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

Year 2024, Early Access, 1 - 18

Yu Shen , C. H. Yan

https://doi.org/10.15672/hujms.1482251

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.

Keywords

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

Ethical Statement

The authors declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Supporting Institution

The National Natural Science Foundation of China

Project Number

NO. 12071225

References

• [1] M. Abel and A. Šostak, Towards the theory of L-bornological spaces, Iranian Journal of Fuzzy Systems, 8(1), 19–28, 2011