A New Kind of Vector Space: Soft Vector Space

Abstract

Molodtsov introduced the concept of soft sets. In this paper, we present the definition of soft vector spaces and construct some basic properties by using vector spaces and Molodtsov's definition of soft sets. We introduce the notions of soft vector spaces, soft subvector spaces, soft v-linear transformations and soft b-linear transformations and some related properties of soft structures over vector spaces are investigated and illustrated by many examples. Also soft v-linear transformation are investigated with respect to the soft linear transformatic image and we show that some structures of soft vector spaces are preserved under soft b-linear transformations.