The concept of multi-fuzzy algebra extends the traditional notions of fuzzy algebra by introducing multi-dimensional membership functions, allowing for a more nuanced representation of uncertainty and vagueness in algebraic structures. This paper explores the properties and algebraic structures of multi-fuzzy algebras over multi-fuzzy field, generalizing the framework of fuzzy vector spaces and fuzzy fields. We introduce a novel approach using a bridge function h to define multi-fuzzy algebras when the dimensions of the multi-fuzzy set on an algebra A and the multi-fuzzy field differ. The paper investigates the influence of this bridge function on the algebraic properties of these spaces and provides a comprehensive analysis of their structure. Key results include the characterization of multi-fuzzy algebras, their intersections, and their behaviour under linear transformations