LitANFIS: Literal-aware Adaptive Neuro-Fuzzy Inference System to learn Conjunctive Normal Form

In this paper, a novel neuro-fuzzy inference system able to learn fuzzy rules based on using both positive and negative predicates (literals) is proposed. We propose a novel fuzzy neuron named Fuzzy Positive–Negative Neuron to decide whether a predicate or its negated form should be considered in a fuzzy rule. Consequently, to exclude a lingual value, there is no need for many fuzzy rules to cover the whole universe of discourse, except that value. Instead, the proposed method can consider its negated lingual value. Moreover, the proposed unit can relax the effect of a variable in forming a fuzzy rule that leads to unstructured fuzzy rules. Since the proposed method can consider literals (positive and negative predicates), it can calculate the Peirce’s arrow which is functionally complete and also forms Conjunctive Normal Form (CNF). Moreover, considering literals improves the interpretability of neuro-fuzzy systems by decreasing the number of fuzzy rules along with making the inference closer to the human’s. Considering the presence of negated predicates, to initialize the rules’ parameters we propose a learning scheme based on minimizing the classification error along with the reconstruction one instead of applying usual clustering approaches. Moreover, dropout regularization is also applied during the training process to extract independent fuzzy rules. The performance and number of fuzzy rules of the proposed method have been compared with state-of-the-art studies, and based on these comparisons, it has the best performance along with the most parsimonious structure.