Covering-based (O,G)-variable precision fuzzy rough set and its application in decision-making

As two non-associative binary fuzzy logical operators, overlap and grouping functions have been integrated into rough set theory. However, research on covering-based variable precision fuzzy rough sets (CVPFRSs) from the perspective of overlap and grouping functions remains limited, leaving several gaps to be addressed. To fill this gap, we propose novel CVPFRS models based on overlap and grouping functions, referred to as (O,G)-CVPFRSs, and develop corresponding multi-attribute decision-making (MADM) methods. First, by employing residual implications and coimplications derived from overlap and grouping functions, we construct four distinct (O,G)-CVPFRS models and systematically investigate their theoretical properties, with particular emphasis on their comparability property. Subsequently, building upon the traditional TOPSIS method, we propose two MADM methods grounded in the (O,G)-CVPFRS models. Finally, we validate the proposed methods through a numerical case study. Comparative analyses with benchmark approaches demonstrate the validity, reliability, and practical effectiveness of the proposed methods in material selection for bone grafting.