Abstract: Fuzzy relation equation can reasonably describe the fuzzy relation between the uncertain quality abnormity and the assignable causes of manufacturing process, but the constraints of its application was formed by solving complexity. By designing an objective function with minimum distance, the fuzzy relation equation was transformed into an optimization problem. A genetic algorithm was proposed to obtain the interval solution. The contribution degree of assignable causes to given uncertain quality abnormity was located based on the interval solution. Uncertain quality abnormity diagnosis of precision-axis machining was taken as an example to introduce the application process of proposed approach in detail, and the result could provide support for assignable causes'location.

Key words: uncertain quality diagnosis, fuzzy relation equation, genetic algorithms, precision-axis machining

摘要： 为合理描述制造过程不确定质量异常与异常原因之间的模糊关系，通过设计一种基于最小距离的目标函数，将模糊关系方程转化为最优化问题的求解，并提出了相应的遗传算法，用来求解模糊关系方程的区间解，实现异常原因对不确定质量异常贡献程度的量化。结合精密轴加工过程不确定质量异常的诊断实例，介绍了方案的应用过程。应用结果可以为异因定位提供决策依据。

关键词: 不确定质量诊断, 模糊关系方程, 遗传算法, 精密轴加工