A new trapezoidal fuzzy linear programming method considering the acceptance degree of fuzzy constraints violated
A new trapezoidal fuzzy linear programming method considering the acceptance degree of fuzzy constraints violated
复制标题
考虑违反模糊约束接受度的梯形模糊线性规划新方法
DOI：
10.1016/j.knosys.2018.02.030
复制
发表时间：
2018-05-15
影响因子：
8.8
通讯作者：
Wan, Shu-Ping
中科院分区：
文献类型：
--
作者：
Dong, Jiu-ying;Wan, Shu-Ping
模糊线性规划在背包问题、投资问题、资本预算问题、运输问题等方面有着广泛的应用.考虑到决策者对模糊约束可能被违反的接受程度，本文提出了一种新的求解目标系数、技术系数和资源均为梯形模糊数的模糊线性规划的方法.首先利用TrFN的区间期望给出了TrFN的序关系。根据TrFN的序关系，将梯形模糊线性规划转化为区间目标规划。结合区间之间的排序关系和模糊约束违背的接受度，将区间目标规划进一步转化为双目标线性规划，并利用所提出的目标规划方法进行求解。该方法不仅数学上严格，而且能充分考虑模糊约束违背的可接受程度。最后通过一个模糊背包问题和一个投资问题验证了该方法的有效性和优越性。最后，开发了一个决策支持系统，所提出的方法。(C)2018爱思唯尔B.V.保留所有权利。
The fuzzy linear program has various applications in knapsack problem, investment problem, capital budgeting problem, and transportation problem, etc. Considering the acceptance degree of decision maker that the fuzzy constraints may be violated, this paper develops a new method for the fuzzy linear program in which all the objective coefficients, technological coefficients and resources are trapezoidal fuzzy numbers (TrFNs). The order relationship for TrFNs is firstly given by using the interval expectation of TrFNs. According to the order relationship of TrFNs, the trapezoidal fuzzy linear program is transformed into the interval objective program. Combined with the ranking order relation between intervals and the acceptance degree of fuzzy constraints violated, the interval objective program is further transformed into the bi-objective linear program which is solved by the proposed goal programming approach. The proposed method of this paper is not only mathematically rigorous, but also can sufficiently consider the acceptance degree of the fuzzy constraints violated. The effectiveness and superiority of the proposed method are verified with a fuzzy knapsack problem and an investment problem. Finally, a decision support system is developed for the proposed method. (C) 2018 Elsevier B.V. All rights reserved.