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Approximations of pythagorean fuzzy sets over dual universes by soft binary relations

 Yager introduced the Pythagorean Fuzzy Set (PFS) to deal with uncertainty in real-world decision-making problems. Binary relations play an important role in mathematics as well as in information sciences. Soft binary relations give us a parameterized collection of binary relations. In this paper, lower and upper approximations of PFSs based on Soft binary relations are given with respect to the aftersets and with respect to the foresets. Further, two kinds of Pythagorean Fuzzy Topologies induced by Soft reflexive relations are investigated and an accuracy measure of a PFS is provided. Besides, based on the score function and these approximations of PFSs, an algorithm is constructed for ranking and selection of the decision-making alternatives. Although many MCDM (multiple criteria decision making) methods for PFSs have been proposed in previous studies, some of those cannot solve when a person is encountered with a two-sided matching MCDM problem. The proposed method is new in the literature. This newly proposed model solved the problem more accurately. The proposed method focuses on selecting and ranking from a set of feasible alternatives depending on the two-sided matching of attributes and determines a ranking based solution for a problem with conflicting criteria to help the decision-maker in reaching a final course of action.