While fuel cell combined with hydrogen (FCH) technology is still largely in its infancy striving to find its footing, the present market stage towards commercialisation is bridged by the pervasive research and development (R&D) and innovation. Providing spare parts and auxiliary components of the FCH systems plays a significant role in advancing the process. For the successful transition, an optimal supplier selection function can flourish the long-term research, and further, address the lack of technological knowledge to manufacture high performance and affordable components. This paper presents an integrated approach based on entropy, Step-wise Weight Assessment Ratio Analysis (SWARA) and Complex Proportional assessment (COPRAS) methods under the Pythagorean fuzzy environment for the FCH supplier selection. In this method, the criteria weights were first calculated by combining the objective weights determined by the entropy-based approach and the subjective weights by the SWARA method. For this purpose, a new entropy measure was proposed through the Pythagorean fuzzy set as one of the new flexible tools to handle the uncertain and inaccurate information arisen in complex MCDM problems. An integrated approach developed in this study can overcome the insufficiencies which arise either in an objective-weighting model or a subjective-weighting model. COPRAS was then utilised to evaluate the ranking order of the alternatives. A real-world case study of the FCH components supplier selection problem was considered to implement the proposed integrated approach. Finally, a comparison and sensitivity analysis were discussed to illustrate the usefulness of the proposed method.