On Non-Archimedean $\mathcal{L}$-Fuzzy Vector Metric Spaces

Abstract

This paper contributes to the broader studies of fuzzy vector metric spaces and fuzzy metric spaces based on order structures beyond the unit interval. It defines the notions of the left (right) order convergence and continuity in non-Arcimedean $\mathcal{L}$-fuzzy vector metric spaces. The notation $\mathcal{M}_E(a,b,s)$ means the nearness between $a$ and $b$ according to any positive vector $s$. This study exemplifies definitions and reaches some well-known results. Moreover, it proposes the concept of $\mathcal{L}$-fuzzy vector metric diameter and studies some of its basic properties. Further, the present paper proves the Cantor intersection theorem and the Baire category theorem via these concepts. Finally, this study discusses the need for further research.