Characterizations of (L,M)-fuzzy pseudo-metrics by pointwise pseudo-metric chains

In this paper, the concept of pointwise pseudo-metric chains is introduced. It is shown that there is a one-to-one correspondence between (L,M)-fuzzy pseudo-metrics in the sense of Shi and pointwise pseudo-metric chains which preserve ∨-∧ operations. Also, it is proved that a pointwise pseudo-metric chain can induce an (L,M)-fuzzy topology which coincides with the (L,M)-fuzzy topology induced by an (L,M)-fuzzy pseudo-metric.