On local bases of fuzzy topological vector spaces

Abstract

In this paper, the relations between neighborhood base introduced by Warren and quasi-coincidence neighborhood base introduced by Pu and Liu in fuzzy topological spaces are studied. The characterizations of these two kind of local bases for fuzzy topological vector spaces are further discussed. Moreover, we prove a necessary and sufficient condition for a family of fuzzy sets in a vector space to be the Q-prebase of a QL-type fuzzy topological vector space.