Pointwise (L, M)-fuzzy uniformities induced by (L, M)-fuzzy pseudo-metric and pointwise pseudo-metric chains

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.