Mackey convergence and separation in $(L, M)$-fuzzy bornological vector spaces

Abstract

This paper aims to introduce the concepts of Mackey convergence degree for sequences and separation degree for spaces in $(L, M)$-fuzzy bornological vector spaces. Additionally, the paper presents the concept of bornological closure degree for fuzzy sets. Moreover, the paper discusses various characteristics of these concepts. Furthermore, the paper examines the degree relationships among a Mackey convergence sequence, a separated space, and a bornologically closed fuzzy set. Finally, the paper analyzes the properties of functors $\omega$ and $\iota$ between $M$-fuzzifying bornological vector spaces and $(L, M)$-fuzzy bornological vector spaces in terms of Mackey convergence degree and separation degree.