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Equitable Waste Load Allocation in Rivers Using Fuzzy Bi-matrix Games

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  • Mohammad Nikoo
  • Reza Kerachian
  • Mohammad Niksokhan

Abstract

This paper presents a new game theoretic methodology for equitable waste load allocation in rivers utilizing fuzzy bi-matrix games, Non-dominated Sorting Genetic Algorithms II (NSGA-II), cooperative game theory, Bayesian Networks (BNs) and Probabilistic Support Vector Machines (PSVMs). In this methodology, at first, a trade-off curve between objectives, which are average treatment level of dischargers and fuzzy risk of low water quality, is obtained using NSGA-II. Then, the best non-dominated solution is selected using a non-zero-sum bi-matrix game with fuzzy goals. In the next step, to have an equitable waste load allocation, some possible coalitions among dischargers are formed and treatment costs are reallocated to discharges and side payments are calculated. To develop probabilistic rules for real-time waste load allocation, the proposed model is applied considering several scenarios of pollution loads and the results are used for training and testing BNs and PSVMs. The applicability and efficiency of the methodology are examined in a real-world case study of the Zarjub River in the northern part of Iran. The results show that the average relative errors of the proposed rules in estimating the treatment levels of dischargers are less than 5 %. Copyright Springer Science+Business Media Dordrecht 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:waterr:v:26:y:2012:i:15:p:4539-4552
    DOI: 10.1007/s11269-012-0165-3
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Hung, Ming-Feng & Shaw, Daigee, 2005. "A trading-ratio system for trading water pollution discharge permits," Journal of Environmental Economics and Management, Elsevier, vol. 49(1), pages 83-102, January.
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    Cited by:

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    2. Zhang, J.L. & Li, Y.P. & Wang, C.X. & Huang, G.H., 2015. "An inexact simulation-based stochastic optimization method for identifying effluent trading strategies of agricultural nonpoint sources," Agricultural Water Management, Elsevier, vol. 152(C), pages 72-90.
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