Affiliations: [a] School of Science, Hunan Institute of Science and Engineering, Yongzhou, P.R. China
| [b] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China
| [c] College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, P.R. China
Correspondence:
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Corresponding author. Zhen-Yu Xiu, College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610000, P.R. China. E-mail: xiuzhenyu112@sohu.com.
Abstract: In this paper, the relations among (L, M)-fuzzy pseudo-metrics, pointwise pseudo-metric chains and pointwise (L, M)-fuzzy uniformities are investigated. It is shown that an (L, M)-fuzzy pseudo-metric can induce a pointwise (L, M)-fuzzy uniformity, and an (L, M)-fuzzy pseudo-metric and its induced pointwise (L, M)-fuzzy uniformity generate the same (L, M)-fuzzy topology. Also, it is proved that a pointwise pseudo-metric chain can induce a pointwise (L, M)-fuzzy uniformity, and a pointwise pseudo-metric chain and its induced (L, M)-fuzzy pseudo-metric generate the same pointwise (L, M)-fuzzy uniformity. Moreover, a pointwise pseudo-metric chain and its induced pointwise (L, M)-fuzzy uniformity generate the same (L, M)-fuzzy topology.
