The fusion of information is a very hectic process whenever we analyze the information. Several frameworks have been introduced to reduce the uncertainty while fusing the information. Among those techniques, the Pythagorean fuzzy rough set (PyFRS), which is based on approximations is a key idea for dealing with uncertainty when data is taken from real-world circumstances. Furthermore, the most adaptable and flexible operational laws based on the parameters for fuzzy frameworks are Aczel-Alsina t-norm (AATNM) and Aczel-Alsina t-conorm (AATCNM). The major goal of this work is to introduce some methods for the basic operations of the information in the shape of Pythagorean fuzzy rough (PyFR) values (PyFRVs). Consequently, the PyFR Aczel-Alsina weighted geometric (PyFRAAWG), PyFR Aczel-Alsina ordered weighted geometric (PyFRAAOWG), and PyFR Aczel-Alsina hybrid weighted geometric (PyFRAAHWG) operators are developed in this article based on AATNM and AATCNM. Further, some basic properties of the developed operators are observed and discussed. Further, the developed approaches are applied to the problem of multi-attribute group decision-making (MAGDM). The obtained results from the MAGDM problem are observed at various values of the parameters involved by AATNM and AATCNM. Moreover, the results are also compared with already existing techniques for the significance of the developed approach.

In order to systematically explore the impact of rising intellectual property rights protection on the driving effects that knowledge spillover exerts on knowledge transfer performance in China’s manufacturing industries, this paper constructs an improved dynamic threshold model with the level of intellectual property rights protection as a threshold variable. The results show that when the level of intellectual property rights protection crosses one of the two thresholds in turn, the driving effect first experiences a rise and then drops sharply, reflecting a significant double threshold feature; the driving effect exhibits the characteristic of spatiotemporal heterogeneity; compared with research and development (R&D) investments, R&D personnel input can more significantly enhance knowledge transfer performance.