Extension of the fuzzy dominance-based rough set approach using ordered weighted average operators

In the article we rst review some known results on fuzzy versions of the dominance-based rough set approach (DRSA) where we expand the theory considering additional properties. Also, we apply Ordinal Weighted Average (OWA) operators in fuzzy DRSA. OWA operators have shown a lot of potential in handling outliers and noisy data in decision tables when it is combined with the indiscernibility-based rough set approach (IRSA).We examine theoretical properties of the proposed combination with fuzzy DRSA

Fuzzy extensions of the dominance-based rough set approach

In this paper, we first review existing fuzzy extensions of the dominance-based rough set approach (DRSA), and advance the theory considering additional properties. Moreover, we examine the application of Ordered Weighted Average (OWA) operators to fuzzy DRSA. OWA operators have shown a lot of potential in handling outliers and noisy data in decision tables, when they are combined with the indiscernibility-based rough set approach (IRSA). We examine theoretical properties of the proposed hybridisation of OWA operators with fuzzy DRSA. At the end, we experimentally compare the robustness of the standard fuzzy DRSA approach with the OWA one

Granular representation of OWA-based fuzzy rough sets

Granular representations of crisp and fuzzy sets play an important role in rule induction algorithms based on rough set theory. In particular, arbitrary fuzzy sets can be approximated using unions of simple fuzzy sets called granules. These granules, in turn, have a straightforward interpretation in terms of human-readable fuzzy "if..., then...'' rules. In this paper, we are considering a fuzzy rough set model based on ordered weighted average (OWA) aggregation over considered values. We show that this robust extension of the classical fuzzy rough set model, which has been applied successfully in various machine learning tasks, also allows for a granular representation. In particular, we prove that when approximations are defined using a directionally convex $t$-norm and its residual implicator, the OWA-based lower and upper approximations are definable as unions of fuzzy granules. This result has practical implications for rule induction from such fuzzy rough approximations