IFRP: A hybrid interval-parameter fuzzy robust programming approach for waste management planning under uncertainty

Nie, Xianghui; Huang, Guohe; Li, Y. P.; Liu, L.

doi:10.1016/j.jenvman.2006.04.006

Cited by 141 publications

(103 citation statements)

References 38 publications

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“…Considering the quality of available data in this study case, such parameters were expressed as triangular fuzzy sets. Fuzzy α-cut levels of 0.2, 0.5 and 0.8 that represented the lower, middle and higher values of fuzzy membership grades, respectively, were considered for all the fuzzy parameters in this study [33][34][35]. Figure 2 shows the total amount of available water resources expressed as fuzzy sets.…”

Section: Data Source and Processingmentioning

confidence: 99%

Optimal Use of Agricultural Water and Land Resources through Reconfiguring Crop Planting Structure under Socioeconomic and Ecological Objectives

Tan

Shan

2017

Water

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Many economic, social and ecological problems can be attributed to the scarcity and mismanagement of water and land resources. In this study, a multi-objective fuzzy-robust programming (MOFRP) method was developed for supporting the optimal use of land and water resources in agriculture. MOFRP improved existing methods through taking ecological services of crop cultivation into account. It was also capable of reflecting fuzziness in preferences, priorities and parameters that were largely neglected in previous agricultural decision making. This method was applied to address a case in arid northwestern China. Optimal plans of crop cultivation reconfiguration were generated for sustaining local development under economic, ecological and social objectives as well as physical restraints in water and land resources. Compared to the status quo, the optimized plan would increase economic and ecological benefits by 12.2% and 18.8%, respectively. The efficiency of irrigation water could also be enhanced with the economic and ecological benefits per unit water being raised and the water consumption per unit land being reduced. The comparisons of the MOFRP model to four alternatives validated that it was capable of achieving satisfactory benefits and reducing system-violation risks without neglecting valuable uncertain information and ecological services of crops. The proposed method was also applicable to other multi-objective management problems under uncertainty without loss of generality.

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Section: Data Source and Processingmentioning

confidence: 99%

Optimal Use of Agricultural Water and Land Resources through Reconfiguring Crop Planting Structure under Socioeconomic and Ecological Objectives

Tan

Shan

2017

Water

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“…To solve the IFRTSRP problem, assumptions are made in this solution process: For each parameter presented as fuzzy boundary interval, the fuzzy sets of the lower and upper bounds have no intersections and dependences (Nie et al 2007). Based on the assumptions, when the water allocation targets (W AE im and W AE in ) are known, the IFRTSRP problem can be solved within an ILP framework by utilizing FRP optimization techniques.…”

Section: Modeling Formulationmentioning

confidence: 99%

“…Thus, according to the related studies (Negoita et al 1976;Luhandjula and Gupta 1996;Huang and Loucks 2000;Liu et al 2003;Nie et al 2007), a two-step method associated with various a-cut levels and the representation theorem can be used to solve model (3). In detail, the first submodel can be formulated as follows:…”

Section: Modeling Formulationmentioning

confidence: 99%

“…Instead, fuzzy robust programming (FRP), which is based on fuzzy set theory, can effectively reflect fuzzy uncertainties in both left-and right-hand sides coefficients (of the model's constraints) as represented by fuzzy membership functions (Liu et al 2003;Singh and Dhillon 2008). By delimiting an uncertain decision space through dimensional enlargement of the original fuzzy constraints, FRP can enhance the robustness of the optimization process (Nie et al 2007;Cai et al 2009). Interval linear programming (ILP) can effectively tackle uncertainties expressed as discrete intervals.…”

Section: Introductionmentioning

confidence: 99%

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An inexact optimization model associated with two robust programming approaches for water resources management

Liu

et al. 2014

Int. J. Environ. Sci. Technol.

