An Interactive Fuzzy Satisficing Method for Multiobjective Linear Programming Problems with Random Fuzzy Variables Using Possibility-based Probability Model
An Interactive Fuzzy Satisficing Method for Multiobjective Linear Programming Problems with Random Fuzzy Variables Using Possibility-based Probability Model
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DOI：
10.13189/cr.2014.020102
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Sakawa;Takeshi Matsui;H. Katagiri
中科院分区：
文献类型：
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作者：
M. Sakawa;Takeshi Matsui;H. Katagiri
本文建立了多目标线性规划问题，其中目标函数的每个系数由一个随机模糊变量表示。假设决策者关心每个目标函数值小于或等于某一目标值的概率，则引入决策者对概率的模糊目标。然后，考虑了基于可能性的概率模型，以最大化相对于所获得概率的可能性程度。为了有效地求解变换后的确定性问题，提出了求解非线性规划问题的粒子群算法。提出了一种交互式模糊满意方法，通过更新参考概率水平来有效地为决策者导出满意解。最后给出了一个算例，验证了该方法的可行性和有效性。
This paper formulates multiobjective linear programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. Assuming that the decision maker concerns about the probability that each of the objective function values is smaller than or equal to a certain target value, the fuzzy goals of the decision maker for the probabilities are introduced. Then, the possibility-based probability model to maximize the degrees of possibility with respect to the attained probability is considered. For solving transformed deterministic problems efficiently, particle swarm optimization for nonlinear programming problems is introduced. An interactive fuzzy satisficing method is presented for deriving a satisficing solution for a decision maker efficiently by updating the reference probability levels. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.