Application of optimistic multi-granulation rough bipolar Pythagorean fuzzy set

Abstract This paper introduces the concept of optimistic multi-granulation rough bipolar Pythagorean fuzzy sets (OMRBPFSs) and their basic properties. OMRBPFSs are presented as an extension of different hybrid models, including rough fuzzy sets, rough bipolar fuzzy sets, rough intuitionistic fuzzy sets, and rough bipolar intuitionistic fuzzy sets. This generalization allows us greater flexibility in expressing uncertainty. OMRBPFSs enhances decision-making by offering a more adaptable representation of uncertainty and preferences. The concepts we introduced are illustrated through examples, highlighting the key properties and operations of the hybrid models. Furthermore, two algorithms are presented, focusing on aftersets and foresets.