A Compromise Ratio Method with an Application to Water Resources Management: An Intuitionistic Fuzzy Set

Water resources management can be regarded as an iterative process of general decision making considering the applications and modifications of waters and related lands within a geographic region. This process helps decision makers to balance their diverse requirements and applications of water as an environmental resource, and to recognize how their activities can have impacts on the long-term sustainability. This paper introduces a new compromise ratio method based on Atanassov’s intuitionistic fuzzy sets under multiple criteria in real-life situations. Atanassov’s intuitionistic fuzzy weighted averaging (AIFWA) operator is applied to aggregate individual judgments of the decision makers to rate the relative importance of the selected criteria and potential alternatives. Then a new Atanassov’s intuitionistic fuzzy ranking index is proposed to analyze the potential alternatives. Finally, the performance of the proposed fuzzy decision-making method is illustrated to a real water resources management problem from the recent literature. Computational results demonstrate that the presented method can be utilized in a large-scale multi-level assessment process to assist the decision makers the optimal solution among the potential alternatives with multiple conflicting and compromising criteria.     

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.     

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.     

城市供水网络的综合安全评判方法及运用

针对供水网络安全性评价具有模糊性的特点,根据相关历史资料建立供水管网安全等级表,引入改进的层次分析法(AHP)确定评价指标的权重,在此基础上,发展了模糊模式识别模型和模糊综合评判相结合的多层次多级复杂系统模糊集评价方法.并对青岛市某区域管网进行了安全评价,提出了该区域供水管网的安全等级.     

基于动态权重的土质岸坡稳定性模糊评价方法

库岸边坡稳定性的快速评价对工程建设及灾害治理具有重要意义。针对传统综合评价法存在指标权重相对固定的不足,提出了一种基于动态权重的边坡稳定性综合评价方法。首先建立土质岸坡的多层次多指标稳定性评价体系,然后采用简单关联函数和层次分析法分别计算指标客观权重和主观权重,通过主客观综合赋权确定一个随指标取值变化的指标动态权重,最后引入可变模糊集理论提出基于动态权重的土质岸坡稳定性多级可变模糊评价方法。运用该方法分析了三峡库区周家坡滑坡在3种库水位下降速率时的稳定性,并采用极限平衡法验证了评价结果,实证研究表明动态权重法简便实用、科学合理,计算结果比传统的静态权重法更贴近工程实际。     

水利投资项目多目标模糊综合评价方法应用探析

 根据水利投资项目具有内部结构复杂，涉及因素众多，影响范围广泛，后果影响重大、深远，且难以预测等特点，以尼尔基水利枢纽工程为例，提出了一种较为完善的、对水利工程具有普遍意义的综合评价指标体系。采用Delphi法与层次分析法相结合的方法求出各指标权重值，并采用多层次模糊综合评价模型对其进行评价，得出了比较全面、客观的结论。     

Water Resources Allocation Using a Cooperative Game with Fuzzy Payoffs and Fuzzy Coalitions

In this paper, two fuzzy cooperative games are utilized for modeling equitable and efficient water allocation among water users in both inter-basin and intra-basin water allocation problems. The proposed all-inclusive water allocation approach consists of three main steps, following Sadegh et al. (Water Resour Manage 24(12):2991?C2310, 2010). In the first step, an initial water allocation is carried out using an optimization model taking into account an equity criterion. In the second step, the water users form crisp coalitions with fuzzy characteristic functions to increase the total net benefit of the system and also their own benefits. In the methodology used in this step, the water users do not need to have exact information about their payoffs and they can evaluate their payoffs as fuzzy numbers. In the second step, based on the Hukuhara difference of fuzzy numbers, optimum water allocation strategies are determined using a game with fuzzy characteristic function. In the third step, we applied another methodology which considers a class of fuzzy games with fuzzy characteristic functions and also fuzzy coalitions for water allocation. The methodology of this step is on the basis of the Hukuhara difference and the Choquet integral. The usefulness of the mentioned methodologies is studied by applying them to three defined real life scenarios in a case study of water allocation in Iran. The results showed that the proposed methodologies are professionally appropriate to real-world uncertain problems of equitable and economic inter-basin and intra-basin water resources allocations.     

