This paper introduces a mathematical framework designed to model and evaluate natural gas pipeline networks with hydrogen infusion. Initially focusing on natural gas conveyance, the model is later expanded to accommodate hydrogen-natural gas blends. The optimization process is structured using a nonlinear approach within the General Algebraic Modelling System (GAMS) and fuzzy multi-criteria decision making (FMCDM). The research investigates the adaptation of current natural gas transmission networks to enable the conveyance of hydrogen-natural gas mixtures. Motivated by proposals to integrate renewable hydrogen into existing natural gas pipeline systems, the study aims to reduce dependency on fossil fuels within energy systems. The primary results highlight that a 1% hydrogen infusion yields the lowest cost (112 M$/year).