Identifying similarities in large datasets is an essential operation in many applications such as bioinformatics, pattern recognition, and data integration. To make the underlying database system similarity-aware, the core relational operators have to be extended. Several similarity-aware relational operators have been proposed that introduce similarity processing at the database engine level, e.g., similarity joins and similarity group-by. This paper extends the semantics of the set intersection operator to operate over similar values. The paper describes the semantics of the similarity-based set intersection operator, and develops an efficient query processing algorithm for evaluating it. The proposed operator is implemented inside an open-source database system, namely PostgreSQL. Several queries from the TPC-H benchmark are extended to include similarity-based set intersetion predicates. Performance results demonstrate up to three orders of magnitude speedup in performance over equivalent queries that only employ regular operators.