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In this study, an interval fuzzy-robust two-stage stochastic-robust programming (IFRTSRP) model is developed for water resources management under uncertainty. The developed IFRTSRP model incorporates two-stage stochastic programming (TSP), fuzzy robust programming (FRP), interval linear programming (ILP), and stochastic robust optimization (SRO) within a general optimization framework. The IFRTSRP model can not only deal with uncertainties presented as probability distributions, fuzzy membership functions, discrete interval numbers, and their combinations, but also provide an effective linkage between the pre-regulated water resources management policies and the associated economic implications. The IFRTSRP model can also enhance the robustness for the optimization process by delimiting the uncertain decision space through dimensional enlargement of the original fuzzy constraints. Moreover, the IFRTSRP model can evaluate the trade-offs between system economy and stability by incorporating the variability measures on penalty costs into the objective function. The IFRTSRP model is applied to a hypothetical case study of water resources management. The results indicate that reasonable solutions would be generated under different levels of k and/or x (non-negative weight coefficients); moreover, a higher net system benefit would correspond to lower system stability and higher system failure risk. Thus, the modeling results can be used for generating decision alternatives and thus help the managers to identify desired water allocation policies based on the reasonable consideration of system economy, system stability, and system failure risk.

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“…Most of them are related to stochastic mathematical programming (SMP) derived from probability theory (Ellis et al, 1985;Ellis et al, 1986;Guldman, 1988;Qin et al, 2010), interval mathematical programming (IMP) based on interval analysis (Li et al, 2006;Li et al, 2010;Lu et al, 2009) and fuzzy mathematical programming (FMP) as a branch of fuzzy sets theory (Liu et al, 2003;Lu et al, 2008). SMP can deal with various probabilistic uncertainties; however, the increased data requirements for specifying the parameters' probability distributions may affect its practicality (Nie et al, 2007). IMP has been proved to be effective in dealing with uncertainties, which does not require distributional information and will not lead to complicated intermediate models.…”

Section: Introductionmentioning

confidence: 99%

A generalized fuzzy linear programming approach for environmental management problem under uncertainty

Fan

Huang

Veawab

2011

Journal of the Air & Waste Management Association

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In this study, a generalized fuzzy linear programming (GFLP) method was developed to deal with uncertainties expressed as fuzzy sets that exist in the constraints and objective function. A stepwise interactive algorithm (SIA) was advanced to solve GFLP model and generate solutions expressed as fuzzy sets. To demonstrate its application, the developed GFLP method was applied to a regional sulfur dioxide (SO 2 ) control planning model to identify effective SO 2 mitigation polices with a minimized system performance cost under uncertainty. The results were obtained to represent the amount of SO 2 allocated to different control measures from different sources. Compared with the conventional interval-parameter linear programming (ILP) approach, the solutions obtained through GFLP were expressed as fuzzy sets, which can provide intervals for the decision variables and objective function, as well as related possibilities. Therefore, the decision makers can make a tradeoff between model stability and the plausibility based on solutions obtained through GFLP, and then identify desired policies for SO 2 -emission control under uncertainty.Implications: The GFLP method is effective in addressing air quality management planning associated with fuzzy parameter in the constraints and objective. The stepwise interactive algorithm proposed to solving the GFLP model would not lead to complicated intermediate submodels. Thus it would be much applicable for large-scale air quality management problems. The applications of the method can help decision makers in (i) generating allocation schemes for SO 2 emissions; (ii) identifying the plausibility of each allocation alternative; and (iii) estimating the total costs of different SO 2 emission control policies.

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IFRP: A hybrid interval-parameter fuzzy robust programming approach for waste management planning under uncertainty

Cited by 141 publications

References 38 publications

Optimal Use of Agricultural Water and Land Resources through Reconfiguring Crop Planting Structure under Socioeconomic and Ecological Objectives

Optimal Use of Agricultural Water and Land Resources through Reconfiguring Crop Planting Structure under Socioeconomic and Ecological Objectives

An inexact optimization model associated with two robust programming approaches for water resources management

A generalized fuzzy linear programming approach for environmental management problem under uncertainty

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