Neural networks based on interval-valued pseudo overlap and grouping functions with applications to fuzzy reasoning and image classification

Pseudo overlap functions (POFs) are critical in image processing, text classification, decision-making systems etc. However, integrating interval-valued pseudo overlap functions (IPOFs) and interval-valued pseudo grouping functions (IPGFs) with neural networks remains underexplored. To address this gap, we propose a systematic framework that fundamentally redesigns neural architectures using IPOFs and IPGFs. First, some new results about IPOFs and IPGFs are introduced, including their pseudo automorphisms, multiplicative generators and additive generators. Then, ANNs and CNNs based on IPOFs (called IV-POG ANNs and IV-POG CNNs) are introduced respectively. The introduction of IPOFs substantially enhance the nonlinearity, asymmetry and bilateral approximation ability of ANNs and CNNs. Third, Takagi–Sugeno–Kang (TSK) fuzzy systems based on IPOFs are introduced and IV-POG ANNs are used to fit these systems and train their parameters. The experiments demonstrate that IPOFs significantly enhance the image classification performance of ANNs and CNNs, while simultaneously strengthening the inference capabilities of TSK fuzzy systems.