Fuzzy multi-criteria acceptability analysis: A new approach to multi-criteria decision analysis under fuzzy environment

•New MCDA approach under fuzzy contexts implements acceptability analysis concept.•Fuzzy Rank Acceptability Analysis gives a ranking and a confidence degree about it.•A fuzzy extension of MAVT method within the FMAA is implemented.•The study of the overestimation problem with fuzzy arithmetic is studied and fixed. Uncertainty is one of the main difficulties that increases the complexity of multi-criteria decision analysis (MCDA) problems, and often uncertainty cannot be managed by probabilistic models. In such cases, the use of fuzzy methods has been successfully applied to multi-criteria decision methods in which the ranking of fuzzy quantities is crucial for the decision analysis. This paper aims to introduce a new approach to MCDA problems defined under fuzzy contexts that implements the concept of acceptability analysis, Fuzzy Multi-Criteria Acceptability Analysis (FMAA), based on the Fuzzy Rank Acceptability Analysis (FRAA), that provides a ranking and a confidence degree about the ranking of fuzzy quantities. Based on the fuzzy extension of MAVT method, the FMAA is implemented and then applied to a case study, and its results are compared with other well-known MCDA methods in order to show its validity, interpretability and consistency.