of the disaster system theory and comprehensive analysis of flood risk factors, including the hazard of the disaster-inducing factors and disaster-breeding environment, as well as the vulnerability of the hazards-bearing bodies, the primary risk assessment index system of flood diversion district as well as its assessment standards were established. Then, a new model for comprehensive flood risk assessment was put forward in this paper based on set pair analysis (SPA) and variable fuzzy sets (VFS) theory, named set pair analysis-variable fuzzy sets model (SPA-VFS), which determines the relative membership degree function of VFS by using SPA method and has the advantages of intuitionist course, simple calculation and good generality application. Moreover, the analytic hierarchy process (AHP) was combined with trapezoidal fuzzy numbers to calculate the weights of assessment indices, thus the weights for flood hazard and flood vulnerability were determined by the fuzzy AHP procedure, respectively. Then SPA-VFS were applied to calculate the flood hazard grades and flood vulnerability grades with rank feature value equation and the confidence criterion, respectively. Under the natural disasters risk expression recommended by the Humanitarian Affairs Department of United Nations, flood risk grades were achieved from the flood hazard grades and flood vulnerability grades with risk grade classification matrix, where flood hazard, flood vulnerability and flood risk were all classified into five grades as very low, low, medium, high and very high. Consequently, integrated flood risk maps could be carried out for flood risk management and decision-making. Finally, SPA-VFS and fuzzy AHP were employed for comprehensive flood risk assessment of Jingjiang flood diversion district in China, and the computational results demonstrate that SPA-VFS is reasonable, reliable and applicable, thus has bright prospects of application for comprehensive flood risk assessment, and moreover has potential to be applicable to comprehensive risk assessment of other natural disasters with no much modification.     

豫01井地下水位模糊分维值的变化与地震的关系

采用了模糊集理论与分形理论相结合的模糊分维方法，计算了河南范县豫01井水位动态的模糊分维值，并分析了与1981年河北宁晋Ms 5.8、1983年山东菏泽Ms 5.9、1985年河北任县Ms 5.0地震的关系。结果显示，模糊分维值在这3次地震前都明显地出现了小于0．75的降维低值异常特征。且震级越大，震中距越小，异常时间越长；反之则相反。     

A new fuzzy linear regression approach for dissolved oxygen prediction

Abstract

A new method for fuzzy linear regression is proposed to predict dissolved oxygen using abiotic factors in a riverine environment, in Calgary, Canada. The proposed method is designed to accommodate fuzzy regressors, regressand and coefficients, i.e. representing full system uncertainty. The regression equation is built to minimize the distance between fuzzy numbers, and generalizes to crisp regression when crisp parameters are used. The method is compared to two existing fuzzy linear regression techniques: the Tanaka method and the Diamond method. The proposed new method outperforms the existing methods with higher Nash-Sutcliffe efficiency, and lower RMSE, AIC and total fuzzy distance. The new method demonstrates that nonlinear membership functions are more suitable for representing uncertain environmental data than the typical triangular representations. A result of this research is that low DO prediction is improved and consequently the approach can be used for risk analysis by water resource managers.

Editor D. Koutsoyiannis; Associate editor T. Okruszko     

INTEGRATED INTERPRETATION OF MARINE ENGINEERING GEOLOGICAL AND GEOPHYSICAL DATA ON THE PRINCIPLES OF EXPERT SYSTEM TECHNOLOGY1

We describe an approach to the construction of an engineering geological expert system for identification of sub-bottom soils in accordance with some predefined nomenclature. The following principles of integrated interpretation of engineering geophysical and geotechnical data are presented: Firstly, the transformation of physical data (compressional- and shear-wave velocities, compressional-wave attenuation coefficients, electrical conductivity, etc.) for each of the medium points into subjective probabilities for the soil belonging to each type listed in the nomenclature, and secondly, the extrapolation of local geotechnical data (primarily drilling data) to the surrounding space by means of diffusion of the initial membership function distribution, resulting in the same set of probabilities for soil types at each point in the medium under consideration. Aggregation of the fuzzy information obtained, sufficient for reaching a conclusion for most points in the medium, is carried out by means of Bayesian summation. An example is given of integrated interpretation of real data obtained from four different sources (compressional- and shear-wave velocity sections V_p(x, z) and V_s(x, z), and two boreholes) related to the same profile.     

