Algebraic structures of q-rung orthopair fuzzy relations with applications in decision-making

Uncertainty is an essential factor in any decision-making process. A q-rung orthopair fuzzy set (q-ROFS) is more practical and robust than a fuzzy set (FS), intuitionistic fuzzy set (IFS), and Pythagorean fuzzy set (PFS) to describe uncertainty in numerous decision-making issues. The most attractive aspect of q‐ROFSs is that they provide a wider space for membership and non-membership degrees and provide decision-makers more liberty in expressing their legitimate opinions. This study introduces the conception of q-rung orthopair fuzzy relation (q-ROFR), which will help to remove certain limitations associated with intuitionistic fuzzy relation (IFR) and Pythagorean fuzzy relation (PFR). Some basic operations in this regard are given for q-ROFRs. The set of all q-ROFRs leads to several algebraic structures for these operations (semi-group, semi-ring, hemi-ring, and bounded distributive lattice). Additionally, an application of the designed approach is proposed for predicting scores in cricket. Moreover, the comparative analysis of the proposed method with some existing techniques is also presented by giving several examples to authenticate the feasibility and superiority of the proposed approach.