(L, M)-Fuzzy k-Pseudo Metric Space

Recently, the notion of a classical k-metric, which make the triangle inequality to a more general axiom: d(x, z) ≤ k(d(x, y) + d(y, z)), has been presented and is applied in many fields. In this paper, the definitions of an (L, M)-fuzzy k-pseudo metric and an (L, M)-fuzzy k-remote neighborhood ball system are introduced. It is proved that the category of (L, M)-fuzzy k-pseudo metric spaces is isomorphic to the category of (L, M)-fuzzy k-remote neighborhood ball spaces. Besides, (L, M)-fuzzy topological structures induced by an (L, M)-fuzzy k-pseudo metric are presented and their properties are investigated. Finally, the concept of a nest of pointwise k-pseudo metrics is proposed and it is shown that there is a one-to-one correspondence between (L, M)-fuzzy k-pseudo metrics and nests of pointwise k-pseudo metrics.