A Fuzzy-Stochastic Modeling Approach for Multiple Criteria Decision Analysis of Coupled Groundwater-Agricultural Systems

The complexity of water resources management increases when decisions about environmental and social issues are considered in addition to economic efficiency. Such complexities are further compounded by multiple uncertainties about the consequences of potential management decisions. In this paper, a new fuzzy-stochastic multiple criteria decision-making approach is proposed for water resources management in which a variety of criteria in terms of economic, environmental and social dimensions are identified and taken into account. The goal is to evaluate multiple conflicting criteria under uncertainties and to rank a set of management alternatives. The methodology uses a simulation-optimization water management model of a strongly interacting groundwater-agriculture system to enumerate criteria based on these bio-physical process interactions. Fuzzy and/or qualitative information regarding the decision-making process for which quantitative data is not available are evaluated in linguistic terms. Afterwards, Monte Carlo simulation is applied to combine these information and to generate a probabilistic decision matrix of management alternatives versus criteria in an uncertain environment. Based on this outcome, total performance values of the management alternatives are calculated using ordered weighted averaging. The proposed approach is applied to a real world example, where excessive groundwater withdrawal from the coastal aquifer for irrigated agriculture has resulted in saltwater intrusion, threatening the economical basis of farmers and associated societal impacts. The analysis has provided potential decision alternatives which can serve as a platform for negotiation and further exploration. Furthermore, sensitivity of different inputs to resulting rankings is investigated. It is found that decision makers’ risk aversion and risk taking attitude may yield different rankings. The presented approach suits to systematically quantify both probabilistic and fuzzy uncertainties associated with complex hydrosystems management.     

A New Integrated MADM Technique Combined with ANP,FTOPSIS and Fuzzy Max-Min Set Method for Evaluating Water Transfer Projects

In sustainable water resources management, it is essential to rank inter-basin water transfer projects. This task is difficult due to many different conflict criteria, complex relations among criteria and various judgments of decision makers. In this paper, an integrated multiple attribute group decision making method consists of ANP (Analytical Network Process), fuzzy TOPSIS and fuzzy max-min set methods is proposed for evaluating water transfer projects. A set of over 60 criteria in social, environmental and economic sectors are used for ranking four water transfer projects in Karun River based on three decision maker judgments. A key novelty of the proposed methodology is its ability to model both complex relations among different criteria in water management and the influence of decision maker judgments’ weights on the final ranking in group decision making problem. The procedure starts by obtaining the priority of water transfer projects and the weight of each decision maker judgments by employing ANP and fuzzy TOPSIS, respectively. These weights are used as inputs in the fuzzy max-min set method. Then the effects of decision maker weights on the final ranking are determined in fuzzy environment. Finally, the sensitivity analysis of decision makers’ weights has been conducted. The results show that the proposed method is an effective tool for group decision making problems by considering different criteria and decision makers’ weights.     

A Multicriteria Group Decision Model to Support Watershed Committees in Brazil

The involvement of multiple decision makers in water resources management can be very complex, involving the possibilities of conflicts amongst the stakeholders and the influence of powerful members over the preference of others. The inherent characteristic of decisions also increases this complexity due to many alternatives being involved and there being multiple criteria. Some of these criteria conflict with each other and the consequences of which will have great impact on those involved and on third parties. Therefore, a group decision support system model based on multicriteria analysis can be a powerful tool to support this kind of management. This study presents a tool to support the committee responsible for the management of the watersheds in Brazil in order to promote decentralization and the participation of all involved in the water resources management. The tool provides a ranking of alternatives for the environmental recuperation of the watershed through the use of the multicriteria method PROMETHEE II. For each decision maker, the alternatives were ranked and then the individual rankings were combined into a global ranking which contained the preferences of the whole group.     

Fuzzy AHP Assessment of Water Management Plans

There are two mainstreams when using the analytic hierarchy process (AHP). One is the standard applications of crisp distributive and ideal mode versions. The other is characterised by fuzzification of the AHP methodology and by attempts to better tackle inherently uncertain and imprecise decision processes with quantitative and qualitative data. The latter is characterised by different approaches to fuzzificating the decision problem; the way of conducting judgment and evaluating process; and finally, in synthesising the results and manipulating fuzzy numbers to devise priorities for the decision alternatives. This paper presents a fuzzy methodology for solving fully structured decision problems with criteria, sub-criteria and alternatives. It follows the logic of AHP in a simple and straightforward manner, efficiently aggregates criteria and sub-criteria into unique hierarchical level and applies a total integral method for comparing decision alternatives. The proposed methodology has been used for the assessment of water management plans in part of the Paraguacu River Basin in Brazil.     

