In this paper we define the space $BV_{\sigma }³eft( p,f,q,s\right) $ on a seminormed complex linear space, by using modulus function. We give various properties and some inclusion relations on this space. Furthermore, we construct the sequence space $BV_{\sigma }³eft( p,f^{k},q,s\right)$ and we give properties and some inclusion relations on this space.