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A fuzzy-Markov-chain-based analysis method for reservoir operation

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Abstract

In this study, a fuzzy-Markov-chain-based stochastic dynamic programming (FM-SDP) method is developed for tackling uncertainties expressed as fuzzy sets and distributions with fuzzy probability (DFPs) in reservoir operation. The concept of DFPs used in Markov chain is presented as an extended form for expressing uncertainties including both stochastic and fuzzy characteristics. A fuzzy dominance index analysis approach is proposed for solving multiple fuzzy sets and DPFs in the proposed FM-SDP model. Solutions under a set of α-cut levels and fuzzy dominance indices can be generated by solving a series of deterministic submodels. The developed method is applied to a case study of a reservoir operation system. Solutions from FM-SDP provide a range of desired water-release policies under various system conditions for reservoir operation decision makers, reflecting dynamic and dual uncertain features of water availability simultaneously. The results indicate that the FM-SDP method could be applicable to practical problems for decision makers to obtain insight regarding the tradeoffs between economic and system reliability criteria. Willingness to obtain a lower benefit may guarantee meeting system-constraint demands; conversely, a desire to acquire a higher benefit could run into a higher risk of violating system constraints.

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Acknowledgments

This research was supported by the National Critical Special Projects for the Control and Management of Polluted Water Bodies (2009ZX07104-004). The authors are very grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

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Authors and Affiliations

  1. MOE Key Laboratory of Regional Energy Systems Optimization, S-C Energy and Environmental Research Academy, North China Electric Power University, Beijing, 102206, China

    D. Z. Fu, Y. P. Li & G. H. Huang

Authors
  1. D. Z. Fu
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  2. Y. P. Li
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  3. G. H. Huang
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Correspondence to Y. P. Li.

Appendix

Appendix

See Tables 8, 9, 10, and 11.

Table 8 Solutions for each route under different α-cut levels and ND fuzzy dominance index
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Table 9 Solutions for each route under different α-cut levels and PSD fuzzy dominance index
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Table 10 Solutions for each route under different α-cut levels and NSD fuzzy dominance index
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Table 11 Solutions for each route under different α-cut levels and PD fuzzy dominance index
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Fu, D.Z., Li, Y.P. & Huang, G.H. A fuzzy-Markov-chain-based analysis method for reservoir operation. Stoch Environ Res Risk Assess 26, 375–391 (2012). https://doi.org/10.1007/s00477-011-0497-1

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