FUZZY TOPOLOGICAL VECTOR-SPACES TOPOLOGICAL GENERATION AND NORMABILITY

Increasing awareness of the utility of fuzzy systems in modeling real life situations necessitates a thorough understanding of fuzzy topological vector spaces. In this paper, the first of several to follow on this topic, the generation of a fuzzy vector topology from an ordinary vector topology on a vector space is discussed. Also obtained is a condition for the fuzzy normability of a fuzzy vector topology induced by a family of fuzzy seminorms. Finally, an example indicating that the earlier mentioned condition is only sufficient is given.