Generalized fuzzy neighborhood system-based multigranulation variable precision fuzzy rough sets with double TOPSIS method to MADM

Abstract

Multigranulation fuzzy rough sets (MFRSs), variable precision fuzzy rough sets (VPFRSs) and their combinations with traditional decision-making methods are fundamental in the research of multi-attribute decision-making (MADM) problems. However, the existing theories and methods have two deficiencies: (1) many existing MFRSs are based on fuzzy relations or fuzzy coverings, which may not effectively solve some MADM problems; (2) VPFRSs usually do not meet the inclusion property, which hinders their further development in theory and application. Noted that both fuzzy relations and fuzzy coverings can generate fuzzy neighborhood systems in a natural way, so the fuzzy neighborhood system provides a broader multigranulation framework. Inspired by this, by using the generalized fuzzy neighborhood system, we propose three multigranulation variable precision fuzzy rough set models, namely optimistic, pessimistic and compromise, respectively. As expected, these models contain many existing models as special cases, thus broadening the framework of rough set. Additionally, we verify that these models fulfill many basic algebra properties, particularly the generalized inclusion properties, which overcome the limitation of VPFRSs. Finally, by combining the proposed fuzzy rough set models with the TOPSIS method, we develop a new method to MADM. A series of experiments show that our method has some obvious advantages.