New covering techniques and applications utilizing multigranulation fuzzy rough sets

In order to conduct an in-depth study of Zhan’s methodology pertaining to the covering of multigranulation fuzzy rough sets (\(\hbox {C}_{{MG}}\)FRSs), we build two families: the family of fuzzy \(\beta \)-minimum descriptions and the family of \(\beta \)-maximum descriptions. Subsequently, utilizing these notions, we proceed to develop two variations of covering via optimistic (pessimistic) multigranuation rough set samples (\(\hbox {CO(P)}_{{MG}}\)FRS). The axiomatic properties are examined. In this study, we examine four models of covering using variable precision multigranulation fuzzy rough sets (\(\hbox {CVP}_{{MG}}\)FRSs). We proceed with analyzing the features of these models. Interconnections between these planned plans are also elucidated. This study explores algorithms that aim to identify innovative strategies for addressing multiattribute group decision-making problems (MAGDM) and multicriteria group decision-making problems (MCGDM). The test examples have been elucidated to provide an inclusive grasp of the efficacy of the offered samples. Ultimately, the distinctions between our methodologies and the preexisting research have been demonstrated.