The aim of this study is to present the concept of an (L, M)-fuzzy (E, K)-soft bornology as a parameterized extension of the LM-valued bornology. By this way, we describe the notions of boundedness and the parameterized degree of boundedness for L-fuzzy soft sets. We examine several fundamental properties of the proposed structures. In addition, we induce a (2, M)-fuzzy (E, K)-soft bornology in a given (2, M)-fuzzy (E, K)-soft topological space with the help of the measures of compactness of a soft set