University of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601The Study of Felbin and $BS$ Fuzzy Normed Linear Spaces496425207910.22130/scma.2022.544742.1033ENFarnazYaqub AzariDepartment of Mathematics, Sahand University of Technology, P.O.Box 53318-17634, Tabriz, Iran.0000-0002-0308-7178IldarSadeqiDepartment of Mathematics, Sahand University of Technology, P.O.Box 53318-17634, Tabriz, Iran.0000-0001-5336-6186Journal Article20211212In 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.https://scma.maragheh.ac.ir/article_252079_e381e776c648062c670cd7f438f1c4bf.pdf