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Fuzzy decision making for multiobjective stochastic programming problems

机译：多目标随机规划问题的模糊决策

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摘要

In this study, we propose a fuzzy decision making method for multiobjective stochastic linear programming problems with variance covariance matrices (MOSLPs), in which the criteria of probability maximization and fractile optimization are simultaneously considered. For a probability maximization model for an MOSLP, the decision maker is required to specify permissible objective levels. However, fewer values of permissible objective levels for minimization problems result in fewer values of the corresponding distribution function because of the conflicts between them. Similarly, for a fractile optimization model for an MOSLP, the decision maker is required to specify permissible probability levels. However, due to conflicts between the probability levels and the corresponding objective functions, larger values of permissible probability levels result in larger values of the corresponding objective function for minimization problems. In this study, it is assumed that the decision maker has fuzzy goals not only for permissible objective levels of a probability maximization model but also for permissible probability levels of a fractile optimization model, and such fuzzy goals are quantified by eliciting the corresponding membership functions. On the basis of the fuzzy decision, the satisfactory solution of the decision maker is obtained by applying a convex programming technique. (C) 2015 Elsevier B.V. All rights reserved.
机译：在这项研究中，我们提出了一种具有方差协方差矩阵（MOSLP）的多目标随机线性规划问题的模糊决策方法，其中同时考虑了概率最大化和分数优化的准则。对于MOSLP的概率最大化模型，决策者需要指定允许的目标水平。但是，用于最小化问题的允许目标级别的值越小，由于它们之间的冲突，导致相应分布函数的值越小。同样，对于MOSLP的分数优化模型，决策者需要指定允许的概率水平。然而，由于概率水平和相应的目标函数之间的冲突，允许的概率水平的较大值导致对应的目标函数的较大值，以使问题最小化。在这项研究中，假设决策者不仅对概率最大化模型的许可目标水平而且对于分数优化模型的许可概率水平都具有模糊目标，并且通过引发相应的隶属函数来量化这种模糊目标。在模糊决策的基础上，采用凸规划技术，可以得到决策者满意的解决方案。 （C）2015 Elsevier B.V.保留所有权利。

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