A note on “Some results on the IF-normed spaces”

Abstract

Recently, Lael and Nourouzi [Some results on the IF-normed spaces. Chaos, Solitons & Fractals 2006; doi:10.1016/j.chaos.2006.10.019] introduced and studied a new notation of IF-normed spaces by using the idea of intuitionistic fuzzy normed spaces due to Saadati and Park [On the intuitionistic fuzzy topological spaces. Chaos, Solitons & Fractals 2006;27:331–44], a special continuous t-norm i.e. min and a special continuous s-norm i.e. max. In this note, we consider the modified definition of IF-normed space i.e. L F -normed spaces and prove the open mapping and closed graph theorems for this space using arbitrary continuous t-norm.