This paper presents highly robust, novel approaches to solving the forward and inverse problems of an Electrical Capacitance Tomography (ECT) system for imaging conductive materials. ECT is one of the standard tomography techniques for industrial imaging. An ECT technique is nonintrusive and rapid and requires a low burden cost. However, the ECT system still suffers from a soft-field problem which adversely affects the quality of the reconstructed images. Although many image reconstruction algorithms have been developed, still the generated images are inaccurate and poor. In this work, the Capacitance Artificial Neural Network (CANN) system is presented as a solver for the forward problem to calculate the estimated capacitance measurements. Moreover, the Metal Filled Fuzzy System (MFFS) is proposed as a solver for the inverse problem to construct the metal images. To assess the proposed approaches, we conducted extensive experiments on image metal distributions in the lost foam casting (LFC) process to light the reliability of the system and its efficiency. The experimental results showed that the system is sensible and superior.