Fuzzy vector spaces under norms

Abstract

In this paper, by using t-norm T, we study purely algebraic properties of fuzzy vector spaces. Next we introduce sum, intersection, direct product and normality of them. Later we prove that sum, intersection, direct product and normality of them is also fuzzy vector
space under t-norm T. Finally, we investigate them under linear transformations and we obtian that image and pre image of them is also fuzzy vector space under t-norms.