Pythagorean Fuzzy Multigranulation Rough Set over Two Universes and Its Applications in Merger and Acquisition

AbstractPythagorean fuzzy set, an extension form of intuitionistic fuzzy set, which owns many advantages for dealing with uncertainties, and it has been developed to deal with various complex decision-making problems. Furthermore, based on lower and upper approximations induced by multiple binary relations, the multigranulation rough set has become one of the most promising directions in rough set theory. To combine the two ideas and explore the practical decision-making problems, we develop a new multigranulation rough set model, called Pythagorean fuzzy multigranulation rough set over two universes. In the framework of our study, we introduce the models of Pythagorean fuzzy rough set over two universes and Pythagorean fuzzy multigranulation rough set over two universes, respectively. Both the definition and basic properties are explored. Finally, we give a general algorithm, which is applied to a decision-making problem in merger and acquisition, and the effectiveness of the algorithm is demonstrated by a numerical example.