Human activity recognition (HAR) is the process of interpreting human activities with the help of electronic devices such as computer and machine version technology. Humans can be explained or clarified as gestures, behavior, and activities that are recorded by sensors. In this manuscript, we concentrate on studying the problem of HAR; for this, we use the proposed theory of Aczel and Alsina, such as Aczel–Alsina (AA) norms, and the derived theory of Choquet, such as the Choquet integral in the presence of Atanassov interval-valued intuitionistic fuzzy (AIVIF) set theory for evaluating the novel concept of AIVIF Choquet integral AA averaging (AIVIFC-IAAA), AIVIF Choquet integral AA ordered averaging (AIVIFC-IAAOA), AIVIF Choquet integral AA hybrid averaging (AIVIFC-IAAHA), AIVIF Choquet integral AA geometric (AIVIFC-IAAG), AIVIF Choquet integral AA ordered geometric (AIVIFC-IAAOG), and AIVIF Choquet integral AA hybrid geometric (AIVIFC-IAAHG) operators. Many essential characteristics of the presented techniques are shown, and we also identify their properties with some results. Additionally, we take advantage of the above techniques to produce a technique to evaluate the HAR multiattribute decision-making complications. We derive a functional model for HAR problems to justify the evaluated approaches and to demonstrate their supremacy and practicality. Finally, we conduct a comparison between the proposed and prevailing techniques for the legitimacy of the invented methodologies.

This paper presents a nonlinear physical model called the (2+1)-dimensional Zomeron equation, which is one of the equations that describes latent evolution. We apply the Power Index Method (PIM) to find analytical solutions of equations using function transformations with optimal indexing of one variable. After selecting index of the variable, then we adopt function transform of another variable that make sure all coefficient terms to change in new variable. PIM is a straightforward mathematical technique in which the indices of the independent variables are adjusted to our selected similarity transformations to effectively reduce the partial differential equation to an Ordinary Differential Equation (ODE). Several exact solutions of the nonlinear Zoumron equation have been built and are presented graphically for some values of the constant parameters. The proposed method has been effectively used to find new exact solutions of nonlinear PDE. Using these transforms, we can easily produce infinitesimal generators of the PDE.