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Multistage stochastic programming with fuzzy probability distribution

机译：具有模糊概率分布的多阶段随机规划

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摘要

In this paper, we introduce the multistage stochastic program with fuzzy probability distribution. We focus on the case where fuzzy probability distribution is defined by (triangular) fuzzy numbers. We extend Ben Abdelaziz and Masri [Stochastic programming with fuzzy linear partial information on probability distribution, European Journal Operational Research 162 (2005) 619-629] solution strategy, for the two-stage stochastic program with fuzzy probability distribution, to solve the multistage model. The proposed solution strategy is based on two transformation steps. In the first step, the fuzzy transformation step, we propose to use the α-cut defuzzification technique. The level a relates to the DM credibility degree on information sources. This step ends with a certainty equivalent program. In the second step, the stochastic transformation step, we decompose the certainty equivalent program based on a minimax approach. The obtained problem is then solved using a modified version of the nested decomposition method. The modification on the nested decomposition method concerns the way in which we generate optimal constraints. The modified nested decomposition algorithm may be used to solve the multistage problem with interval probability distribution.
机译：在本文中，我们介绍了具有模糊概率分布的多阶段随机程序。我们关注由（三角）模糊数定义模糊概率分布的情况。我们将Ben Abdelaziz和Masri [具有概率分布的模糊线性部分信息的随机规划，欧洲期刊社运营研究162（2005）619-629]的扩展策略扩展为具有模糊概率分布的两阶段随机程序，以求解多阶段模型。提出的解决方案策略基于两个转换步骤。在第一步，即模糊变换步骤中，我们建议使用α-cut反模糊化技术。级别a与DM在信息源上的可信度有关。该步骤以确定性等效程序结束。在第二步（随机转换步骤）中，我们基于最小极大值方法分解确定性等效程序。然后使用嵌套分解方法的修改版本解决获得的问题。嵌套分解方法的修改涉及生成最佳约束的方式。改进的嵌套分解算法可用于解决具有间隔概率分布的多阶段问题。

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