Fuzzy topology and fuzzy topology reduction method of rough set model based on axiomatic fuzzy sets

Fuzzy sets and rough sets are mathematical tools for dealing with uncertain and inconsistent problems due to their complementary characteristics. Most fuzzy rough sets are obtained by combining Zadeh fuzzy sets and Pawlak rough sets. Compared to Zadeh fuzzy sets, axiomatic fuzzy sets are clearer, stricter, and more explicit. For this reason, we propose a rough set model based on axiomatic fuzzy sets, with emphasis on the properties of approximation operators and topological structure of the proposed model. First, we propose a novel fuzzy rough set model and explore its basic properties. Second, we construct a topology, which is a set composed of lower approximation sets. Meanwhile, we discuss the properties of topologies induced by different fuzzy relations. Finally, we present a fuzzy reduction method based on fuzzy topology and illustrate the reduction method through an example.