The given statement is: "Acids are substances that dissociate in water to give hydrogen ions \(H^+\) (aq), and bases are substances that produce hydroxyl ions \(OH^−\) (aq)." To determine which concept this statement is based on, let's briefly review each option:

1. Arrhenius Concept: This is one of the earliest acid-base theories, which defines acids as substances that increase the concentration of hydrogen ions \(H^+\) in aqueous solutions, whereas bases are substances that increase the concentration of hydroxyl ions \(OH^−\).
2. Brønsted-Lowry Concept: This concept defines acids as proton donors and bases as proton acceptors; it does not specifically focus on the presence of \(OH^−\) ions in solutions.
3. Lewis Acid-Base Concept: This theory looks at acids as electron pair acceptors and bases as electron pair donors, which is broader and includes non-aqueous reactions.
4. Conjugate Acid-Base Concept: This involves pairs of substances within the context of acid-base reactions, typically related to Brønsted-Lowry theory where an acid turns into its conjugate base and vice versa after the transfer of a proton.

The given statement directly mentions hydrogen ions and hydroxyl ions, aligning with the Arrhenius definition of acids and bases. Thus, the statement is based on the Arrhenius concept.

Therefore, the correct answer is: Arrhenius concept.