On I-topology generated by fuzzy norm

In this paper, we point out that an I-topology T∥·∥ on the fuzzy normed linear space (X,∥·∥,min,max) constructed by Das and Das [Fuzzy topology generated by fuzzy norm, Fuzzy Sets and Systems 107 (1999) 349–354] is incompatible with the linear structure on X, that is, (X,∥·∥,min,max) is not an I-topological vector space with respect to the I-topology T∥·∥. Therefore, we construct a new I-topology on the fuzzy normed linear space (X,∥·∥,L,R) by using fuzzy norm ∥·∥. We study some of its properties and prove that if R⩽max, then (X,∥·∥,L,R) is a Hausdorff locally convex I-topological vector space with respect to the I-topology . In addition, we also study the relations among three I-topologies , T∥·∥ and ω(τ), where ω(τ) is the induced I-topology of the crisp vector topology τ determined by fuzzy norm ∥·∥.