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

摘要

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 T-similarity relation is equivalent to a fuzzy relation that is reflexive and T-Euclidean, where T-denotes a t-norm. Therefore, T-Euclidean condition is redundant for IC model satisfying all properties listed in the work of D'eer et al. (C) 2015 Elsevier B.V. All rights reserved.