Abstract
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 T ∥ · ∥ * 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 T ∥ · ∥ * . In addition, we also study the relations among three I-topologies T ∥ · ∥ * , T ∥ · ∥ and ω ( τ ) , where ω ( τ ) is the induced I-topology of the crisp vector topology τ determined by fuzzy norm ∥ · ∥ .
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