Alternating Bi-Objective Optimization for Explainable Neuro-Fuzzy Systems

Adaptive Neuro-Fuzzy Inference System (ANFIS) was designed to combine the learning capabilities of neural network with the reasoning transparency of fuzzy logic. However, conventional ANFIS architectures suffer from structural complexity, where the product-based inference mechanism causes an exponential explosion of rules in high-dimensional spaces. We herein propose the Kolmogorov-Arnold Neuro-Fuzzy Inference System (KANFIS), a compact neuro-symbolic architecture that unifies fuzzy reasoning with additive function decomposition. KANFIS employs an additive aggregation mechanism, under which both model parameters and rule complexity scale linearly with input dimensionality rather than exponentially. Furthermore, KANFIS is compatible with both Type-1 (T1) and Interval Type-2 (IT2) fuzzy logic systems, enabling explicit modeling of uncertainty and ambiguity in fuzzy representations. By using sparse masking mechanisms, KANFIS generates compact and structured rule sets, resulting in an intrinsically interpretable model with clear rule semantics and transparent inference processes. Empirical results demonstrate that KANFIS achieves competitive performance against representative neural and neuro-fuzzy baselines.

Predicting when maritime systems require maintenance can be critical, avoiding hazards and costly consequences. To address this problem, this paper proposes an explainable decision-making framework that integrates a neuro-fuzzy prediction model with a two-stage explainable component. The first stage of this component produces feature-attribution explanations, using gradient-based saliency maps, and the second stage extracts local rules using a fuzzy decision tree. The proposed framework is generic and can be integrated into any deep learning-based approach, rendering it explainable. To the best of our knowledge, this is the first fuzzy logic-based framework enabling both feature-level and local rule-based explanations of black box models. This approach aims to foster trustworthiness in decision making through user-understandable machine inferences. The performance of the proposed framework using a deep residual-based neural backbone is evaluated on various general-purpose public benchmark datasets, and its utility in maritime is demonstrated in the context of early fault detection in a naval propulsion system dataset. The results indicate that it can provide predictions outperforming relevant state-of-the-art approaches, with an average AUC-ROC (Area Under the Receiver Operating Characteristic Curve) value, reaching up to 99%, while offering the advantage of explainability.

CounterFactual Examples (CFEs) are a cornerstone of eXplainable Artificial Intelligence (XAI), offering local, post hoc, and model-agnostic explanations by identifying minimal input modifications that alter a model's prediction. Yet, in order to be intelligible, these modifications must also be semantically meaningful to the explainee. This paper proposes to integrate knowledge expressed as a fuzzy linguistic vocabulary to represent the explainee's perception and interpretation of the data. The domain induced by this fuzzy vocabulary imposes structural constraints that make the features dependent, preventing the use of gradient-based optimisation methods for CFE generation, e.g., DiCE. The paper proposes a continuous data embedding in this linguistic domain and exploits it to define a variant of DiCE that allows personalisation for the explainee, named DiCEf. As illustrated by experimental results on a real-world dataset, this extension of the DiCE method enables the generation of CFEs that are linguistically perceptible while preserving cost minimality, sparsity, and diversity.