A new method for inducing a set of interpretable fuzzy partitions and fuzzy inference systems from data

To improve the interpretability of a fuzzy rule base generated from data, three conditions are necessary: semantic integrity must be respected, the number of rules should be small, and incomplete rules have to be handled. An incomplete rule is a rule defined only by a few variables. The presence of incomplete rules reflects the fact that all the variables do not have the same importance for all rules.We propose a new method for learning a fuzzy rule base. A hierarchy of fuzzy partitions is generated for each input variable, based on a special metric suitable for fuzzy partitioning, before being used in building fuzzy inference systems of increasing complexity. Then the rule base is simplified. We introduce an intermediate selection level represented by a group of rules. The simplification tolerates some loss of accuracy while being guided by indices complementary to the usual numerical performance index.The proposed approach is applied to a rice quality evaluation problem.