Measurement, modeling, reduction of decision-theoretic multigranulation fuzzy rough sets based on three-way decisions

Variable precision multigranulation fuzzy rough sets (VP-MFRSs) use two direct integrations: the maximum and minimum. Their optimistic pessimistic models facilitate uncertainty informatization but also imply a potential limitation of extremes. This study improves VP-MFRSs for extension balance, thus, decision-theoretic (DT-MFRSs) are proposed by systematically fusing For DT-MFRSs, their tri-level analysis measurement, modeling, reduction is deeply acquired via three-way decisions. First, minimum membership degrees linearly combined, weight parameter guides generalized degree. adjustable measure motivates DT-MFRSs with positive, negative, boundary regions, while attitude-preference values 1, 0, 0.5 respectively produce optimistic, pessimistic, compromised models. Then, nonmonotonicity model regions determined, these fundamental characteristics induce new criteria region preservations. Also, attribute reducts preserving positive–negative systematic relationships obtained. Finally, results measures, models, validated table examples data experiments. In this study, extend improve fusion contain etc., thereby exhibiting extended diversity applied robustness. perfects optimization.