Ranking of relevant objects plays an important role in various applications especially in multimedia database systems and information retrieval systems. In contrast to traditional database systems, multimedia database systems deal with similarity queries returning a list of objects ranked by the objects’ overall score. The overall score for objects in the database is calculated using a scoring rule which is commonly based on similarity functions and fuzzy logic. One aspect which enhances the user’s flexibility to formulate preferences regarding the search criteria, is to assign weights to each argument in a query. In this paper a formal specification of the requirements for an adequate weighted scoring rule is given. Based on this specification different methods for incorporating weights into scoring rules are evaluated and their limitations are shown. Furthermore, we discuss that weighting on different levels in complex queries is necessary. Therefore, multi-level weighting is introduced and different possibilities to assign weights on different levels are shown. Finally, an extended specification for weighted scoring rules with multi-level weighting is proposed.