Ciprian-Daniel Neagu and Vasile Palade
In recent years, the hybrid neural systems have drawn an increasing research interest.A framework of new unified neural and neuro-fuzzy approaches for integrating implicit and explicit knowledge in neuro-symbolic systems is proposed. In the developed hybrid system, training data set is used for building neuro-fuzzy modules, and represents implicit domain knowledge. On the other hand, the explicit domain knowledge is represented by fuzzy rules, which are directly mapped into equivalent neural structures. Three methods to combine the explicit and implicit knowledge modules are proposed. Steps for building the hybrid system, called NEIKeS - Neural Explicit and Implicit Knowledge-based expert System - are described. The proposed structures and methods argue the use of connectionist systems in symbolic processing. Since the presented EKMs (Explicit Knowledge Modules) are identical to Discrete Fuzzy Rule-based Systems, the homogenous integration of explicit rules and training data sets allows a better covering of the problem domain. We applied the proposed approaches with very good results for the prediction of the daily NO2 maximum concentration for a single representative measuring station. Comparisons between the different structures used in our study are presented in the paper. The constraint of the size of neural networks is solved by the modularity paradigm. EKMs represent explicit rules identified by expert or refined from IKM (Implicit Knowledge Module) structures; IKMs are useful for complex problems described by complex (and noisy) data. The EKM and IKM combination encourages compact solutions for problems described by both, data sets distributed in compact domains in the hyperspace, and isolated data, situated in intersection of compact sub-domains or inhomogeneous intervals. After training, different expert networks compute different functions mapping different regions of the input space.