Type-2 fuzzy mixed-integer bi-level programming approach for multi-source multi-user water allocation under future climate change

Abstract Global climate change and increasing pressure of water shortage reinforce the necessity of optimal water management. In this study, a type-2 fuzzy mixed-integer bi-level programming (T2FMBP) approach is developed for the identification of reasonable water allocation policies by incorporating type-2 fuzzy sets, mixed-integer linear programming, bi-level programming and Stewart model into a general optimization framework. The T2FMBP model improves upon conventional bi-level programming for handling tradeoffs between two-level decision makers considering multiple water allocation processes. It is capable of addressing parameter uncertainties caused by natural conditions and human activities, and supporting in-depth analysis of water allocation schemes associated with future climate change. In this study, group opinion aggregation method for fuzzy number construction, critical value method for type-2 fuzzy number defuzzification, and fuzzy coordination method for solving bi-level programming are adopted. Then, the model was demonstrated for a real-world case study in the Zhanghe Irrigation District for multi-source multi-user water resources planning. The results show that the proposed model can tackle tradeoffs among hierarchical decision makers’ conflicting concerns under uncertainties characterized as type-2 fuzzy numbers. Besides, the results can help generate water allocation schemes among different water sectors as well as different crop growth stages effectively under three hydrological years (wet year, normal year, and dry year) and three representative concentration pathway (RCP) scenarios (RCP 2.6, RCP 4.5, and RCP 8.5). Furthermore, comparison was made between T2FMBP model and four single-level models with same constraints. The comparison reveals that T2FMNP model considers all the targets and makes excellent balance between two-level decision makers. A comparison between current situation and RCP scenarios will help make policies for foresight. The formulated framework is applicable for similar regions to determine water strategies in a changing environment, thus promote sustainable development of socio-economic and water resources system.

[1]  Xiaosheng Qin,et al.  Agricultural effluent control under uncertainty: An inexact double-sided fuzzy chance-constrained model , 2010 .

[2]  Ibrahim A. Baky,et al.  TOPSIS for bi-level MODM problems , 2013 .

[3]  Hua Zhu,et al.  Inexact Fuzzy Chance-Constrained Nonlinear Programming Approach for Crop Water Allocation under Precipitation Variation and Sustainable Development , 2014 .

[4]  Guo H. Huang,et al.  An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty , 2005, Eur. J. Oper. Res..

[5]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[6]  Ferenc Szidarovszky,et al.  Nash bargaining and leader–follower models in water allocation: Application to the Zarrinehrud River basin, Iran , 2014 .

[7]  Y. P. Li,et al.  A multistage irrigation water allocation model for agricultural land-use planning under uncertainty , 2013 .

[8]  Chongfeng Ren,et al.  Integrated multi-objective stochastic fuzzy programming and AHP method for agricultural water and land optimization allocation under multiple uncertainties , 2019, Journal of Cleaner Production.

[9]  Xiaohong Chen,et al.  Fuzzy chance-constrained linear fractional programming approach for optimal water allocation , 2014, Stochastic Environmental Research and Risk Assessment.

[10]  Fan Zhang,et al.  An interval nonlinear multiobjective programming model with fuzzy-interval credibility constraint for crop monthly water allocation , 2018, Agricultural Water Management.

[11]  M. K. Rowshon,et al.  Modeling climate-smart decision support system (CSDSS) for analyzing water demand of a large-scale rice irrigation scheme , 2019, Agricultural Water Management.

[12]  David Molden,et al.  Adapting to intersectoral transfers in the Zhanghe Irrigation System, China. Part I. In-system storage characteristics , 2008 .

[13]  Guangqian Wang,et al.  A Multi-objective Linear Programming Model with Interval Parameters for Water Resources Allocation in Dalian City , 2011 .

[14]  Pute Wu,et al.  GANN models for reference evapotranspiration estimation developed with weather data from different climatic regions , 2014, Theoretical and Applied Climatology.

[15]  Shanshan Guo,et al.  A bi-level multi-objective linear fractional programming for water consumption structure optimization based on water shortage risk , 2019, Journal of Cleaner Production.

[16]  Dipak Kumar Jana,et al.  Expectations of the reductions for type-2 trapezoidal fuzzy variables and its application to a multi-objective solid transportation problem via goal programming technique , 2017 .

[17]  Yian-Kui Liu,et al.  Methods of critical value reduction for type-2 fuzzy variables and their applications , 2011, J. Comput. Appl. Math..

[18]  Bo Cheng,et al.  A conceptual decision-making for the ecological base flow of rivers considering the economic value of ecosystem services of rivers in water shortage area of Northwest China , 2019, Journal of Hydrology.

[19]  Qiang Fu,et al.  Agricultural Multi-Water Source Allocation Model Based on Interval Two-Stage Stochastic Robust Programming under Uncertainty , 2018, Water Resources Management.

[20]  Velimir V. Vesselinov,et al.  Energy-water nexus: Balancing the tradeoffs between two-level decision makers , 2016 .

[21]  Ping Guo,et al.  Simulation and optimization for crop water allocation based on crop water production functions and climate factor under uncertainty , 2013 .

[22]  Zongxue Xu,et al.  Climate change scenarios generated by using GCM outputs and statistical downscaling in an arid region , 2015 .

[23]  Liming Yao,et al.  Sustainable water allocation strategies under various climate scenarios: A case study in China , 2019, Journal of Hydrology.