Developing Strategies for Agricultural Water Management of Large Irrigation and Drainage Networks with Fuzzy MCDM

Sustainable water resources management aims at increasing the efficient use of water and achieving food security. This work proposes a generalized novel spatial fuzzy strategic planning (SFSP) in combination with multi-criteria decision making (MCDM) and a conceptual agricultural water use model for determining sustainable agricultural water management strategies. The proposed framework is applied to an irrigation and drainage network in Iran, which constitutes a large-scale water resource system. A spatial strength, weakness, opportunity, and threat (SWOT) analysis of internal and external factors related to agricultural water management is applied in this work. Possible water management strategies were ranked with the MCDM approach that combines the Analytic Hierarchy Process (AHP) and the Fuzzy technique for order-preference by similarity to ideal solution (TOPSIS). The AHP estimates the criteria weights and the TOPSIS model prioritizes the agricultural water management strategies. The results of SWOT analysis show that the final scores of the internal and external factors are equal to 2.9 and 2.73, respectively. Accordingly, the most attractive strategic type is a SO (aggressive) strategy, and a combination of structural and non-structural strategies (SO, ST, and WO strategies) are the top-ranked ones. Proposed strategies for water supply and demand management are the development and rehabilitation of the physical structure of water resources system of irrigation network, improvement of operation management and maintenance of water resources system, wastewater management, and inter-basin water transfer within the irrigation network. The results indicate that the total annual volume of agricultural water under normal conditions is about 1.8 billion cubic meters, of which about 1707 million cubic meters (95%) issue from surface water sources and 90 million cubic meters (5%) from groundwater sources. The proposed model and the calculated results provide viable and effective solutions for the implementation of sustainable management of water resources and consumption in large-scale water resources systems.

     

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.     

Variable Sets and Fuzzy Rating Interval for Water Allocation Options Assessment

Optimal water allocation is an important means of improving water use efficiency. However, since water allocation options are usually characterized by multi-region, multi-principle and multi-criterion factors, decision-makers often have difficulty in making objective decisions using them because the many available water allocation options often make the ratings of the options so close to be ranked. This study present a hierarchy variable sets (VS) model, based on the single-layer variable sets model, for ranking the water allocation options of Jining City, China. The ratings of the options are evaluated using a fuzzy rating interval (FRI) that can overcome homogenization in the ratings. The structure of the model presented in this study is clear with a simple procedure of computation and the result is rational. The case study used illustrates that this model can help decision-makers know the rating of water allocation options partially and overall. The computed result from this model appears more convincing than a previous water allocation approach for the city based on the maximum entropy principle.     

基于水资源环境价值论的水价确定方法与例证

在充分考虑自然、社会和经济等各方面的因素的基础上，从水资源环境价值理论入手，采用模糊数学层次分析法，建立水资源价值模糊综合评价指标体系与综合评判数学模型，对水资源价值进行综合评价；然后引入价格向量进行转化，成为考虑了各方面影响因素的水价；并运用所建立的方法，以所调查的大量基础资料为数据支撑，分析计算了石家庄市2001典型年、不同用途用水户的水价。     

基于模糊层次分析法的农村水库大坝安全二级模糊综合评价

基于《水库大坝安全评价导则》构建了农村地区水库大坝安全二级模糊综合评价体系,选取17个一级影响因素、5个二级影响因素作为评价指标。采用模糊层次分析法计算各指标一级权重和二级权重。该方法充分地体现了因素相对重要性比较的模糊性,有效地解决了传统的层次分析法的不足,明确了隶属函数的意义,对正态分布隶属函数进行修正,使隶属函数更加符合实际情况。采用多位专家评分的办法给出定性指标的量化值,以便得出单因素的隶属度使得因素隶属度更加合理和可信。最后,分别进行一级模糊综合评价和二级模糊综合评价。运用该方法对某农村地区水库大坝安全性进行评价,其结果合理,可供工程实践参考和借鉴。     

太湖流域水资源承载能力模糊综合评价

在充分考虑太湖流域水资源开发利用现状及社会经济发展状况的基础上,采用驱动力-压力-状态-影响-反应模型,突出生态环境影响因子,建立符合太湖流域自身特点的水资源承载能力综合评价指标体系,并按照水资源状态、水资源与社会经济、水资源与生态环境3个方面对指标进行分类,运用层次分析法计算各指标权重,对太湖流域2000—2006年水资源承载能力进行模糊综合评价。评价结果表明,太湖流域水资源承载能力总体水平处于适载与超载的临界状态,提升空间有限。     

基于组合权重的模糊物元模型在输水管材选型中的应用

在输调水工程中,管材选型问题具有模糊不相容和多目标性的特点,是工程技术人员面临的技术难题。建立了一种基于变异系数和层次分析法的模糊物元评价方法,分析了影响管材选择的各种指标,构建了管材类型选择的综合评价指标体系;引入了变异系数法修正层次分析法确定指标权重时的主观性,从而确定了评价指标的组合权重,建立了模糊物元评价模型,并利用欧式贴近度结合价值工程原理判断最优管型。在研究过程中,以新疆某引水管线工程的管材选型为例进行评价模型的工程应用,经计算可得最适宜该工程的管材类型为玻璃纤维增强塑料夹砂管(FRPM)。结果表明,利用本模型进行管材选型,可以根据实地工程条件以及管材技术特性,考虑技术、经济、施工、安全等多方面影响因素,选择出适宜本工程条件的最优管型。     

