Interactive fuzzy random cooperative two-level linear programming through level sets based probability maximization
Interactive fuzzy random cooperative two-level linear programming through level sets based probability maximization
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DOI：
10.1016/j.eswa.2012.08.048
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
M. Sakawa;Takeshi Matsui
中科院分区：
文献类型：
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作者：
M. Sakawa;Takeshi Matsui
本文假设决策者具有合作行为，研究模糊随机环境下的两级线性规划问题。为了处理表述的模糊随机两层线性规划问题，引入了模糊随机变量的α-水平集，并定义了α-随机两层线性规划问题，以保证问题的可实现程度。考虑决策者判断的模糊性，引入模糊目标，将α-随机两级线性规划问题转化为每个模糊目标满意度最大化的问题。通过概率最大化，将转化后的随机两级规划问题简化为确定性规划问题。在考虑决策者之间的合作关系的情况下，提出了一种基于交互模糊规划的上层决策者满意解的求解方法。算例说明了该方法的可行性和有效性。
In this paper, assuming cooperative behavior of the decision makers, two-level linear programming problems under fuzzy random environments are considered. To deal with the formulated fuzzy random two-level linear programming problems, α-level sets of fuzzy random variables are introduced and an α-stochastic two-level 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 two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through probability maximization, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.