TY  - JOUR
T1  - On Non-Archimedean $\mathcal{L}$-Fuzzy Vector Metric Spaces
AU  - Eminoğlu, Şehla
PY  - 2023
DA  - December
DO  - 10.53570/jnt.1351848
JF  - Journal of New Theory
JO  - JNT
PB  - Naim ÇAĞMAN
WT  - DergiPark
SN  - 2149-1402
SP  - 46
EP  - 56
IS  - 45
LA  - en
AB  - 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.
KW  - Non-Archimedean $\mathcal{L}$-fuzzy vector metrics
KW  - left and right order convergence
KW  - $\mathcal{L}$-fuzzy vector diameter
KW  - Riesz spaces
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UR  - https://doi.org/10.53570/jnt.1351848
L1  - https://dergipark.org.tr/en/download/article-file/3370579
ER  -