Generalized fuzzy k-pseudo metric and its representation theorem

Abstract

In this paper, the definition of a generalized fuzzy k-pseudo metric and some typical examples are given. Then we point out that a generalized fuzzy k-pseudo metric can be constructed from a nest of k-pseudo metrics. Besides, we verify that a nest of k-pseudo metrics can also be constructed from a generalized fuzzy k-pseudo metric. Therefore, it can be shown that there exists a one-to-one correspondence between generalized fuzzy k-pseudo metrics and a nest of k-pseudo metrics.