含分段线性隶属函数的模糊规划建模方法

针对具有分段线性隶属函数的模糊规划问题,提出了一种新的模糊规划建模方法。通过对二元变量的合理配置,准确地表达出了隶属函数的各分段之间的关系。这种方法可以有效地避免常规建模方法解决模糊规划时出现的系统失去约束的问题,使得优化问题能够获得满意的最优解。并且,在一些情况下可以使用比普通方法更少的二元项进行优化问题的建模,从而使得计算更为简便。详细地给出了两种相关的建模方法,并通过实例进行了验证。

Modeling methodology for fuzzy programming with piecewise linear membership functions

To formulate the fuzzy programming with piecewise linear membership function，a novel modeling methodology is proposed.By means of compatible configuration of binary variables，the relationship between the sub-membership functions is explicitly characterized，which helps the fuzzy optimization efficiently prevent the constraint-free problem happened in the general modeling methodologies，achieving satisfied optimal solutions.Additionally，compared with the conventional modeling methodologies，fewer binary items are required to model the membership function in some scenarios，possibly reducing the complexity of the calculations.In this paper，two methods consistent with this approach are introduced in detail，along with a numerical example employed to demonstrate the benefits of the contribution.