Abstract: It is hard to determine the membership function and inference rules in fuzzy reasoning. By studying the fuzzy reasoning process and the characteristics of B-spline function, the reasoning method on the application of B-spline function fitting to fuzzy membership function was improved. Through the calculation and selection of the extreme points of error and the extreme point of curvature, the B-spline function data points were obtained. After obtaining the control points by inversing data points, the curve fitting of the membership function was increased and the B-spline membership function fitting problem was solved on the curve of the B-spline by increasing the control points. B-spline inference rule was established and B-spline inference system was constructed, and then the final result of the system was calculated as a B-spline hypersurface. Finally, the experimental results validate the effectiveness and feasibility of this method.

Key words: B-spline function, fitting, membership function, B-spline surface

摘要： 隶属函数和推理规则的确定是模糊推理的难点。通过研究模糊推理过程和B样条函数的特性，对应用B样条函数拟合模糊隶属函数进行推理的方法进行改进。通过对误差极值点、曲率极值点的计算和筛选，得到B样条函数的型值点。反算求得控制点之后，通过自适应增加控制点对曲线进行调整，增加曲线对隶属函数的拟合度，解决了B样条函数对隶属函数的拟合问题。建立B样条推理规则，构造实现了B样条推理系统，并求出该系统的最终结果为B样条超曲面。最后，通过实验验证了该方法的有效性和可行性。

关键词: B样条函数, 拟合, 隶属函数, B样条曲面