Representation Learning for Latent Disease Identification based on the Multidimensional Hesitant Fuzzy xLSTM Network

Latent disease representation learning plays a pivotal role in disease identification. However, this process is often influenced by the subjective judgments of experts or decision-makers, which introduces inherent ambiguity and uncertainty. To address this challenge, this study leverages the hesitant fuzzy set (HFS), known for its ability to handle subjective and imprecise inputs, and proposes an intelligent identification framework based on extended LSTM (xLSTM). Within this framework, we define the ascending hesitant fuzzy set (AHFS) and multidimensional hesitant fuzzy set (MHFS) to better capture and optimize the dynamic interactions between patients and healthcare providers. Key features are extracted through representation learning, enabling the system to accurately identify latent diseases. To manage varying membership degrees in HFS, we integrate the KNN algorithm into a data expansion mechanism for hesitant fuzzy data and propose a multidimensional hesitant fuzzy xLSTM (MHFxLSTM) to handle both fuzzy and real-valued data. To further enhance the system's adaptability and reduce the risk of misdiagnosis, an expert review mechanism is incorporated at the output layer. Additionally, we develop an optimization algorithm with a detailed implementation plan and pseudocode for MHFxLSTM, enhancing the framework's reliability. A case study on obesity risk assessment demonstrates the feasibility and effectiveness of the proposed method. The system's performance is further validated through comprehensive comparative analysis, underscoring its potential in latent disease identification.