This paper proposes the modeling and simulation of a single-phase matrix converter as a converter for domestic AC induction heating applications. In this paper, a single-phase matrix converter employing IGBT-based bi-directional switches is used for this purpose. The technique employed to generate the pulses for the matrix converter is Fuzzy Logic, which is illustrated in detail. The performance and content analysis of the single-phase matrix converter have been carried out in MATLAB/SIMULINK, and the results have been successfully verified. Additionally, the working principle and control strategy of the Fuzzy Logic-based matrix converter are explained in detail.