A new definition of fuzzy k-pseudo metric and its induced fuzzifying structures

In this paper, a new definition of a fuzzy $k$-pseudo metric is introduced and its induced fuzzifying structures are constructed, such as a fuzzifying neighborhood system, a fuzzifying topology, a fuzzifying closure operator, a fuzzifying uniformity.Besides, it is shown that there is a one-to-one correspondence between fuzzy $k$-pseudo metrics and nests of crisp $k$-pseudo metrics.