On paradox of fuzzy modeling: Supervised learning for rectifying fuzzy membership function

The paradox of fuzzy modeling is recognized due to the co-existence of its effectiveness of solving uncertain problems in the real world and the skepticism of its reasonability in membership function. In this paper, a revised membership function by means of supervised machine learning is introduced, in which the membership function curve is revised from the learning data of existing samples. It points that the information from supervised machine learning by samples is in the same argument to the statistic data from observation in the probability model. The formulations of supervised fuzzy machine learning by samples for revising the membership function are presented, and satisfactory results by the revised membership function compared with the experimental data are shown. It steps forward in promoting the pragmatic application of fuzzy methods in real world problems.