关于模糊关系合成运算一个性质的商榷

A Discussion on the Property of Composition of the Fuzzy Relations

针对清华大学出版社出版的教材《智能控制基础》,给出的模糊关系合成运算一条性质,经过实例验证,发现该性质并不成立。于是对该问题进行严格的数学分析和推导,得出正确的结论,并将其推广到更一般的情形,同时也表明《智能控制基础》中的部分结论是错误的。最后,举出两个实例,计算结果进一步验证所得出的结论的正确性。

The monograph Fundamentals of Intelligent Control published by Tsinghua University Press gave a property of composition of the fuzzy relations,however,the author of this article found that this property was not true by calculation from some practical examples. Then the study on this problem is carried out by strict mathematical analysis and derivation,and some new conclusions are obtained,and these new results are extended to a more general case,it shows that some corresponding conclusions are incorrect in Fundamentals of Intelligent Control. In the end,two examples are given to verify that the new results are correct.