Already faced with tight competition and low profit margins, the airline industry is going through major changes in the wake of the current pandemic resulting in travel restrictions and slump demands, prompting airlines to curtail services and investments in every aspect of business. To that end, developing a comprehensive method of improving airline performance measures is crucial. However, this type of problem is complex to solve due to a large number of factors, requiring a systematic approach. It entails taking into account a multitude of conflicting, or sometimes interrelated criteria, hence becoming an inherently multiple criteria decision making problem. This study is aimed to assess the competitiveness of airlines and evaluate their financial and operational performances in relation to such criteria. We test FAHP, TOPSIS, and a hybrid method of combining FAHP and TOPSIS methods. In particular, regarding the hybrid method, FAHP is employed to determine the influential weights of criteria that are utilized in TOPSIS for preference values among alternatives. We demonstrate the applicability of the proposed methods to solving a MCDM problem of airline performance assessments using real data sets. Further, this study focuses on examining the relationship between financial and operational performance criteria, as well as gleaning insights for airlines to build an evaluation system that would aid in understanding their strength and weakness in the performance metrics. The computational experiment results of our hybrid FAHP-TOPSIS model support the efficacy of incorporating fuzzy values concerning influential weight criteria. By judiciously distributing criteria weights that are specific to the airline industry, our proposed model captures preference scores reflective of industry-related and concurrent measures. This modeling framework can help airlines better evaluate the systematic influential relation structure among criteria in critical financial and operational dimensions.