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首页> 外文期刊>Fuzzy Optimization and Decision Making: A Journal of Modeling and Computation Under Uncertainty >Enumeration of All Possibly Optimal Vertices with Possible Optimality Degrees in Linear Programming Problems with a Possibilistic Objective Function
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Enumeration of All Possibly Optimal Vertices with Possible Optimality Degrees in Linear Programming Problems with a Possibilistic Objective Function

机译：具有可能目标函数的线性规划问题中所有可能具有最优程度的最优顶点的枚举

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摘要

In this paper, we treat linear programming problems with fuzzy objective function coefficients. To such a problem, the possibly optimal solution set is defined as a fuzzy set. It is shown that any possibly optimal solution can be represented by a convex combination of possibly optimal vertices. A method to enumerate all possibly optimal vertices with their membership degrees is developed. It is shown that, given a possibly optimal extreme point with a higher membership degree, the membership degree of an adjacent extreme point is calculated by solving a linear programming problem and that all possibly optimal vertices are enumerated sequentially by tracing adjacent possibly optimal extreme points from a possibly optimal extreme point with the highest membership degree.
机译：在本文中，我们用模糊目标函数系数处理线性规划问题。对于这样的问题，可能的最优解集被定义为模糊集。结果表明，任何可能的最优解都可以由可能的最优顶点的凸组合表示。开发了一种用其隶属度枚举所有可能的最佳顶点的方法。结果表明，给定一个具有较高隶属度的最优极点，通过求解线性规划问题可以计算出一个相邻极点的隶属度，并通过追踪从中得到的相邻最优极点来依次枚举所有可能的最优顶点。具有最高隶属度的可能最佳极端。

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