Abstract
The aim of this paper is to introduce the concepts of soft rough q-rung orthopair fuzzy set (SRqROFS) and q-rung orthopair fuzzy soft rough set (gROPFSRS) based on soft rough set and fuzzy soft relation, respectively. We define some fundamental operations on both SRqROFS and qROPFSRS and discuss some key properties of these models by using upper and lower approximation operators. The suggested models are superior than existing soft rough sets, intuitionistic fuzzy soft rough sets and Pythagorean fuzzy soft rough sets. These models are more efficient to deal with vagueness in multi-criteria decision-making (MCDM) problems. We develop Algorithm i (i = 1, 2, 3, 4, 5) for the construction of SRqROFS, construction of qROFSRS, selection of a smart phone, ranking of beautiful public parks, and ranking of government challenges, respectively. The notions of upper reduct and lower reduct based on the upper approximations and lower approximations by variation of the decision attributes are also proposed. The applications of the proposed MCDM methods are demonstrated by respective numerical examples. The idea of core is used to find a unanimous optimal decision which is obtained by taking the intersection of all lower reducts and upper reducts.