Notes on a comprehensive study of implicator–conjunctor-based and noise-tolerant fuzzy rough sets: Definitions, properties and robustness analysis

D'eer et al. evaluated the implicator–conjunctor-based fuzzy rough set model or shortly, IC model and different noise-tolerant fuzzy rough set models. However, neither IC model nor Fuzzy Variable Precision Rough Set (FVPRS) model satisfies (ID) property without the reflexivity of fuzzy relation. Upper approximation operator in IC model cannot necessarily be expressed by fuzzy granules. Moreover, a fuzzy TT-similarity relation is equivalent to a fuzzy relation that is reflexive and TT-Euclidean, where TT denotes a t-norm. Therefore, TT-Euclidean condition is redundant for IC model satisfying all properties listed in the work of D'eer et al.