Grey fuzzy optimization model for water quality management of a river system

A grey fuzzy optimization model is developed for water quality management of river system to address uncertainty involved in fixing the membership functions for different goals of Pollution Control Agency (PCA) and dischargers. The present model, Grey Fuzzy Waste Load Allocation Model (GFWLAM), has the capability to incorporate the conflicting goals of PCA and dischargers in a deterministic framework. The imprecision associated with specifying the water quality criteria and fractional removal levels are modeled in a fuzzy mathematical framework. To address the imprecision in fixing the lower and upper bounds of membership functions, the membership functions themselves are treated as fuzzy in the model and the membership parameters are expressed as interval grey numbers, a closed and bounded interval with known lower and upper bounds but unknown distribution information. The model provides flexibility for PCA and dischargers to specify their aspirations independently, as the membership parameters for different membership functions, specified for different imprecise goals are interval grey numbers in place of a deterministic real number. In the final solution optimal fractional removal levels of the pollutants are obtained in the form of interval grey numbers. This enhances the flexibility and applicability in decision-making, as the decision-maker gets a range of optimal solutions for fixing the final decision scheme considering technical and economic feasibility of the pollutant treatment levels. Application of the GFWLAM is illustrated with case study of the Tunga–Bhadra river system in India.     

Effects of variable attribute weights on landform classification

This paper focuses on the attribute weight issue and advocates use of modi?able attribute weights in terrain‐based environmental analysis and classi?cation. A question was asked: ‘How much will the result of a terrain‐based environmental analysis be affected if the weights of used terrain attributes are changed?’ The literature on landform classi?cation and the fuzzy k‐means method was reviewed in particular to help clarify the background and importance of this weight assignment issue. As an example, the effects of modifying attribute weights were evaluated for fuzzy k‐means landform classi?cation in a case study area. A total of 102 classi?cations were compared with each other and with a soil map, and comparison methods were speci?cally designed to evaluate the differences between these classi?cations. The results show that fuzzy k‐means landform classi?cation is sensitive to weight adjustments of adopted terrain attributes. The sensitivity is particularly high when the attribute weights started to be tuned away from the standard (i.e. uniform) weight of one. Better matching between landform classi?cation and a soil map may be produced when attribute weights are tuned. In all, we advocate the widespread adoption of an exploratory attitude in assigning attribute weights for environmental analysis and classi?cation. Copyright © 2006 John Wiley & Sons, Ltd.     

Transmissivity and storage coefficient estimation by coupling the Cooper–Jacob method and modified fuzzy least-squares regression

Traditionally the Cooper–Jacob equation is used to determine the transmissivity and the storage coefficient for an aquifer using pump test results. This model, however, is a simplified version of the actual subsurface and does not allow for analysis of the uncertainty that comes from a lack of knowledge about the heterogeneity of the environment under investigation. In this paper, a modified fuzzy least-squares regression (MFLSR) method is developed that uses imprecise pump test data to obtain fuzzy intercept and slope values which are then used in the Cooper–Jacob method. Fuzzy membership functions for the transmissivity and the storage coefficient are then calculated using the extension principle. The supports of the fuzzy membership functions incorporate the transmissivity and storage coefficient values that would be obtained using ordinary least-squares regression and the Cooper–Jacob method. The MFLSR coupled with the Cooper–Jacob method allows the analyst to ascertain the uncertainty that is inherent in the estimated parameters obtained using the simplified Cooper–Jacob method and data that are uncertain due to lack of knowledge regarding the heterogeneity of the aquifer.     

An interval-valued fuzzy linear programming with infinite ��-cuts method for environmental management under uncertainty

In this study, an interval-valued fuzzy linear programming with infinite α-cuts (IVFLP-I) method is developed for municipal solid waste (MSW) management under uncertainty. IVFLP-I can not only tackle uncertainties expressed as intervals and interval-valued fuzzy sets, but also take all fuzzy information into account by discretizing infinite α-cut levels to the interval-valued fuzzy membership functions. Through adoption of the interval-valued fuzzy sets, IVFLP-I can directly communicate information of waste managers’ confidence levels over various subjective judgments into the optimization process. Compared to the existing methods in which only finite α-cut levels exist, IVFLP-I would have enhanced the robustness in the optimization efforts. A MSW management problem is studied to illustrate the applicability of the proposed method. Four groups of optimal solutions can be obtained through assigning different intervals of α-cut levels. The results indicate that wider intervals of α-cut levels could lead to a lower risk level of constraint violation associated with a higher system cost; contrarily, narrower intervals of α-cut levels could lead to a lower cost with a higher risk of violating the constraints. The solutions under different intervals of α-cut levels can support in-depth analyses of tradeoffs between system costs and constraint-violation risks.     

