As markets and industries continue to evolve rapidly, technology opportunity discovery (TOD) has become critical to a firm's survival. From a common consensus that TOD based on a firm’s capabilities is a valuable method for small and medium-sized enterprises (SMEs) and reduces the risk of failure in technology development, studies for TOD based on a firm’s capabilities have been actively conducted. However, previous studies mainly focused on a firm's technological capabilities and rarely on business capabilities. Since discovered technologies can create market value when utilized in a firm's business, a firm’s current business capabilities should be considered in discovering technology opportunities. In this context, this study proposes a TOD method that considers both a firm's business and technological capabilities. To this end, this study uses patent data, which represents the firm's technological capabilities, and trademark data, which represents the firm's business capabilities. The proposed method comprises four steps: 1) Constructing firm technology and business capability matrices using patent classification codes and trademark similarity group codes; 2) Transforming the capability matrices to preference matrices using the fuzzy function; 3) Identifying a target firm’s candidate technology opportunities using the collaborative filtering algorithm; 4) Recommending technology opportunities using a portfolio map constructed based on technology similarity and applicability indices. A case study is conducted on a security firm to determine the validity of the proposed method. The proposed method can assist SMEs that face resource constraints in identifying technology opportunities. Further, it can be used by firms that do not possess patents since the proposed method uncovers technology opportunities based on business capabilities.