Sahand Communications in Mathematical Analysis (Jun 2022)
The Study of Felbin and $BS$ Fuzzy Normed Linear Spaces
Abstract
In this paper, we first show that the induced topologies by Felbin and Bag-Samanta type fuzzy norms on a linear space $X$ are equivalent. So all results in Felbin-fuzzy normed linear spaces are valid in Bag-Samanta fuzzy normed linear spaces and vice versa. Using this, we will be able to define a fuzzy norm on $FB(X,Y)$, the space of all fuzzy bounded linear operators from $X$ into $Y$, where $X$ and $Y$ are fuzzy normed linear spaces.
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