This study proposes a new perspective of the TOPSIS and VIKOR methods using the recently introduced spherical fuzzy sets (SFSs) to handle the vagueness in subjective data and the uncertainties in objective data simultaneously. When implementing these techniques using SFSs, two main problems might arise that can lead to incorrect results. Firstly, the reference points might change with the utilized score function. Secondly, the distance between reference points might not be the largest, as known, among the available ratings. To overcome these deficiencies and increase the robustness of these two methods, they are implemented without utilizing any reference points to minimize the effect of defuzzification and without measuring the distance to eliminate the effect of distance formulas. In the proposed methods, when using an SFS to express the performance of an alternative for a criterion, this SFS per se can be viewed as a measure of proximity to the aspired level. On the other hand, the conjugate of the SFS can be viewed as a measure of proximity to the ineffectual level. Two practical applications are presented to demonstrate the proposed techniques. The first example handles a warehouse location selection problem. The second example evaluates hydrogen storage systems for automobiles with different types of data (crisp, linguistic variables, type 1 fuzzy sets). These data are transformed to SFSs to provide a more comprehensive analysis. A comparative study is conducted with earlier versions of TOPSIS and VIKOR to explicate the adequacy of the proposed methods and the consistency of the results.

Spherical fuzzy sets (SFSs) were recently introduced to reflect experts’ judgements explicitly and in a more informative manner. TOmada de Decisão Interativa e Multicritério (TODIM) is one of the multi-criteria decision-making techniques. It is founded on the prospect theory that considers the decision-makers psychological behaviours under risk. In this article, TODIM is extended using the novel concept of SFSs to exploit its superior features to incorporate a new point of view in fuzzy decision-making under risk, allowing the decision-makers to express their hesitation independently. To establish the TODIM strategy, two evaluation functions are employed to form the partial dominance degree matrices: the importance evaluation function and the performance evaluation function. A practical example in supplier selection is solved, and a case study on selecting green occupational health and safety (OHS) equipment supplier is given. The results are compared with the results of the spherical fuzzy Technique of Order Preference by Similarity to an Ideal Solution (SF-TOPSIS) and the spherical fuzzy VIsekriterijumska optimizacija i KOmpromisno Resenje (SF-VIKOR). The effect of the attenuation factor of losses on the solution is examined. Finally, a different implementation of the SF-TODIM is used and the processing time of the two implementations is compared.