This study addresses the effectiveness of employing the Core Stabilization Method (CSM) in the pursuit of high-efficiency klystron design. Through simulations and design considerations, the suitability of CSM as a technique for achieving high efficiency is rigorously assessed. Initially, simulations were conducted on a 1 GHz klystron design to evaluate the efficiency of CSM in a 2.5D simulations compared to 1D simulations. Subsequently, AJDisk 1D simulations were employed to investigate the impact of the gap coupling factor (M) on minimizing electron crossovers, observed through Applegate diagrams. Adjustments to the gap coupling factors were made to enhance minimal electron crossovers and, consequently, efficiency. Magic 2D simulations were then performed on 800 MHz CSM 23 klystron preceding the gap coupling optimisation, yielding notable efficiency improvements. Furthermore, a novel fuzzy logic method is introduced, demonstrating its usefulness in expediting klystron optimization for 1/1.5D simulations and markedly reducing the optimisation time compared to conventional methods. The results show the potential of CSM and fuzzy logic optimization in enhancing klystron efficiency, augmented by the time saving gains facilitated by the fuzzy logic optimization approach.