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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 5

$L$-fuzzifying rough sets based on $KM$-fuzzy pseudo metrics

Yu Zhong(North China University of Technology)0009-0008-8333-3519
Shuang Lin(Jinyinhu High School)0009-0007-8953-9721
Shi Yi(Nanjing Institute of Technology)0000-0003-1712-9495
Zhihui Yang(North China University of Technology)0009-0003-9734-188X
Pages
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Publication Date
2026-10-28
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Finally, we get the conclusions that$\underline{R}^{\mathcal{D}}\leq {\underline{R}^{M}}^{\mathcal{D}}$ and ${\overline{R}^{M}}^{\mathcal{D}}\leq \overline{R}^{\mathcal{D}}$.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we construct an $L$-fuzzifying lower and an $L$-fuzzifying upper approximation operator ($L$ denotes a completely distributive De Morgan algebra) based on a $KM$-fuzzy pseudo metric and study their properties.Then we discuss some equivalent characterizations of the corresponding axiom of $KM$-fuzzy pseudo metrics via its induced $L$-fuzzifying rough set, respectively.Moreover, we explore the relationships between the crisp rough set induced by a $KM$-fuzzy pseudo metric $M$ and the crisp rough set induced by the corresponding crisp pseudo metrics $d_{a}^{M}$.Besides, we investigate the relationships between the $L$-fuzzifying rough set induced by a family of crisp pseudo metrics $\mathcal{D}$ and the $L$-fuzzifying rough set induced by the corresponding $KM$-fuzzy pseudo metric ${M}^{\mathcal{D}}$.
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Key Findings & Data:In this paper, we construct an $L$-fuzzifying lower and an $L$-fuzzifying upper approximation operator ($L$ denotes a completely distributive De Morgan algebra) based on a $KM$-fuzzy pseudo metric and study their properties.Then we discuss some equivalent characterizations of the corresponding axiom of $KM$-fuzzy pseudo metrics via its induced $L$-fuzzifying rough set, respectively.Moreover, we explore the relationships between the crisp rough set induced by a $KM$-fuzzy pseudo metric $M$ and the crisp rough set induced by the corresponding crisp pseudo metrics $d_{a}^{M}$.Besides, we investigate the relationships between the $L$-fuzzifying rough set induced by a family of crisp pseudo metrics $\mathcal{D}$ and the $L$-fuzzifying rough set induced by the corresponding $KM$-fuzzy pseudo metric ${M}^{\mathcal{D}}$.
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Conclusion & Impact:Finally, we get the conclusions that$\underline{R}^{\mathcal{D}}\leq {\underline{R}^{M}}^{\mathcal{D}}$ and ${\overline{R}^{M}}^{\mathcal{D}}\leq \overline{R}^{\mathcal{D}}$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:L-fuzzifying lower approximation operator · L-fuzzifying upper approximation operator · L-fuzzifying rough set

Abstract

In this paper, we construct an $L$-fuzzifying lower and an $L$-fuzzifying upper approximation operator ($L$ denotes a completely distributive De Morgan algebra) based on a $KM$-fuzzy pseudo metric and study their properties.Then we discuss some equivalent characterizations of the corresponding axiom of $KM$-fuzzy pseudo metrics via its induced $L$-fuzzifying rough set, respectively.Moreover, we explore the relationships between the crisp rough set induced by a $KM$-fuzzy pseudo metric $M$ and the crisp rough set induced by the corresponding crisp pseudo metrics $d_{a}^{M}$.Besides, we investigate the relationships between the $L$-fuzzifying rough set induced by a family of crisp pseudo metrics $\mathcal{D}$ and the $L$-fuzzifying rough set induced by the corresponding $KM$-fuzzy pseudo metric ${M}^{\mathcal{D}}$. Finally, we get the conclusions that$\underline{R}^{\mathcal{D}}\leq {\underline{R}^{M}}^{\mathcal{D}}$ and ${\overline{R}^{M}}^{\mathcal{D}}\leq \overline{R}^{\mathcal{D}}$.

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Cite This Article

Zhong, Y., Lin, S., Yi, S., Yang, Z. (2026). $L$-fuzzifying rough sets based on $KM$-fuzzy pseudo metrics. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 5. https://doi.org/10.15672/hujms.1854627

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