A1305
Title: A geometric discriminant framework for classification of fuzzy data
Authors: Ana Belen Ramos-Guajardo - Fundacion Universidad de Oviedo (Spain) [presenting]
Gil Gonzalez-Rodriguez - University of Oviedo (Spain)
Abstract: A classification framework for fuzzy valued data is proposed for situations in which imprecision is an intrinsic part of the observed features. Each variable is described by a fuzzy number whose $\alpha$ cuts reflect gradual variability rather than measurement error. A metric combining midpoint and spread information across all levels induces a Hilbert-type geometry that makes it possible to define meaningful class centers and measures of dispersion. Within this setting, discriminant directions arise from an optimization criterion analogous to classical separation ideas, leading to a tractable eigenvalue formulation. The resulting methodology allows class differences to be detected not only through changes in location but also through distinct imprecision patterns. Classification rules for two and multiple classes are based only on distances between fuzzy projections and class representatives. Simulation results highlight the benefits of exploiting the full fuzzy structure, particularly in settings where standard methods fail to capture imprecision driven discrimination.