Identifying Optimal Water Resources Allocation Strategies through an Interactive Multi-Stage Stochastic Fuzzy Programming Approach

In this study, an interactive multi-stage stochastic fuzzy programming (IMSFP) approach has been developed through incorporating an interactive fuzzy resolution (IFR) method within an inexact multi-stage stochastic programming framework. IMSFP can deal with dual uncertainties expressed as fuzzy boundary intervals that exist in the objective function and the left- and right-hand sides of constraints. Moreover, IMSFP is capable of reflecting dynamics of uncertainties and the related decision processes through constructing a set of representative scenarios within a multi-stage context. 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 (i.e., risk of constraint violation) has been generated for planning the water resources allocation. They can not only help quantify the relationship between the objective-function value and the risk of violating the constraints, but also enable decision makers (DMs) to identify, in an interactive way, a desired compromise between two factors in conflict: satisfaction degree of the goal and feasibility degree of constraints. Besides, a number of decision alternatives have been generated under different policies for water resources management, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic penalties when the promised water-allocation targets are violated, and thus help DMs to identify desired water-allocation schemes under uncertainty.     

Integrated Use of a Continuous Simulation Model and Multi-Attribute Decision-Making for Ranking Urban Watershed Management Alternatives

The objective of this paper is to introduce a continuous simulation-based screening procedure for ranking urban watershed management alternatives using multi-attribute decision making (MADM). The procedure integrates continuous urban runoff simulation results from the United States Environmental Protection Agency’s Storm Water Management Model (SWMM) with the use of an alternative evaluation index (AEI) and MADM techniques, following the driver-pressure-state-impact-response (DPSIR) approach. The analytic hierarchy process estimates the weights of the criteria, and SWMM results are used to quantify the effects of the management alternatives on water quantity and quality metrics. In addition, the tendency of AEI to reflect resident preferences toward management objectives is incorporated to include stakeholder participation in the decision-making process. This systematic decision support process is demonstrated for a Korean urban watershed. According to the AEI, seven alternatives were divided into three groups: poor (0∼0.3), acceptable (0.3∼0.6), and good (0.6∼1). The use of multiple MADM techniques provided a consistency check. The demonstration illustrates the ability of the continuous simulation-based MADM approach to provide decision makers with a ranking of suitable urban watershed management alternatives which incorporate stakeholder feedback.     

Voting Under Uncertainty: A Stochastic Framework for Analyzing Group Decision Making Problems

Water resources policy making often involves consideration of a broader scope of environmental, economic, and social issues. This inevitably complicates policy making since consensus among multiple stakeholders with different interests is needed to implement decisions. This work employs several practical and popular voting methods to solve a multi-stakeholder hydro-environmental management problem. Conventionally, voting methods or social choice rules have been applied for consensus development in small groups and elections. This work combines voting methods with a Monte-Carlo selection, in order to help with social choice making under uncertainty. This process is intended to aid decision-makers with understanding of the risks associated with potential decision alternatives. The Sacramento-San Joaquin Delta’s water export conflict is solved here as a benchmark problem to illustrate the proposed framework for social decision making and analysis under uncertainty.     

A Fuzzy Multi-Criteria Group Decision-Making Model Based on Weighted Borda Scoring Method for Watershed Ecological Risk Management: a Case Study of Three Gorges Reservoir Area of China

In watershed ecological risk management, a series of alternatives will be analyzed in terms of multiple complex criteria, and different stakeholders with conflicting risk attitudes will be involved, which means that ecological risk management decision-making is a process surrounded by a wide range of uncertainties derived from scarcity of data, lack of knowledge, deficiency of assumptions and lexical vagueness. Based on modified Borda scoring method, this paper discusses how to apply a fuzzy multi-criteria group decision-making (FMCGDM) model into such a process. Then, a two-stage, 12-step MCDM methodology is proposed to obtain the optimal alternative decided by multiple decision-makers (DMs) from a given alternatives set. Firstly, all DMs make their own independent choice respectively, then, all the independent conclusions are integrated by using their subjective/objective weights. A modified Borda method is followed to rate and rank the weighted alternatives; in which the one with the highest score will be selected as the final preferable option. This model is demonstrated to be applicable and reliable by an application in the ecological risk decision making process of Three Gorges Reservoir area located in the upper reaches of Yangtze River in China. Of course, this method can also be applied in other research fields of environmental management.     

