The increasing reliance on fossil fuels and the consequent surge in harmful emissions have stimulated widespread investigation into alternative fuel options. As a response to these challenges, natural gas has emerged as a comparatively cleaner and ecologically substitute for energy. This research paper focuses on the cost-effectiveness of transmitting natural gas through pipeline networks. It includes three case studies from previous work with different network topologies: linear, branch, and cyclic. The innovative network optimization techniques involve the integration of the General Algebraic Modeling System (GAMS) and the fuzzy multi-criteria decision analysis technique (FMCDA) in the research. GAMS is employed to determine the optimal pipe diameters and compressor locations, considering specific constraints such as flow rate, pressure range, and pipe length. On the other hand, FMCDA is utilized to identify the most efficient solution scheme by considering objectives such as maximizing line pack, minimizing compressor power, and reducing fuel consumption. The research shows that optimized models can determine the optimal objective function for natural gas pipeline networks, leading to cost reduction. For example, a linear topology with a flow rate of 17 MMSCMD and a pipe with an optimum diameter of 36 inches reduced the total cost to $292 million per year. The branched topology, with the same flow rate but with a shorter length, required less power so the cost was reduced to $78 million per year. While the cyclic topology, with a higher flow rate of 28 MMSCMD, required more power, achieving a total cost of 327 million dollars per year.