Flood Control Operations Based on the Theory of Variable Fuzzy Sets

Flood control decisions are often involved with quantitative and qualitative criteria. In this paper, a decision model is presented for flood control operations based on the theory of variable fuzzy sets. Using dual comparison, two models computing relative membership grades with qualitative and quantitative criteria are established, respectively. A method integrating subjective preference and iterative weights is proposed for weight-assessment. First, an initial solution of criteria weights is obtained by using proposed fuzzy optimal iteration model. Then, according to their knowledge related to real time flood operations, operators may modify the initial weights if necessary. When the relative membership grades of alternatives belonging to all rankings are fixed by using multi-criterion variable fuzzy model proposed, the decision alternative is chosen according to the ranking characteristic value computed using a defuzzification equation. The case study of Fengman Reservoir flood operation (in China) is provided to illustrate the application of the proposed method. With the incorporation of operator’s knowledge related to flood operations, the proposed model is flexible and practical.     

A Fuzzy Robust Nonlinear Programming Model for Stream Water Quality Management

An interval-parameter fuzzy robust nonlinear programming (IFRNP) approach was developed for stream water quality management under uncertainty. The interval and fuzzy robust programming methods were incorporated within a general framework to address uncertainties associated with the nonlinear objective and the left- and right-hand sides of the constraints. A piecewise linearization approach was developed to deal with the nonlinear cost function. IFRNP could explicitly address complexities of various system uncertainties, where parameters were represented as both interval numbers and fuzzy membership functions. Furthermore, the dual uncertain information associated with the lower and upper bounds of each interval parameter could be effectively tackled through the concept of fuzzy boundary interval. The proposed IFRNP method was applied to a case of water quality management in the Guoyang section of the Guo River in Anhui province, China. A number of cost-effective schemes for water quality management were generated, and allowable wastewater discharge amounts were recommended. The results indicated that IFRNP was applicable to water quality management problems, where high nonlinearities and dual uncertainties exist.     

修正的模糊综合评判法在地下水水质评价中的应用

模糊综合评判法在水质评价中越来越为更多的环境水文地质工作者所采用,但在地下水质量评价中存在确定隶属度问题和模糊数学综合评判法的复合运算问题。通过对存在的问题进行简单的处理,对评价方法加以修正,并将修正前后的方法应用同一案例,进行评价效果对比。结果显示,由于所采用的案例区域地下水水质较差,因此导致评价结果与改进前的"相乘取大"和"取小取大"算子相似性较强,但评价结果仍显示,改进后的方法更为真实的反映了地下水水质状况,方法可行,评价结果可信,有一定的借鉴意义。     

区域水资源模糊多目标规划模型及求解

针对区域水资源系统规划的多目标性和各目标的不精确性，建立了区域水资源系统模糊多目标线性规划模型。该模型改变了以往按确定性目标进行优化的思路，只需要给定目标值一个范围，就可以在规定的目标范围内进行优化求解。在求解过程中，建立了以各模糊目标隶属度值最大化为目标的模糊目标规划模型，采用目标隶属函数正负偏差量变量替换的方法，用线性目标规划的方法求解。经过实例验证，该模型求解比较简单，求解结果合理，与普通规划结果相比水资源模糊目标规划在规定目标的范围内取得了更好的优化结果。     

An Interactive Fuzzy Satisfying Approach for Sustainable Water Management in the Yellow River Delta,China

This paper proposes using an interactive fuzzy satisfying method to solve multi-objective optimization problems in integrated water management of the Yellow River Delta, China. The approach involves economic, social and ecological objectives represented by net returns, water deficiency and ecological water requirements, respectively. It considers the decision-maker’s preferences in terms of fuzzy satisfying of each objective and holistic satisfying of all objectives based on Euclid distance. The method avoids the subjectivity of having decision-makers assigning weights to the multiple objectives to some degree. The method is applied to the Yellow River Delta, China. Results indicate that considerably more water should be allocated to ecological uses of water in the Yellow River than currently occurs. An interactive fuzzy satisfying approach for the multi-objective optimization problems has significant potential in the field of integrated water management.     

基于层次分析和灰色分析的水质风险评价方法

给出一种基于层次分析和灰色分析的水质风险评价方法:用层次分析法计算水质评价因子权重,用带权重的灰色分析法评价多因素影响下的纯净水水质。结果表明,用层次分析法为评价因子赋权能够全面考虑各评价因子对水质影响的不同;用灰色分析法计算纯净水的风险度值和风险级别,考虑了水质评价中的模糊性和不确定性,比较符合纯净水水质评价的实际情况。