A new perspective to the Mazur-Ulam problem in $2$-fuzzy $2$-normed linear spaces

Abstract

In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%<br />-Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give a<br />new generalization of the Mazur-Ulam theorem when $X$ is a $2$-fuzzy $2$%<br />-normed linear space or $Im (X)$ is a fuzzy $2$-normed linear space, that<br />is, the Mazur-Ulam theorem holds, when the $2$-isometry mapped to a $2$%<br />-fuzzy $2$-normed linear space is affine.