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• An auxiliary algorithm is proposed to construct initial stage of the MCDM methods. • A multi-objective fuzzy optimization model is formulated. • An extensive comparative analysis is conducted in terms of the addressed methods. • The stability and validity of the results are tested and discussed. • Key findings and managerial insights are provided. This paper examines the performances of the multi-criteria decision-making (MCDM) methods and optimization model in solving multi-attribute shortest path problems such as the safest shortest path under a fuzzy environment. To the best of the knowledge of the authors, this is the first study performing comparative analysis on finding the multi-attribute shortest path by employing well-known techniques in terms of computational effort and results in a fuzzy environment. To this end, the safest shortest path problem, where the risk and distance values concerning arcs on a directed network are defined as triangular fuzzy numbers, is handled. The solution process is carried out under two main headings: (i) To start the solution with MCDM methods, an auxiliary algorithm that constructs a fuzzy decision matrix is proposed. Then, Fuzzy-Technique for Order Preference by Similarity to Ideal Solution (F-TOPSIS), Fuzzy Simple Additive Weighting (F-SAW), and Fuzzy Evaluation Based on Distance from Average Solution (F-EDAS), that are fuzzy-based MCDM methods, are employed to rank the alternative paths. (ii) A multi-objective fuzzy optimization model is formulated, and the most reasonable paths are obtained considering different α-cut levels. Following that, comparative analysis is performed through a set of scenarios considering the different weights of the criteria to see the variability in the rankings. Besides, the addressed fuzzy-based MCDM methods are compared in terms of computational complexity. Overall, the main findings and managerial insights regarding the effectiveness and performance of the methods discussed in the solution process are provided. [ABSTRACT FROM AUTHOR]