Mean-based hesitant fuzzy spaces with an application to medical prediagnosis

Uncertainty in intelligent decision-support systems frequently arises from heterogeneous, multi-source, and linguistically expressed information. Hesitant fuzzy sets (HFSs) provide a flexible representation of such uncertainty by allowing multiple possible membership degrees for a single element. However, most existing HFS-based models operate at the membership level and lack a unified space-level structure to organize hesitant information within a consistent compositional framework. To address this limitation, this paper introduces a mean-based hesitant fuzzy space that includes a refined mean-induced total ordering along with its corresponding lattice structure. The proposed framework establishes a structured ambient domain in which hesitant fuzzy elements can be consistently compared, aggregated, and manipulated. Mean lattices and mean M -sublattices are developed to support order-theoretic operations, and hesitant fuzzy subspaces are formalized with corresponding structural properties. To demonstrate its practical relevance, the proposed hesitant fuzzy space is integrated into a medical prediagnosis pipeline. Hesitant clinical assessments are encoded within the mean-based lattice, transformed into lattice-consistent numerical features, and then used as inputs to a Nearest Centroid classifier. This pipeline is illustrated with a worked numerical example designed to make each computational step transparent and verifiable; it serves as a proof-of-concept demonstration rather than an empirical evaluation on real clinical data. The proposed framework provides a coherent mathematical foundation for uncertainty-aware intelligent systems and offers a flexible, scalable machine-learning-ready feature representation layer for future classification and decision-support applications.