Atrial Fibrillation (AF) is the most common cardiac arrhythmia. Generally, the therapeutic options for managing AF include the use of anticoagulant drugs that prevent the coagulation of blood. New Oral Anticoagulants (NOACs) are not optimally prescribed to patients, despite their efficacy. In Canada, NOAC medications are not directly available to patients who belong to provincial benefits programs, rather a NOAC special authorization process establishes the eligibility of a patient to receive a NOAC and be paid by the provincial Pharmacare program. This special authorization process is tedious and paper-based which inhibits physicians to prescribe NOAC leading to suboptimal AF care to patients. In this paper, we present a computerized NOAC Authorization Decision Support System (NOAC-ADSS), accessible to physicians to help them (a) determine a patient eligibility for NOAC based on Canadian AF clinical guidelines, and (b) complete the special authorization form. We present a semantic web based system to ontologically model the NOAC eligibility criteria and execute the knowledge to determine a patient NOAC eligibility and dosage.