. In this paper we present the parameterized extension of the concept of bornology. In doing so, we introduce the notions of soft bornology and an M-valued soft bornology where the parametrization plays the key role. Furthermore, we introduce boundedness and parameterized degree of boundedness for soft sets in such spaces, respectively. We observe some of the elementary properties of the proposed spaces. Finally, we looked bounded soft mappings in the corresponding spaces.