In this paper, on the basis of the three-dimensional Chen system, a smooth continuous nonlinear flux-controlled memristor model is used as the positive feedback term of this system, a hyper-chaotic circuit system is successfully constructed, and a simulated equivalent circuit is built for simulation using Multisim software, which agrees with the numerical simulation results by comparison. Meanwhile, a new impulsive control mode called the three-stage-impulse is put forward. It is a cyclic system with three components: continuous inputs are exerted in the first and third parts of the cycle while giving no input in the second part of the cycle, an impulse is exerted at the end of each continuous subsystem, the controller is simple in structure and effective in stabilizing most existing nonlinear systems. The Chen hyper-chaotic system will be controlled based on the three-stage-impulse control method combined with the Lyapunov stability principle. At the end of this paper, we have employed and simulated a numerical example; the experimental results show that the controller is effective for controlling and stabilizing the newly designed hyper-chaotic system.

The process of computing correlation among attributes of an ordinary database is significant in the analysis and classification of a data set. Due to the uncertainties embedded in data classification, encapsulating correlation techniques using Pythagorean fuzzy information is appropriate to curb the uncertainties. Although correlation coefficient between Pythagorean fuzzy data (PFD) is an applicable information measure, its output is not reliable because of the intrinsic effect of other interfering PFD. Due to the fact that the correlation coefficients in a Pythagorean fuzzy environment could not remove the intrinsic effect of the interfering PFD, the notion of Pythagorean fuzzy partial correlation measure (PFPCM) is necessary to enhance the measure of precise correlation between PFD. Because of the flexibility of Pythagorean fuzzy sets (PFSs), we are motivated to initiate the study on Pythagorean fuzzy partial correlation coefficient (PFPCC) based on a modified Pythagorean fuzzy correlation measure (PFCM). Examples are given to authenticate the choice of the modified PFCM in the computational process of PFPCC. For application, we discuss a case of pattern recognition and classification using the proposed PFPCC after computing the simple correlation coefficient between the patterns based on the modified correlation technique. To be precise, the contributions of the work include the enhancement of an existing PFCC approach, development of PFPCC using the enhanced PFCC, and the application of the developed PFPCC in pattern recognition and classifications.

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