Axiomatic characterizations of metric-based L-fuzzy variable precision rough set

Abstract

The fuzzy variable precision rough set (FVPRS) model, in comparison to traditional rough sets, exhibits fault-tolerant and anti-interference capabilities, which have garnered widespread attention. However, its axiomatic characterization remains challenging to achieve due to inherent complexity. In the context of this research, we propose a new metric-based L-fuzzy variable precision rough set (MLFVPRS) valued in a complete co-residuated lattice and study the axiomatic characterizations. Initially, a pair of mappings accompanied by three axioms is employed to describe the upper (resp., lower) approximation operator within the context of MLFVPRS. This methodology stands in contrast to the approach adopted for defining similar operators in fuzzy rough sets, which relies on a single mapping coupled with two axioms. After that, three axioms are combined into a single axiom by using a specific fuzzy set mapping. Finally, the MLFVPRS generated via reflexive, symmetric, and transitive generalized L-metric along with their compositions are characterized through axiom sets and single axiom respectively.