A robust Pythagorean fuzzy OPARA decision making approach for evaluating hybrid machine translation in language education

The application of hybrid machine translation systems has become more and more crucial in language education in order to assist multilingual communication, language learning, and delivery of educational content. However, finding the most suitable hybrid machine translation system is a complex multi-criteria decision-making (MCDM) problem, because there are many conflicting evaluation criteria and uncertainty in expert evaluations. Current MCDM methods are generally based on normalization procedures, which may alter the original information of the decision and make the ranking less reliable. To overcome these drawbacks, this research proposes a Pythagorean fuzzy objective pairwise-adjusted ratio analysis (PyF-OPARA) MCDM method for evaluating hybrid machine translation systems in language education. The proposed approach combines Pythagorean fuzzy sets (PyFS) and the OPARA methodology to handle uncertain expert judgments while preserving the original properties of the evaluation data via a normalization-free pairwise-adjusted-ratio mechanism. Three typical machine translation systems are considered as a case study and evaluated with three evaluation criteria. Computational results demonstrate the feasibility and usefulness of the proposed approach for obtaining a consistent ranking of competing alternatives, with the Hybrid Neural Translator being the most appropriate system. In addition, sensitivity analysis results show the stability of the proposed approach in rankings across various parameter values, and comparisons with existing MCDM approaches indicate that the proposed approach exhibits greater ability to handle uncertainty, preserve information, and achieve stable rankings. The PyF-OPARA framework is an effective decision-support tool for evaluating educational technology and can be applied to other complex decisions with uncertain information, which could be expanded.