Planning of municipal solid waste management systems under dual uncertainties: a hybrid interval stochastic programming approach

In this study, a random-boundary-interval linear programming (RBILP) method is developed and applied to the planning of municipal solid waste (MSW) management under dual uncertainties. In the RBILP model, uncertain inputs presented as interval numbers can be directly communicated into the optimization process; besides, intervals with uncertain lower and upper bounds can be handled through introducing the concept of random boundary interval. Consequently, robustness of the optimization process can be enhanced. To handle uncertainties with such complex presentations, an integrated chance-constrained programming and interval-parameter linear programming approach (ICCP) is proposed. ICCP can help analyze the reliability of satisfying (or risk of violating) system constraints under uncertainty. The applicability of the proposed RBILP and ICCP approach is validated through a case study of MSW management. Violations for capacity constraints are allowed under a range of significant levels. Interval solutions associated with different risk levels of constraint violation are obtained. They can be used for generating decision alternatives and thus helping waste managers to identify desired policies under various environmental, economic, and system-reliability constraints.     

Probabilistic-fuzzy health risk modeling

Health risk analysis of multi-pathway exposure to contaminated water involves the use of mechanistic models that include many uncertain and highly variable parameters. Currently, the uncertainties in these models are treated using statistical approaches. However, not all uncertainties in data or model parameters are due to randomness. Other sources of imprecision that may lead to uncertainty include scarce or incomplete data, measurement error, data obtained from expert judgment, or subjective interpretation of available information. These kinds of uncertainties and also the non-random uncertainty cannot be treated solely by statistical methods. In this paper we propose the use of fuzzy set theory together with probability theory to incorporate uncertainties into the health risk analysis. We identify this approach as probabilistic-fuzzy risk assessment (PFRA). Based on the form of available information, fuzzy set theory, probability theory, or a combination of both can be used to incorporate parameter uncertainty and variability into mechanistic risk assessment models. In this study, tap water concentration is used as the source of contamination in the human exposure model. Ingestion, inhalation and dermal contact are considered as multiple exposure pathways. The tap water concentration of the contaminant and cancer potency factors for ingestion, inhalation and dermal contact are treated as fuzzy variables while the remaining model parameters are treated using probability density functions. Combined utilization of fuzzy and random variables produces membership functions of risk to individuals at different fractiles of risk as well as probability distributions of risk for various alpha-cut levels of the membership function. The proposed method provides a robust approach in evaluating human health risk to exposure when there is both uncertainty and variability in model parameters. PFRA allows utilization of certain types of information which have not been used directly in existing risk assessment methods.     

A fuzzy‐based simulation method for modelling hydrological processes under uncertainty

In this study, a fuzzy‐based simulation method (FBSM) is developed for modelling hydrological processes associated with vague information through coupling fuzzy vertex analysis technique with distributed hydrological model. The FBSM can handle uncertainties existed as fuzzy sets in the hydrological modelling systems, and solutions under an associated number of α‐cut levels can be generated by solving 2ⁿ deterministic models. The lower reach of the Tarim River Basin in China is selected as a study case for demonstrating applicability of the proposed method. The developed model is calibrated and validated against observed groundwater elevation for four wells during the period 2000–2001, and generally performed acceptable for model Nash–Sutcliffe coefficient (R2) and correlation coefficient (R). The R2 is approximately over 0·65 and the correlation coefficient is higher than 0·90. Based on the technique of fuzzy simulation, the uncertainties of two parameters (K_H and LC) are reflected under different α‐cut levels. The results indicate that, under a lower degree of plausibility, the interval between the lower and upper bounds of the groundwater elevation is wider; conversely, a higher degree of plausibility would lead to a narrow interval. The main effect of K_H is more significant than the effect of LC at most well sites. The proposed method is useful for studying hydrological processes within a system containing multiple factors with uncertainties and providing support for identifying proper water resources management strategies. Copyright © 2010 John Wiley & Sons, Ltd.     

自然灾害危害度模糊模式识别

本文根据文献[1]提出的相对隶属度概念和模糊模式识别理论，讨论了相对隶属度及模糊模式识别用于自然灾害危害度评价的原理和过程，并结合贵州毕节地区泥石流危害度评价，阐述相对隶属度和模糊模式识别用于自然灾害危害度评价的合理性和可行性，收到满意的效果。     

基于主客观赋权模糊综合评价法的湖泊水生态系统健康评价

运用湖泊营养状态指数判断湖泊的富营养化状态,并根据湖泊的水质、沉积物和水生生物群落的现状和特点,运用主观赋权法中的层次分析法和客观赋权法中的熵权法结合模糊综合评价法,对长江中游地区江汉湖群37个湖泊的水生态系统进行健康状态评价.对湖泊富营养化的调查结果表明,海口湖处于中营养状态,18个湖泊处于富营养化状态,18个湖泊处于超富营养化状态.湖泊生态系统健康评价的研究结果表明,37个湖泊中,处于健康状况"优"的湖泊只有海口湖,处于健康状况"良"的湖泊有5个,分别为东西汊湖、花马湖、梁子湖、童家湖和涨渡湖,其余31个湖泊均处于健康状况"差"的状态.经过与湖泊营养状态指数的对照,本研究结果表明,由主观赋权的专家评分的层次分析法结合模糊综合评价法对江汉湖群湖泊水生态健康状态的评价效果相比客观赋权的熵权模糊综合评价法更贴合实际.     

