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

Abstract

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