Three-way concept lattices triggered by Pythagorean fuzzy set and interval set

Three-way concept lattices offer a robust and flexible framework for analyzing complex data and understanding relationships and patterns within datasets. Their ability to handle uncertainty and ambiguity makes them a valuable tool in various applications involving data analysis and knowledge extraction. However, objects values, attributes values and the relationships between objects and attributes in information system, may lack specificity or even be missing. Managing imprecise and ambiguous data is crucial as it mirrors real-world complexities and aligns with realistic decision-making. To address this, we use Pythagorean fuzzy set to accurately depict the uncertain relations between objects and attributes in an information system, and interval set to describe the values of objects and attributes. Additionally, we construct Pythagorean fuzzy three-way interval set concept lattices model to acquire important knowledge. The investigation into the properties of the proposed model reveals that the extension set and the intension set of the Pythagorean fuzzy interval set concept lattices encompass those of existing Pythagorean fuzzy concept lattices, and the proposed model offers finer concept lattices with richer information compared to other existing concept lattices. Finally, a real-life example is provided to showcase the effectiveness and advantages of our proposed model.