Probability-credibility health risk assessment under uncertain environment

The ability to describe variables in a health risk model through probability theory enables us to estimate human health risk. These types of risk assessment are interpreted as probabilistic risk assessment (PRA). Generally, PRA requires specific estimate of the parameters of the probability density of the input variables. In all circumstances, such estimates of the parameters may not be available due to the lack of knowledge or information. Such types of variables are treated as uncertain variables. These types of information are often termed uncertainty which are interpreted through fuzzy theory. The ability to describe uncertainty through fuzzy set theory enables us to process both random variable and fuzzy variable in a single framework. The method of processing aleatory and epistemic uncertainties into a same framework is coined as hybrid method. In this paper, we are going to talk about such type of hybrid methodology for human health risk assessment. Risk assessment on human health through different pathways of exposure has been attempted many a times combining Monte Carlo analysis and extension principle of fuzzy set theory. The emergence of credibility theory enables transforming fuzzy variable into credibility distribution function which can be used in those hybrid analyses. Hence, an attempt, for the first time, has been made to combine probability theory and credibility theory to estimate risk in human health exposure. This method of risk assessment in the presence of credibility theory and probability theory is identified as probabilistic-credibility method (PCM). The results obtained are then interpreted through probability theory, unlike the other hybrid methodology where the results are interpreted in terms of possibility theory. The results obtained are then compared with probability-fuzzy risk assessment (PFRA) method. Generally, decision under hybrid methodology is made on the index of optimism. An optimistic decision maker estimates from the \(\alpha\)-cut at 1, whereas a pessimistic decision maker estimates from the \(\alpha\)-cut at 0. The PCM is an optimistic approach as the decision is always made at \(\alpha\)=1.     

Uncertainty assessment of a process-based integrated catchment model of phosphorus

Despite the many models developed for phosphorus concentration prediction at differing spatial and temporal scales, there has been little effort to quantify uncertainty in their predictions. Model prediction uncertainty quantification is desirable, for informed decision-making in river-systems management. An uncertainty analysis of the process-based model, integrated catchment model of phosphorus (INCA-P), within the generalised likelihood uncertainty estimation (GLUE) framework is presented. The framework is applied to the Lugg catchment (1,077 km²), a River Wye tributary, on the England–Wales border. Daily discharge and monthly phosphorus (total reactive and total), for a limited number of reaches, are used to initially assess uncertainty and sensitivity of 44 model parameters, identified as being most important for discharge and phosphorus predictions. This study demonstrates that parameter homogeneity assumptions (spatial heterogeneity is treated as land use type fractional areas) can achieve higher model fits, than a previous expertly calibrated parameter set. The model is capable of reproducing the hydrology, but a threshold Nash-Sutcliffe co-efficient of determination (E or R ²) of 0.3 is not achieved when simulating observed total phosphorus (TP) data in the upland reaches or total reactive phosphorus (TRP) in any reach. Despite this, the model reproduces the general dynamics of TP and TRP, in point source dominated lower reaches. This paper discusses why this application of INCA-P fails to find any parameter sets, which simultaneously describe all observed data acceptably. The discussion focuses on uncertainty of readily available input data, and whether such process-based models should be used when there isn’t sufficient data to support the many parameters.     

Non-linear fuzzy-set based uncertainty propagation for improved DO prediction using multiple-linear regression

In this paper, a new non-linear fuzzy-set based methodology is proposed to characterize and propagate uncertainty through a multiple linear regression (MLR) model to predict DO using flow and water temperature as the regressors. The output is depicted as probabilistic rather than deterministic and is used to calculate the risk of low DO concentration. To demonstrate the new method, data from the Bow River in Calgary, Alberta from 2006 to 2008 are used. Low DO concentration has been occasionally observed in the river and correctly predicting, and quantifying the associated uncertainty and variability of DO is of interest to the City of Calgary. Flow, temperature and DO data were used to construct five MLR models, using different combinations of linear and non-linear fuzzy membership functions. The results show that non-linear representation of variance is superior to the linear approach based on model performance. Normal and Gumbel based membership functions produced the best results. The outputs from two non-linear fuzzy membership models were used to calculate risk of low DO. The predicted risk was between 3.9 and 4.9 %. This is an improvement over the traditional method, which can not indicate a risk of low DO for the same time period. This study demonstrates that water resource managers can adequately use MLR models to predict the risk of low DO using abiotic factors.