Application of Multi-Criterion Decision Making Analysis to Integrated Water Resources Management

In the context of integrated water resources management (IWRM), account should be taken of a wide range of factors including economic, social and environmental issues. Multi-criterion decision making (MCDM) approaches are applied to the case study in this paper to integrate different objectives into the planning, management and decision making process. A variety of criteria in terms of economic, social and environmental dimensions are identified and formulated for the purpose of MCDM analysis. A set of different management scenarios is proposed for the desired goals. They include reductions in irrigated areas, improved irrigation efficiencies, increased system loss for groundwater irrigation and changes in cropping pattern. An integrated water resources optimisation model (IWRO) is used to optimise surface and groundwater allocation, through which the identified criteria can be enumerated. Compromise programming (CP), which results in a compromise solution located as close as possible to an ideal solution, is adopted to carry out the MCDM analysis for the case study. The sensitivity of different sets of weights and different values of parameters related to CP is investigated. Results indicate that compromise programming is able to lead to satisfactory solutions. Performance of different alternatives is evaluated based on the compromise programming analysis, and potential decisional alternatives are proposed for further investigation.     

Interval-parameter Two-stage Stochastic Semi-infinite Programming: Application to Water Resources Management under Uncertainty

In this study, an interval-parameter two-stage stochastic semi-infinite programming (ITSSP) method was developed for water resources management under uncertainty. As a new extension of mathematical programming methods, the developed ITSSP approach has advantages in uncertainty reflection and policy analysis. In order to better account for uncertainties, the ITSSP approach is expressed with discrete intervals, functional intervals and probability density functions. The ITSSP method integrates the two-stage stochastic programming (TSP), interval programming (IP) and semi-infinite programming (SIP) within a general optimization framework. The ITSSP has an infinite number of constraints because it uses functional intervals with time (t) being an independent variable. The different t values within the range [0, 90] lead to different constraints. At same time, ITSSP also includes probability distribution information. The ITSSP method can incorporate pre-defined water resource management policies directly into its optimization process to analyze various policy scenarios having different economic penalties when the promised amounts are not delivered. The model is applied to a water resource management system with three users and four periods (corresponding to winter, spring, summer and fall, respectively). Solutions of the ITSSP model provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable interval solutions were generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of stream flow. The obtained solutions are useful for decision makers to obtain insight regarding the tradeoffs between environmental, economic and system reliability criteria.     

A Framework for Ground Water Management Based on Bayesian Network and MCDM Techniques

Groundwater resources are steadily subjected to increasing water demands. The aquifers are considered as the most accessible source of fresh water. In recent years, they have been faced with severe water withdrawal in arid and semi-arid countries like Iran and thus some aquifers was considered as forbidden aquifers that it means the water withdrawal from these aquifers is unauthorized. Given a critical situation, groundwater resources management in the form of tools such as monitoring the level of the aquifers and developing the restoring scenarios is essential. Therefore, for this purpose, a framework has been developed based on prediction of groundwater level using Bayesian Networks (BNs) model. Furthermore, Multi Criteria Decision Making methods (MCDM) techniques proposed and employed for ranking of proposed groundwater management scenarios. This framework was evaluated for restoring the Birjand aquifer in Iran in different hydrological conditions. A probabilistic Dynamic BN was proposed for groundwater level prediction under uncertainties. After analyzing the obtained results, the applicable short term scenarios for groundwater management as well as appropriate economic, social and technical criteria were defined for decision making procedure. Then, using elicitation of decision makers’ opinions on the relative importance and performance of criteria, SAW, TOPSIS and PROMETHEE-II techniques were applied to rank the scenarios and the obtained results were aggregated by Borda method for final ranking of the scenarios. Lastly, the final results demonstrates the capability of the proposed framework for groundwater resources planning and management which can be employed for reducing the risk of aquifer level declining.     

