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A Two-Step Infinite α-Cuts Fuzzy Linear Programming Method in Determination of Optimal Allocation Strategies in Agricultural Irrigation Systems

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  • H. Lu
  • G. Huang
  • Y. Lin
  • L. He

Abstract

A two-step infinite α-cuts fuzzy linear programming (TSIFP) method is developed in this study. The introduction of infinite α-cuts to conventional fuzzy linear programming frameworks makes it possible to generate more reliable optimal results than conventional fuzzy linear programming, where finite α-cuts were assumed to be sufficient in representing all fuzzy information of the membership functions. In contrast to the previous studies, the proposed TSIFP can be noted as the first attempt in solving FLP without any unreasonable simplification and assumption. An agricultural irrigation system is then provided for demonstrating its applicability. The results show that reasonable solutions and allocation strategies are obtained. As a typical finite α-cuts fuzzy linear programming method, fuzzy robust linear programming (FRLP) is further considered to solve the same problem; results from this method are then compared with those from TSIFP. It is indicated that, due to the constraints being relaxed in FRLP, more water beyond the system’s capacity would be over-allocated for pursuing higher system benefits, implying the unreliability of FRLP in being extended to real-world practices. Two scenario analyses under different α-level cutting means for FRLP are also investigated. Copyright Springer Science+Business Media B.V. 2009

Suggested Citation

  • H. Lu & G. Huang & Y. Lin & L. He, 2009. "A Two-Step Infinite α-Cuts Fuzzy Linear Programming Method in Determination of Optimal Allocation Strategies in Agricultural Irrigation Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(11), pages 2249-2269, September.
    • Handle: RePEc:spr:waterr:v:23:y:2009:i:11:p:2249-2269
    DOI: 10.1007/s11269-008-9380-3
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    References listed on IDEAS

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    Cited by:

    1. Javier Alarcón & Alberto Garrido & Luis Juana, 2014. "Managing Irrigation Water Shortage: a Comparison Between Five Allocation Rules Based on Crop Benefit Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(8), pages 2315-2329, June.
    2. Yang, Gaiqiang & Guo, Ping & Huo, Lijuan & Ren, Chongfeng, 2015. "Optimization of the irrigation water resources for Shijin irrigation district in north China," Agricultural Water Management, Elsevier, vol. 158(C), pages 82-98.
    3. M. Li & P. Guo & G. Yang & S. Fang, 2014. "IB-ICCMSP: An Integrated Irrigation Water Optimal Allocation and Planning Model Based on Inventory Theory under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(1), pages 241-260, January.
    4. H. Lu & G. Huang & L. He, 2012. "Simulation-Based Inexact Rough-Interval Programming for Agricultural Irrigation Management: A Case Study in the Yongxin County, China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(14), pages 4163-4182, November.
    5. Jiaqi Zhang & Li He & Hongwei Lu & Jing Li, 2014. "Importance Analysis of Groundwater Remediation Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(1), pages 115-129, January.
    6. J. Alarcón & L. Juana, 2016. "The Water Markets as Effective Tools of Managing Water Shortages in an Irrigation District," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(8), pages 2611-2625, June.
    7. Mohammadi, M. & Dehbari, S. & Vahdani, Behnam, 2014. "Design of a bi-objective reliable healthcare network with finite capacity queue under service covering uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 15-41.
    8. He, Li & Huang, Guo H. & Lu, Hongwei, 2011. "Bivariate interval semi-infinite programming with an application to environmental decision-making analysis," European Journal of Operational Research, Elsevier, vol. 211(3), pages 452-465, June.
    9. D. Morankar & K. Srinivasa Raju & D. Nagesh Kumar, 2013. "Integrated Sustainable Irrigation Planning with Multiobjective Fuzzy Optimization Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(11), pages 3981-4004, September.

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