增量极坐标编码的贝赛尔曲线智能优化算法

Intelligent optimized Bezier curves based on incremental polar coordinate coding

针对基于统计的隶属度函数确定方法进行了改进,使用贝塞尔曲线作为隶属度函数的上升或下降沿,使隶属度函数可以经过统计结果规定的任意中间点。使用新的增量极坐标编码对贝塞尔曲线控制点进行表达,解决了传统贝塞尔曲线优化中的控制点约束问题。采用差分进化算法对贝塞尔曲线控制点进行优化,可智能拟合经过任意点的最佳贝塞尔曲线。算法可扩展到任意阶贝塞尔曲线,所得隶属度函数较非贝塞尔曲线方法更为合理。

This study improves the method of determining the statistic-based membership function for membership function selection in fuzzy classification. Bezier curves are used as the ascendant or descendant edge of the membership function, to ensure that the membership function goes through any arbitrary points stipulated in statistical results. The control points of the Bezier curves are expressed by incremental polar coordinate coding, which solves the control point constraint problem in optimization of traditional Bezier curves. In addition, the differential evolution algorithm is used to optimize the control points of Bezier curves, and this can intelligently fit the best Bezier curve that goes through any arbitrary point. Results show that the proposed algorithm can be extended to any order Bezier curve, and the obtained membership functions are more reasonable than those of the non-Bezier curve method.