Fuzzy TOPSIS Multi-Criteria Decision Analysis Applied to Karun Reservoirs System

Water resource systems, with an abundance of project purposes and resource values, are subject to conflicting policy, planning, and management decisions. Multi-criteria decision making methods (MCDM) provide a framework to help water managers identify critical issues, attach relative priorities to those issues, select best compromise alternatives, and facilitate communication to gain general acceptance. This paper addresses a method that incorporates several system factors/components within a general framework for providing a holistic analysis of the problems and comprehensive evaluation of the related mitigation/adaptation measures and policy responses. The method accounts for uncertainties in both the quantification and importance of objectives in the ranking process. The proposed fuzzy multi-criteria decision making process uses the well known Technique for Order Preference by Similarity of Ideal Solution (TOPSIS) method in both deterministic and uncertain environments. The performance of the proposed approach to a real water resource management problem in Iran is illustrated. Results show that the model may be used in a large-scale multi-level assessment process. Ranks of the alternatives are presented using deterministic and fuzzy based models.     

大连市水资源利用与宏观经济协调发展规划多目标群决策模型与方法

以大连市水资源开发利用与宏观经济协调可持续发展为研究背景，建立了大连市宏观经济水资源发展规划多目标群决策模型。根据该决策模型具有的多层次多目标多决策者的特点，结合陈守煜建立的工程模糊集理论与切比雪夫决策方法，提出了模糊切比雪夫多目标群决策方法。结果表明，该决策模型与模糊切比雪夫多目标群决策方法是有效和可行的。     

Extension of Fuzzy Delphi AHP Based on Interval-Valued Fuzzy Sets and its Application in Water Resource Rating Problems

Water resource management problems are complex by nature and are often accompanied by many uncertainties, requiring suitable decision-making tools to solve. If decision makers cannot agree on a method of defining linguistic variables based on the fuzzy sets, favorable results and more accurate modeling can be achieved by using interval-valued fuzzy sets (IVFSs), which provide an additional degree of freedom to represent the uncertainty and fuzziness of the real world. Accordingly, this study is aimed to extend a fuzzy Delphi analytic hierarchy process (AHP) based on IVFSs (Interval-Valued Fuzzy Delphi AHP) and its application to large-scale rating problems related to water resource management. The proposed method is subsequently applied to select an optimal strategy for the rural water supply of Nohoor Village in northeast Iran, as a case study and actual water resource rating problem. According to sensitivity analyses of the results and a comparison of the results with a real project, the proposed method offers good outcomes for water resource rating problems.     

Planning for Regional Water System Sustainability Through Water Resources Security Assessment Under Uncertainties

A leader-follower relationship in multiple layers of decision makers under uncertainties is a critical challenge associated with water resources security (WRS). To address this problem, a credibility-based chance-constrained hierarchical programming model with WRS assessment is developed for regional water system sustainability planning. This model can deal with the sequential decision-making problem with different goals and preferences, and reflect uncertainties presented as fuzzy sets. The effectiveness of the developed model is demonstrated through a real-world water resources management system in Beijing, China. A leader-follower interactive solution algorithm based on satisfactory degree is utilized to improve computational efficiency. Results show the that: (a) surface water, groundwater, recycled water, and off water would account for 27.01, 27.44, 23.11, and 22.44% of the total water supplies, respectively; (b) the entire pollutant emissions and economic benefits would consequently decrease by 31.53 and 22.88% when the statue changes from quite safe to extremely far from safe; and (c) a high credibility level would correspond to low risks of insufficient water supply and overloaded pollutant emissions, which lowers economic benefits and pollutant emissions. By contrast, a low credibility level would decrease the limitations of constraints, which leads to high economic benefits and pollutant emissions, but system risk would be increased. These findings can aid different decision makers in identifying the desired strategies for regional water resources management under multiple uncertainties, and support the in-depth analysis of the interrelationships among water security, system efficiency, and credibility level.     

Pareto Optimization of Water Resources Using the Nexus Approach

The continuously growing population in combination with the escalating urbanization and economic growth increase the pressure on water, energy and food resources of our planet. This entails an urgent need for proper water resources management within the water-energy-food (WEF) nexus concept. The WEF nexus considers water, energy and food as three continuously interconnected sectors, whose complex interactions lead to an increased number of trade-offs and potential conflicts. Computational modeling can be used to quantify these interactions, reduce trade-offs and promote synergies. We investigate the water resources in the Upper Blue Nile River (UBNR) basin, one of the two main sources of the Nile, using the Hydronomeas tool. Hydronomeas is based on the parameterization-simulation-optimization method; optimization is implemented in two levels, using a holistic approach and multiple criteria. We assign various targets, constraints and priorities to the UBNR system of reservoirs, hydropower plants and irrigation projects and derive a Pareto front that contains alternative, optimal solutions, for which improvement of one objective can be achieved only at the expense of another. By visualizing the trade-offs between the conflicting objectives of hydropower and irrigation, we aim to help decision makers understand changes due to different management policies and thus, achieve greater efficiency in water resources management in the Nile region.     

