Possibility linear programming with trapezoidal fuzzy numbers
Possibility linear programming with trapezoidal fuzzy numbers
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DOI：
10.1016/j.apm.2013.09.006
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发表时间：
2014-03
影响因子：
5
通讯作者：
S. Wan;Jiu-ying Dong
中科院分区：
文献类型：
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作者：
S. Wan;Jiu-ying Dong
考虑了梯形模糊数的模糊线性规划问题，提出了一种新的求解方法。在该方法中，TrFNs用于捕获不精确的客观系数和/或不精确的技术系数和/或可用资源的不精确或不确定信息。构造辅助多目标规划，求解相应的具有TrFNs的可能性线性规划。辅助多目标规划包括4个目标：左侧传播最小化、右侧传播最大化、模式左侧端点最大化和模式中间点最大化。针对构造的辅助多目标规划问题，提出了三种求解方法：乐观法、悲观法和基于隶属函数的线性和法。通过一个投资实例和一个运输问题来说明该方法的实施过程。对比分析表明，本文提出的带trfn的模糊线性规划推广了带三角形模糊数的可能性线性规划。
Fuzzy linear programming with trapezoidal fuzzy numbers (TrFNs) is considered and a new method is developed to solve it. In this method, TrFNs are used to capture imprecise or uncertain information for the imprecise objective coefficients and/or the imprecise technological coefficients and/or available resources. The auxiliary multi-objective programming is constructed to solve the corresponding possibility linear programming with TrFNs. The auxiliary multi-objective programming involves four objectives: minimizing the left spread, maximizing the right spread, maximizing the left endpoint of the mode and maximizing the middle point of the mode. Three approaches are proposed to solve the constructed auxiliary multi-objective programming, including optimistic approach, pessimistic approach and linear sum approach based on membership function. An investment example and a transportation problem are presented to demonstrate the implementation process of this method. The comparison analysis shows that the fuzzy linear programming with TrFNs developed in this paper generalizes the possibility linear programming with triangular fuzzy numbers.