Stackelberg solutions for fuzzy random bilevel linear programming through level sets and probability maximization
Stackelberg solutions for fuzzy random bilevel linear programming through level sets and probability maximization
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DOI：
10.1007/s12351-010-0090-2
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发表时间：
2010-10
影响因子：
2.7
通讯作者：
M. Sakawa;H. Katagiri;Takeshi Matsui
中科院分区：
文献类型：
--
作者：
M. Sakawa;H. Katagiri;Takeshi Matsui
本文考虑模糊随机环境下双层线性规划问题的 Stackelberg 解。为了处理公式化的模糊随机二层线性规划问题，引入模糊随机变量的α层集，并定义α-随机双层线性规划问题以保证问题的实现程度。考虑到决策者判断的模糊性，引入模糊目标，将α-随机二层线性规划问题转化为对每个模糊目标满足度最大化的问题。通过随机规划中的概率最大化，可以将变换后的随机双层规划问题简化为确定性双层规划问题。介绍了Stackelberg解的扩展概念并给出了计算方法。提供了一个数值示例来说明所提出的方法。
This paper considers Stackelberg solutions for bilevel linear programming problems under fuzzy random environments. To deal with the formulated fuzzy random bilevel linear programming problem, α-level sets of fuzzy random variables are introduced and an α-stochastic bilevel linear programming problem is defined for guaranteeing the degree of realization of the problem. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the α-stochastic bilevel linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through probability maximization in stochastic programming, the transformed stochastic bilevel programming problem can be reduced to a deterministic bilevel programming problem. An extended concept of Stackelberg solution is introduced and a computational method is also presented. A numerical example is provided to illustrate the proposed method.