[24]  Fan Zhang,et al.  An inexact irrigation water allocation optimization model under future climate change , 2018, Stochastic Environmental Research and Risk Assessment.

[25]  Y. P. Li,et al.  A type-2 fuzzy chance-constrained programming method for planning Shanghai’s energy system , 2017 .

[26]  Yunzhong Jiang,et al.  Rule-based water resource allocation in the Central Guizhou Province, China , 2016 .

[27]  Dongguo Shao,et al.  Simulation-Optimization Modeling of Conjunctive Operation of Reservoirs and Ponds for Irrigation of Multiple Crops Using an Improved Artificial Bee Colony Algorithm , 2016, Water Resources Management.

[28]  S. R. Arora,et al.  Interactive fuzzy goal programming approach for bilevel programming problem , 2009, Eur. J. Oper. Res..

[29]  Qiang Fu,et al.  An intuitionistic fuzzy multi-objective non-linear programming model for sustainable irrigation water allocation under the combination of dry and wet conditions , 2017 .

[30]  Z. Samani,et al.  Estimating Potential Evapotranspiration , 1982 .

[31]  Guohe Huang,et al.  An inexact stochastic-fuzzy optimization model for agricultural water allocation and land resources utilization management under considering effective rainfall , 2017, Ecological Indicators.

[32]  Qiang Fu,et al.  Efficient allocation of agricultural land and water resources for soil environment protection using a mixed optimization-simulation approach under uncertainty , 2019, Geoderma.

[33]  Qiong Yue,et al.  A Nonlinear Inexact Two-Stage Management Model for Agricultural Water Allocation under Uncertainty Based on the Heihe River Water Diversion Plan , 2019, International journal of environmental research and public health.

[34]  Pei Liu,et al.  A solid transportation problem with type-2 fuzzy variables , 2014, Appl. Soft Comput..

[35]  S. M. Shah-Newaz,et al.  The impact of climate change on regional water balances in Bangladesh , 2016, Climatic Change.

[36]  Yujun Yi,et al.  Multi-Water Source Joint Scheduling Model Using a Refined Water Supply Network: Case Study of Tianjin , 2018, Water.

[37]  Chi-Bin Cheng,et al.  Group opinion aggregationbased on a grading process: A method for constructing triangular fuzzy numbers , 2004 .

[38]  Ruotong Wang,et al.  Multi-Model Projections of Climate Change in Different RCP Scenarios in an Arid Inland Region, Northwest China , 2019, Water.

[39]  Mar Ortega-Reig,et al.  Comparative studies of water governance: a systematic review , 2018 .

[40]  Vijay P. Singh,et al.  An uncertainty-based framework for agricultural water-land resources allocation and risk evaluation. , 2016 .

[41]  László T. Kóczy,et al.  Comparative study on credibility measures of type-2 and type-1 fuzzy variables and their application to a multi-objective profit transportation problem via goal programming , 2017 .

[42]  Guohe Huang,et al.  A robust risk analysis method for water resources allocation under uncertainty , 2013, Stochastic Environmental Research and Risk Assessment.

[43]  David Molden,et al.  Adapting to intersectoral transfers in the Zhanghe Irrigation System, China: Part II: Impacts of in-system storage on water balance and productivity , 2008 .

[44]  Min-Won Jang,et al.  A spatial reasoning approach to estimating paddy rice water demand in Hwanghaenam-do, North Korea , 2007 .

[45]  N. Arnell,et al.  A global assessment of the impact of climate change on water scarcity , 2016, Climatic Change.

[46]  Yian-Kui Liu,et al.  Type-2 fuzzy variables and their arithmetic , 2010, Soft Comput..

[47]  Edmar I. Teixeira,et al.  Towards an integrated assessment of climate and socio-economic change impacts and implications in New Zealand , 2019, Environ. Model. Softw..

[48]  Ibrahim A. Baky.  Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems , 2009, Fuzzy Sets Syst..

[49]  Guohe Huang,et al.  A Hybrid Dynamic Dual Interval Programming for Irrigation Water Allocation under Uncertainty , 2012, Water Resources Management.

[50]  Kenneth D. Frederick,et al.  Climate Change and Water Resources , 1997 .

[51]  Dongguo Shao,et al.  An interval multistage water allocation model for crop different growth stages under inputs uncertainty , 2017 .

[52]  Chenglong Zhang,et al.  A generalized fuzzy credibility-constrained linear fractional programming approach for optimal irrigation water allocation under uncertainty , 2017 .

[53]  Guohe Huang,et al.  A robust inexact trapezoidal T2 fuzzy approach coupling possibility degrees for solid waste disposal allocation with integrated optimal greenhouse gas control under uncertainty , 2019 .

[54]  Masson-Delmotte,et al.  The Physical Science Basis , 2007 .

[55]  Vijay P. Singh,et al.  Modeling Rainwater Storage in Distributed Reservoir Systems in Humid Subtropical and Tropical Savannah Regions , 2011 .

[56]  D. G. Regulwar,et al.  Irrigation Planning Under Uncertainty—A Multi Objective Fuzzy Linear Programming Approach , 2011 .

[57]  Ferhan Çebi,et al.  Multi-Criteria and Multi-Stage Facility Location Selection under Interval Type-2 Fuzzy Environment: A Case Study for a Cement Factory , 2015, Int. J. Comput. Intell. Syst..

[58]  Y P Li,et al.  An integrated bi-level optimization model for air quality management of Beijing's energy system under uncertainty. , 2018, Journal of hazardous materials.