Mamdani模糊系统I/O关系的表示及隶属函数优化

探讨一类高效率Mamdani模糊系统隶属函数优化方法.首先通过严密的理论分析将MISO(多输入单输出)_Mamdani模糊系统的输入/输出函数表示成系统隶属函数的局部线性表达式;论证了这个表达式中系统隶属函数项的系数仅由该点所对应的2p个隶属函数值,按大小排成的序列决定.以此为基础,提出了根据输入/输出样本集误差对系统隶属函数进行优化的新方法.该方法近似地将隶属函数优化问题转换成一组线性规划问题进行求解.本文提供的仿真结果也进一步证实了该方法的有效性.

Mamdani fuzzy system I/O relation representative and membership function optimization

An efficient method to optimize membership function of Mamdani fuzzy system is studied.Firstly,through strictly theoretical analysis the input/output function of a MISO(multi-input/single-output)-Mamdani fuzzy system can be represented as a local linear function of their membership functions.Next,every coefficient in the local linear function is proved to be solely determined by the sequence of the 2p values of the related membership arranged in the order of magnitudes.Based on this conclusion,a new method to optimize the membership function is presented in which the optimization problem is approximately transformed into a group of linear programming problems.The simulation results validate this method.