A numerical investigation of three-dimensional hybrid nanomaterial micropolar fluid flow across an exponentially stretched sheet is performed. Recognized similarity transformations are adopted to convert governing equations from PDEs into the set ODEs. The dimensionless system is settled by the operating numerical approach bvp4c. The impacts of the nanoparticle volume fraction, dimensionless viscosity ratio, stretching ratio parameter, and dimensionless constant on fluid velocity, micropolar angular velocity, fluid temperature, and skin friction coefficient in both x-direction and y-direction are inspected. Graphical outcomes are shown to predict the features of the concerned parameters into the current problem. These results are vital in the future in the branches of technology and industry. The micropolar function  Rη increases for higher values of the micropolar parameter and nanoparticle concentration. Micropolar function Rη declines for higher values of the micropolar parameter and nanoparticle concentration. Temperature function is enhanced for higher values of solid nanoparticle concentration. Temperature function declines for higher values of the micropolar parameter. The range of the physical parameters are presented as: 0.005<ϕ2<0.09, Pr=6.2, 0<K<2, 0<a<2.0, ϕ1=0.1, and 0<c<1.5.

Soft set theory is a good tool to deal with uncertain problems. The study of reduction problem is an important part of soft set theory. Different decision-making criteria lead to different reduction methods. In this paper, the problem of parameter reduction of soft sets is studied based on the score decision criteria. Four cases of dispensable sets are discussed in parameter reduction. Then, a newly parameter reduction method is proposed. Finally, a comparison is shown between the new proposed parameter reduction method and the previous parameter reduction method based on the choice value decision criteria, and remarks are given.

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