New entropy propositions for interval-valued spherical fuzzy sets and their usage in an extension of ARAS (ARAS-IVSFS)

The spherical fuzzy set (SFS) concept and its interval-valued version (IVSFS) are among the recent developments aiming at handling the hesitancy representation issue in multiple attribute decision-making problems. In SFS, decision-makers can assign independent membership, non-membership, and hesitancy degrees. IVSFS extends this feature by assigning intervals to these three degrees. In this manner, the uncertainty, vagueness, and ambiguity hidden in human judgements can be quantified and processed more comprehensively. In multiple attribute decision-making problems, the attribute weights are not commonly known. To determine these weights, there are two families of methods: subjective and objective ones. While subjective methods need expert judgements in weighting, objective methods can reveal the weights from the current dataset. Entropy-based weighting technique is one of the well-known objective methods. In the study, two IVSFS entropy expressions are introduced, and their practicality is presented in obtaining objective weights. Then, an IVSFS extension of Additive Ratio Assessment Method is proposed and integrated with the entropy-based weighting schema. The proposition is applied in solving a 3D printer selection problem and a comparative analysis is conducted to check its robustness and validity.