Multi-criteria ranking of drying systems for germinated brown rice processing using an integrated Shannon–Gibbs entropy framework

Drying-system selection is a critical decision in germinated brown rice processing because drying performance affects storage stability, microbial safety, product appearance, and commercial quality. However, drying systems often exhibit conflicting performance across multiple quality indicators, making single-criterion evaluation insufficient. This study proposes an integrated Shannon–Gibbs entropy framework for multi-criteria ranking of drying systems for germinated brown rice processing. Three drying alternatives were evaluated: a tray dryer, a stand-alone electric dryer, and a hybrid dryer integrating electric heating with solar air heating. Five product-quality criteria were considered: moisture content, water activity, lightness (L*), redness/greenness (a*), and yellowness/blueness (b*). Shannon entropy was used to determine objective criterion weights from the normalized decision matrix, while an updated Gibbs entropy ranking method was applied to obtain entropy-adjusted performance scores. In the proposed Gibbs entropy formulation, the Shannon-normalized matrix was directly used to construct the weighted normalized performance matrix, the Gibbs constant was defined as the reciprocal of the row sum of weighted normalized values, and the final ranking was derived from normalized entropy-adjusted scores. The Shannon entropy results showed that b* was the most influential criterion, with a weight of 0.544916, followed by a* at 0.198931, moisture content at 0.122783, L* at 0.082475, and water activity at 0.050896. The updated Gibbs entropy ranking identified the hybrid dryer as the best alternative (Si*=1.000000), followed by the stand-alone dryer (Si*=0.997008) and the tray dryer (Si*=0.822019). The ranking was consistent with WASPAS, COPRAS, and TOPSIS, confirming the robustness of the proposed framework. The findings demonstrate that the integrated Shannon–Gibbs entropy approach provides a transparent, data-driven, and uncertainty-aware decision-support tool for selecting drying technologies in value-added rice processing.