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Water Resources Allocation Using Solution Concepts of Fuzzy Cooperative Games: Fuzzy Least Core and Fuzzy Weak Least Core

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  • Mojtaba Sadegh
  • Reza Kerachian

Abstract

In this paper, two new solution concepts for fuzzy cooperative games, namely Fuzzy Least Core and Fuzzy Weak Least Core are developed. They aim for optimal allocation of available water resources and associated benefits to water users in a river basin. The results of these solution concepts are compared with the results of some traditional fuzzy and crisp games, namely Fuzzy Shapley Value, Crisp Shapley Value, Least Core, Weak Least Core and Normalized Nucleolus. It is shown that the proposed solution concepts are more efficient than the crisp games. Moreover, they do not have the limitation of Fuzzy Shapley Value in satisfying the group rationality criterion. This paper consists of two steps. In the first step, an optimization model is used for initial water allocation to stakeholders. In the second step, fuzzy coalitions are defined and participation rates of water users (players) in the fuzzy coalitions are optimized in order to reach a maximum net benefit. Then, the total net benefit is allocated to the players in a rational and equitable way using Fuzzy Least Core, Fuzzy Weak Least Core and some traditional fuzzy and crisp games. The effectiveness and applicability of the proposed methodology is examined using a numerical example and also applying it to the Karoon river basin in southern Iran. Copyright Springer Science+Business Media B.V. 2011

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  • 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.
    • Handle: RePEc:spr:waterr:v:25:y:2011:i:10:p:2543-2573
    DOI: 10.1007/s11269-011-9826-x
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    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.
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    16. 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.
    17. Alireza Mojarabi-Kermani & Ehsan Shirangi & Amin Bordbar & Amir Abbas Kaman Bedast & Alireza Masjedi, 2019. "Stochastic Optimal Reservoir Operation Management, Applying Group Conflict Resolution Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(8), pages 2847-2865, June.
    18. 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.
    19. 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.
    20. Hamidreza Manshadi & Mohammad Niksokhan & Mojtaba Ardestani, 2015. "A Quantity-Quality Model for Inter-basin Water Transfer System Using Game Theoretic and Virtual Water Approaches," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(13), pages 4573-4588, October.
    21. 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.
    22. 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.
    23. Mohammad S. Khorshidi & Mohammad Reza Nikoo & Mojtaba Sadegh & Banafsheh Nematollahi, 2019. "A Multi-Objective Risk-Based Game Theoretic Approach to Reservoir Operation Policy in Potential Future Drought Condition," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(6), pages 1999-2014, April.
    24. Mohammad Reza Nikoo & Pouyan Hatami Bahman Beiglou & Najmeh Mahjouri, 2016. "Optimizing Multiple-Pollutant Waste Load Allocation in Rivers: An Interval Parameter Game Theoretic Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(12), pages 4201-4220, September.
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