A three-way decision approach with S-shaped utility function under Pythagorean fuzzy information

• Provide a new perspective for three-way decision-making model. • Construct a new condition probability for the three-way decision. • Conduct a new way to measure action utility function and risk based on S-shaped utility. • Develop a Pythagorean fuzzy three-way decision model based on utility function. Three-way decision, as opposed to conventional two-way decision-making, can more effectively reduce decision-making risks by adding a postponed decision-making. With respect to the three-way decision problem consisting of Pythagorean fuzzy information, considering the risk attitudes of decision makers(DMs), we exploit Pythagorean fuzzy sets (PFNs), S-shaped utility and three-way decision to establish a new Pythagorean three-way decision model. The model realizes the effective integration of Pythagorean fuzzy theory and three-way decision, and enriches three-way decision based on risk preference. Firstly, we define a new PFN score function and construct a new condition probability by using Pythagorean fuzzy similarity, which not only reflects the difference in distance but conforms to human cognitive habits. Subsequently, considering the impact of the changes in risk preferences on the measurement of decision risks, we define an action utility function and construct the gain and loss matrix function based on S-shaped utility function, calculate the thresholds by employing optimization formulation. According to key steps and algorithm, the Pythagorean fuzzy three-way decision rules based on S-shaped utility function can be obtained. Finally, we utilize an example of selecting film projects to validate the interpretability and applicability of our proposed model.