Decision-Making Based on q-Rung Orthopair Fuzzy Soft Rough Sets

Recently, Yager presented the new concept of q-rung orthopair fuzzy (q-ROF) set (q-ROFS) which emerged as the most significant generalization of Pythagorean fuzzy set (PFS). From the analysis of q-ROFS, it is clear that the rung q is the most significant feature of this notion. When the rung q increases, the orthopair adjusts in the boundary range which is needed. Thus, the input range of q-ROFS is more flexible, resilient, and suitable than the intuitionistic fuzzy set (IFS) and PFS. The aim of this manuscript is to investigate the hybrid concept of soft set ( S) and rough set with the notion of q-ROFS to obtain the new notion of q-ROF soft rough (q-ROF R) set (q-ROF RS). In addition, some averaging aggregation operators such as q-ROF R weighted averaging (q-ROF RWA), q-ROF R ordered weighted averaging (q-ROF ROWA), and q-ROF R hybrid averaging (q-ROF RHA) operators are presented. Then, the basic desirable properties of these investigated averaging operators are discussed in detail. Moreover, we investigated the geometric aggregation operators, such as q-ROF R weighted geometric (q-ROF RWG), q-ROF R ordered weighted geometric (q-ROF ROWG), and q-ROF R hybrid geometric (q-ROF RHG) operators, and proposed the basic desirable characteristics of the investigated geometric operators. The technique for multicriteria decision-making (MCDM) and the stepwise algorithm for decision-making by utilizing the proposed approaches are demonstrated clearly. Finally, a numerical example for the developed approach is presented and a comparative study of the investigated models with some existing methods is brought to light in detail which shows that the initiated models are more effective and useful than the existing methodologies.