Dimensionality Reduction Method for Fuzzy Interval Data Using Deep Learning

Neural network principal component analysis (NNPCA) is an extension of principal component analysis (PCA) for fuzzy interval data, which enables dimensionality reduction while maintaining the format of fuzzy intervals. However, since NNPCA is a linear autoencoder-type model with one hidden layer and an identity function as the activation function, it cannot perform appropriate dimensionality reduction for complex data that contain nonlinearity or high levels of noise. Therefore, this paper proposes a multilayer fuzzy autoencoder (ML-FAE) that extends NNPCA by stacking multiple layers to perform nonlinear, hierarchical dimensionality reduction. In addition, the proposed model introduces a batch normalization method that considers the characteristics of fuzzy interval data to stabilize learning and improve expressiveness. In performance evaluations using simulated and real data, it was confirmed that even in cases where appropriate dimensionality reduction is difficult using NNPCA, the proposed method significantly improves classification performance as a task and visualization in low-dimensional space, demonstrating that more effective dimensionality reduction can be achieved.