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

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  • Armaghan Abed-Elmdoust
  • Reza Kerachian

Abstract

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):2991–2310, 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. Copyright Springer Science+Business Media B.V. 2012

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  • Armaghan Abed-Elmdoust & Reza Kerachian, 2012. "Water Resources Allocation Using a Cooperative Game with Fuzzy Payoffs and Fuzzy Coalitions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(13), pages 3961-3976, October.
    • Handle: RePEc:spr:waterr:v:26:y:2012:i:13:p:3961-3976
    DOI: 10.1007/s11269-012-0115-0
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    References listed on IDEAS

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    1. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 129(3), pages 596-618, March.
    2. Mohammad Nikoo & Reza Kerachian & Hamed Poorsepahy-Samian, 2012. "An Interval Parameter Model for Cooperative Inter-Basin Water Resources Allocation Considering the Water Quality Issues," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(11), pages 3329-3343, September.
    3. Li, Shujin & Zhang, Qiang, 2009. "A simplified expression of the Shapley function for fuzzy game," European Journal of Operational Research, Elsevier, vol. 196(1), pages 234-245, July.
    4. Mehmet Kucukmehmetoglu, 2009. "A Game Theoretic Approach to Assess the Impacts of Major Investments on Transboundary Water Resources: The Case of the Euphrates and Tigris," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(15), pages 3069-3099, December.
    5. Mojtaba Sadegh & Reza Kerachian, 2011. "Water Resources Allocation Using Solution Concepts of Fuzzy Cooperative Games: Fuzzy Least Core and Fuzzy Weak Least Core," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(10), pages 2543-2573, August.
    6. Mojtaba Sadegh & Najmeh Mahjouri & Reza Kerachian, 2010. "Optimal Inter-Basin Water Allocation Using Crisp and Fuzzy Shapley Games," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(10), pages 2291-2310, August.
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    Cited by:

    1. Mahdi Zarghami & Nasim Safari & Ferenc Szidarovszky & Shafiqul Islam, 2015. "Nonlinear Interval Parameter Programming Combined with Cooperative Games: a Tool for Addressing Uncertainty in Water Allocation Using Water Diplomacy Framework," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(12), pages 4285-4303, September.
    2. Armaghan Abed-Elmdoust & Reza Kerachian, 2013. "Incorporating Economic and Political Considerations in Inter-Basin Water Allocations: A Case Study," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(3), pages 859-870, February.
    3. Maryam Ghashghaie & Safar Marofi & Hossein Marofi, 2014. "Using System Dynamics Method to Determine the Effect of Water Demand Priorities on Downstream Flow," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(14), pages 5055-5072, November.
    4. Shen, Jianjian & Cheng, Chuntian & Zhang, Xiufei & Zhou, Binbin, 2018. "Coordinated operations of multiple-reservoir cascaded hydropower plants with cooperation benefit allocation," Energy, Elsevier, vol. 153(C), pages 509-518.
    5. Shawei He & Keith Hipel & D. Kilgour, 2014. "Water Diversion Conflicts in China: A Hierarchical Perspective," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(7), pages 1823-1837, May.
    6. Parna Parsapour-Moghaddam & Armaghan Abed-Elmdoust & Reza Kerachian, 2015. "A Heuristic Evolutionary Game Theoretic Methodology for Conjunctive Use of Surface and Groundwater Resources," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(11), pages 3905-3918, September.
    7. Ben Li & Guangming Tan & Gang Chen, 2016. "Generalized Uncooperative Planar Game Theory Model for Water Distribution in Transboundary Rivers," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(1), pages 225-241, January.
    8. Kai Zhang & Haishu Lu & Bin Wang, 2024. "Benefit Distribution Mechanism of a Cooperative Alliance for Basin Water Resources from the Perspective of Cooperative Game Theory," Sustainability, MDPI, vol. 16(16), pages 1-33, August.
    9. S. Jamshid Mousavi & Nasrin Rafiee Anzab & Bentolhoda Asl-Rousta & Joong Hoon Kim, 2017. "Multi-Objective Optimization-Simulation for Reliability-Based Inter-Basin Water Allocation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(11), pages 3445-3464, September.
    10. Armaghan Abed-Elmdoust & Reza Kerachian, 2014. "Evaluating the Relative Power of Water Users in Inter-Basin Water Transfer Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(2), pages 495-509, January.
    11. Hamed Poorsepahy-Samian & Reza Kerachian & Mohammad Nikoo, 2012. "Water and Pollution Discharge Permit Allocation to Agricultural Zones: Application of Game Theory and Min-Max Regret Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(14), pages 4241-4257, November.
    12. Boyang Dai & Xiangfeng Yang & Xiaoyue Liu, 2022. "Shapley Value of Uncertain Coalitional Game based on Hurwicz Criterion with Application to Water Resource Allocation," Group Decision and Negotiation, Springer, vol. 31(1), pages 241-260, February.
    13. Chunlong Li & Jianzhong Zhou & Shuo Ouyang & Chao Wang & Yi Liu, 2015. "Water Resources Optimal Allocation Based on Large-scale Reservoirs in the Upper Reaches of Yangtze River," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(7), pages 2171-2187, May.
    14. Mohammad Nikoo & Reza Kerachian & Mohammad Niksokhan, 2012. "Equitable Waste Load Allocation in Rivers Using Fuzzy Bi-matrix Games," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(15), pages 4539-4552, December.
    15. Keighobad Jafarzadegan & Armaghan Abed-Elmdoust & Reza Kerachian, 2013. "A Fuzzy Variable Least Core Game for Inter-basin Water Resources Allocation Under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(9), pages 3247-3260, July.
    16. Zhen Zhou & Meijia Zhang & Xiaohui Yu & Xijun He & Kang Wang & Quan Shao & Jie Wang & Hongxia Sun, 2019. "PM 2.5 Cooperative Control with Fuzzy Cost and Fuzzy Coalitions," IJERPH, MDPI, vol. 16(7), pages 1-14, April.
    17. Ben Li & Guangming Tan & Gang Chen, 2016. "Generalized Uncooperative Planar Game Theory Model for Water Distribution in Transboundary Rivers," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(1), pages 225-241, January.

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