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

Document Type : Research Paper

Authors

1 College of Science, North China University of Technology, Beijing 100144, P.R. China

2 Department of Mathematics, University of Latvia, Riga LV-1084, and Institute of Mathematics and Computer Science, University of Latvia, Riga LV-1459, Latvia

Abstract

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.

Keywords