An evolving neuro-fuzzy system based on uni-nullneurons with advanced interpretability capabilities

This paper proposes a hybrid architecture based on neural networks, fuzzy systems, and n-uninorms for solving pattern classification problems, termed as ENFS-Uni0 (short for evolving neuro-fuzzy system based on uni-nullneurons). The model can produce knowledge in an on-line (single-pass) and evolving learning context in a particular form of neuro-fuzzy rules representing the dependencies among input features through IF-THEN type relations. The rules antecedents are thereby realized through uni-nullneurons, which are constructed from n-uninorms, leading to the possibility to express both, AND- and OR-connections (and a mixture of these) among the single antecedent parts of a rule (and thus achieving an advanced interpretability aspect of the rules). The neurons’ evolution is done through an extended version of an autonomous data partition method (ADPA). On-line interpretation of the timely evolution of rules is addressed by (i) a concept for tracking the degree of changes of the rules over data stream samples, which may indicate experts/operators how much dynamics is in the process and may be used as a structural active learning component to request operator’s feedback in the case of significant changes and (ii) a concept for updating feature weights incrementally. These weights express the (possibly changing) impact degrees of features on the classification problem: features with low weights can be seen as unimportant and masked out when showing rules to an expert ( rule length reduction). The rules’ consequents are represented by certainty vectors and are recursively updated by an indicator-based recursive weighted least squares (I-RWLS) approach (one RWLS estimator per class) where the weights are given through the neuron activation levels in order to gain stable local learning. The model proposed in this paper was successfully compared to related hybrid and evolving approaches in the literature for classifying binary and multi-class patterns. The results obtained by the proposed model show an outperformance of the related works in terms of higher accuracy trend lines over time, while offering a high degree of interpretability through coherent neuro-fuzzy rules to solve the classification problems.