A Multi-parameter Fuzzy Set Framework for Classifying Red, Blue, and Green Valley Galaxies

Abstract

We present a data-driven fuzzy set framework for classifying galaxies into the red sequence, blue cloud, and green-valley populations using multiple observables from the Sloan Digital Sky Survey (SDSS DR18). Unlike traditional methods based on hard boundaries in colour or stellar mass, our approach assigns continuous membership degrees using sigmoidal functions derived from bimodal galaxy properties, including $(u-r)$ colour, specific star formation rate (sSFR), and $D4000$. Membership functions are constructed via Gaussian mixture modeling and combined using a conservative fuzzy minimum operator. Applying this method to a volume-limited sample of 88,579 galaxies, we compare with the empirical classification of \citet{schawinski14}. The fuzzy approach reduces contamination in the red and green-valley populations and yields more physically consistent distributions of star formation and morphology. Red galaxies show a unimodal low-sSFR distribution, while green-valley galaxies exhibit clearer signatures of morphological evolution. We also examine the dependence of active galactic nucleus (AGN) fraction on stellar mass and find no significant differences between methods, indicating robust global AGN trends. However, clustering analysis reveals subtle differences: fuzzy-classified red galaxies show enhanced large-scale clustering, suggesting a stronger association with highly biased dark matter halos. These results demonstrate that fuzzy classification provides a flexible, physically motivated alternative to hard-cut methods, enabling a more accurate and interpretable view of galaxy populations and their evolution.