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- Title
Fundamental properties of fuzzy rough sets based on triangular norms and fuzzy implications: the properties characterized by fuzzy neighborhood and fuzzy topology.
- Authors
Wang, Zhaohao
- Abstract
Fuzzy rough set models are useful tools for dealing with fuzzy and real-valued data. They have been used in many real-world applications. In this paper, we investigate the fuzzy rough set model based on triangular norms and fuzzy implications. First, we extend some results in the published literature by removing the condition that is the continuity of triangular norms, and obtain more general conclusion about fuzzy upper approximation operators. Then, for the fuzzy neighborhood and the fuzzy lower approximation operator based on fuzzy implications, we investigate their characterization with each other. Finally, we establish the relationships between fuzzy rough sets and fuzzy topology. In this work, researches on the properties of fuzzy rough sets based on triangular norms which need not be continuous provide generalization results for fuzzy rough set theory from viewpoint of mathematics.
- Subjects
FUZZY sets; ROUGH sets; TRIANGULAR norms; FUZZY topology; NEIGHBORHOODS
- Publication
Complex & Intelligent Systems, 2024, Vol 10, Issue 1, p1103
- ISSN
2199-4536
- Publication type
Article
- DOI
10.1007/s40747-023-01213-1