Conflict distance-based variable precision Pythagorean fuzzy rough set in Pythagorean fuzzy decision systems with applications in decision making

Real-life decision-making problems are hard to handle by any single uncertainty method because of the complex and uncertain nature of the physical world and the human limitations in understanding it. Therefore, we naturally consider combining the benefits of various uncertainty theories to create a more effective hybrid soft decision-making method. Based on this idea, we use the variable precision rough sets (VPRSs) and Pythagorean fuzzy sets approach to build a new Pythagorean fuzzy rough set (PFRS) model. Since the information system is Pythagorean fuzzy, we use the Pythagorean fuzzy similarity measure to define the new type of distance based on conflict. Then, we merge this notion with the VPRSs to form a variable precision PFRS model and study its properties. We also propose an algorithm for attribute reduction based on this model and apply it to a case study to test its feasibility and performance. The results demonstrate that our model enhances the classification capability of previous models, and it achieves accurate classification by deriving the decision rules.