Fuzzy pattern trees as an alternative to rule-based fuzzy systems: Knowledge-driven, data-driven and hybrid modeling of color yield in polyester dyeing

This paper advocates a novel approach to fuzzy systems modeling called fuzzy pattern trees. This approach is largely motivated by alleged disadvantages of rule-based system architectures that still dominate the field. Due to its hierarchical, modular structure and the use of different types of (nonlinear) aggregation operators, a fuzzy pattern tree has the ability to represent functional dependencies in a more flexible and more compact way, thereby offering a reasonable balance between accuracy and model transparency. We evaluate this new model class in the context of a concrete case study, namely the modeling of color yield in polyester high temperature dyeing as a function of disperse dyes concentration, temperature and time. To this end, we compare three possibilities for model construction: purely knowledge-driven, purely data-driven and a hybrid approach combining these two. Our results show that, in comparison to conventional fuzzy modeling using Mamdani rules, fuzzy pattern trees are not only more accurate but also more compact and therefore more easily interpretable, regardless of whether the models are constructed in a knowledge-driven, data-driven or hybrid manner. Moreover, we show that a hybrid modeling approach can outperform a purely data-driven and a purely knowledge-driven approach if expert knowledge and model calibration are combined in a suitable way.