带有非线性隶属函数的FLP问题的求解

带有非线性隶属函数(NLMF)的模糊线性规划(FLP)问题。通常是一个非线性规划(NLP)问题。本文利用“较大”、“较小”型隶属函数的特点,把求解原FLP问题最优解的过程化为求解一个参数线性规划(LP)问题及修正参数的交替迭代过程。通过构造不同的参数LP问题及修正参数的方法,得到了求解原问题的“试点法”和“收缩法”,在此基础上,综合得出兼有两法优点的“加速算法”,理论分析及实例都证明这些算法尤其是加速算法在求解带有非线性隶属函数的FLP问题时是有效的.

Solving the FLP Problem with Nonlinear Membership Function

The fuzzy linear programming (FLP) problem with nonlinear membership function (NLMF) is usually a nonlinear programming (NLP) problem. In this paper, we, by use of the characteristies of the membership function of the form 'smaller' and 'larger', transform the solving of the original FLP problem into the processing for solving a supplementary parameter linear programming (LP) problem and modifying the parameter value, alternatively. By constructing different supplementary parameter LP problem or different method of modifying the parameter value, we set foward the trial and error method and the contracting method. Then, we further set foward the speed-up algorithm on the basis of the two methods . These proposed methods all have a simple algorithm structure, and converge rapidly. The analysis and example show that these algorithms, espeeially the speed-up algorithm, are good algorithms for solving the FLP problem with nonlinear membership function.