An Integrated Approach of System Dynamics,Orthogonal Experimental Design and Inexact Optimization for Supporting Water Resources Management under Uncertainty

An integrated approach of system dynamics (SD), orthogonal experimental design (OED) and inexact optimization modeling was proposed for water resources management under uncertainty. The developed method adopted a combination of SD and OED to identify key scenarios within multiple factors, through which interval solutions for water demands could be obtained as input data for consequential optimization modeling. Also, optimal schemes could be obtained in the combination of inexact two-stage stochastic programming and credibility constrained programming. The developed method was applied to a real-world case study for supporting allocation of multiple-source water resources to multiple users in Dalian city within a multi-year context. The results indicated that a lower credibility-satisfaction level would generate higher allocation efficiency, a higher system benefit and a lower system violation risk. The developed model could successfully reflect and address the variety of uncertainties through provision of credibility levels, which corresponds to the decision makers’ preference regarding the tradeoffs between system benefits and violation risks.     

Editorial Comments on the World Commission on Water for the 21stCentury

Abstract

In this study, in order to create a decision-making model on water resources projects, a hierarchy of criteria has been developed by public participation. The Value Management methodology has been used for extraction of the effective criteria and attributes in the scope of Integrated Water Resources Management (IWRM). The hierarchy is generic for water resources management in the Islamic Republic of Iran. Since the evaluations of alternatives with respect to some attributes are uncertain and vague, fuzzy set theory has been used. By merging fuzzy set theory and multi-attribute decision-making a new Decision Support System (DSS), namely FDM, has been developed to compare different alternatives. As an innovation, FDM accepts evaluations of alternatives with respect to the attributes as crisp variables, fuzzy variables, and linguistic variables. FDM embodies an expert system whose duty is to choose an appropriate method among the SAW, Fuzzy SAW, TOPSIS or Fuzzy TOPSIS based on the characteristics of the problem.

The central and Southeastern regions of Iran are considered arid regions, suffering from water shortages. In this paper, water transfers to the Zayanderud basin in Iran have been modeled by FDM. Successful application of this DSS in this study allows for its application by water authorities in other case studies.     

Evaluating Water Transfer Projects Using Analytic Network Process (ANP)

This article introduces the analytic network process (ANP) as an effective tool for ranking water transfer projects. Water resources are the main basis of stable development around the world. Uneven water distribution and the shortage of water in some areas have caused water managers to consider interbasin water transfer as a solution to these water problems. Due to the many different conflict criteria in ranking water projects, ranking execution projects is one of the most critical and difficult tasks in water management. Multiple Attribute Decision Making (MADM) is a collection of methodologies to compare, select, or rank multiple alternatives that typically involve incommensurate attributes. Many decision problems cannot be structured hierarchically because they involve the interaction and dependence of higher-level elements in a hierarchy on lower-level ones. This study deals with ranking water transfer projects as a MADM problem. Due to the fact that many of the criteria are related to each other, the Analytic Network Process (ANP) is proposed for ranking projects. Ten water transfer projects in Karun River are investigated. Thirty influential factors are identified. They are classified under benefit, cost and risk criteria. The objective of this investigation is ranking alternatives with respect to different criteria in network form. Finally, sensitivity analysis is introduced.     

Multi-criteria Decision Analysis: A Strategic Planning Tool for Water Loss Management

Water utilities particularly in the developing countries continue to operate with considerable inefficiencies in terms of water and revenue losses. With increasing water demand and scarcity, utilities require effective strategies for optimum use of available water resources. Diverse water loss reduction options exist. Deciding on which option to choose amidst conflicting multiple criteria and different interests of stakeholders is a challenging task. In this paper, an integrated multi-criteria decision-aiding framework for strategic planning of water loss management is presented. The PROMETHEE II method was applied within the framework in prioritizing water loss reduction options for Kampala city. A strategic plan that combines selective mains and service lines replacement and pressure management as priorities is the best compromise based on preferences of the decision makers and seven evaluation criteria characterized by financial-economic, environmental, public health, technical and social impacts. The results show that the most preferred options are those that enhance water supply reliability, public health and water conservation measures. This study demonstrates how decision theory coupled with operational research techniques could be applied in practice to solve complex water management and planning problems.