Bidirectional normalized q-rung orthopair fuzzy projectionand extended TOPSIS approach to multiattribute group decision making

q-rung orthopair fuzzy sets (q-ROFSs), as a generalization of intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets(PFSs), can depict uncertain attitudes more flexibly and bear decision information more extensively. Innumerable fuzzy assessment verdicts that exceed IFSs or PFSs can be captured by q-ROFSs. To make the evaluation process more adaptive,in this article, we explore the application of q-ROFSs to multi attribute group decision making (MAGDM) by employing the technique for order preference by similarity to ideal solution (TOPSIS) approach. In view of the comprehensive tool of projection method for measuring the proximity of decision vectors, we further propose innovative bidirectional normalized projection measures that consider not only distance but also spatial angle to replace traditional distance measures such as Hamming and Euclidean. A new extension of TOPSIS methodology is then addressed in the context of MAGDM with q-ROFSs, which eliminates the transformation and aggregation steps to ensure less information loss. At length, the effectiveness and superiority of the proposed framework are demonstrated by an example of ship equipment reliability evaluation with comparative analysis, and future research directions are also suggested.