The correlation coefficient between two variables is an important aspect of statistics. The accuracy of assessments of correlation relies on information from a set of discourses. Data collected in statistical studies are often full of exceptions. Pythagorean fuzzy soft sets (PFSS) are a parametrized family of extended Pythagorean fuzzy sets (PFS). They comprise a generalization of intuitionistic fuzzy soft sets which may be used to accurately assess deficiencies and uncertainties in evaluations. PFSS can accommodate uncertainty more competently than intuitionistic fuzzy soft sets and are the most important strategy when dealing with fuzzy information in decision-making processes. Herein, the concept and characteristics of correlation coefficients and the weighted correlation coefficients in PFSS are discussed. We also introduce the Pythagorean fuzzy soft weighted average (PFSWA) and Pythagorean fuzzy soft weighted geometric (PFSWG) operators and discuss their desirable characteristics. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) under the PFSS environment based on correlation coefficients and weighted correlation coefficients will be introduced. Through the proposed methodology, a technique for decision-making is developed. Additionally, an application of the proposed TOPSIS technique is presented for green supplier selection in green supply chain management (GSCM). The practicality, efficacy, and flexibility of the proposed approach is proved through comparative analyses, drawing upon existing studies.

The Pythagorean fuzzy soft sets (PFSS) is a parametrized family and one of the appropriate extensions of the Pythagorean fuzzy sets (PFS). It’s also a generalization of intuitionistic fuzzy soft sets, used to accurately assess deficiencies, uncertainties, and anxiety in evaluation. The most important advantage of PFSS over existing sets is that the PFS family is considered a parametric tool. The PFSS can accommodate more uncertainty comparative to the intuitionistic fuzzy soft sets, this is the most important strategy to explain fuzzy information in the decision-making process. The main objective of the present research is to progress some operational laws along with their corresponding aggregation operators in a Pythagorean fuzzy soft environment. In this article, we introduce Pythagorean fuzzy soft weighted averaging (PFSWA) and Pythagorean fuzzy soft weighted geometric (PFSWG) operators and discuss their desirable characteristics. Also, develop a decision-making technique based on the proposed operators. Through the developed methodology, a technique for solving decision-making concerns is planned. Moreover, an application of the projected methods is presented for green supplier selection in green supply chain management (GSCM). A comparative analysis with the advantages, effectiveness, flexibility, and numerous existing studies demonstrates the effectiveness of this method.

Nanofluids have unique features that make them potentially valuable in a variety of medicinal, technical, and industrial sectors. The widespread applications of nanotechnology in modern science have prompted researchers to study nanofluid models from different perspectives. The objective of the current research is to study the flow of non-Newtonian nanofluid over an inclined stretching surface immersed in porous media by employing the Darcy–Forchheimer model. Both titanium oxide ($Ti{O}_2$) and aluminum oxide ($A{l}_2{O}_3$) are nanoparticles which can be found in blood (based fluid). The consequences of viscous dissipation, thermal radiations, and heat generation are also incorporated. Boundary layer approximations are employed to model the governing system of partial differential equations (PDEs). The governing PDEs with their associated boundary conditions are further altered to a dimensionless form by employing appropriate transformations. The results of the transformed model are collected using local non-similarity approach up to the second level of truncation in association with the built-in finite difference code in MATLAB (bvp4c). Additionally, the impacts of emerging factors on the fluid flow and thermal transport features of the considered flow problem are displayed and analyzed in graphical forms after achieving good agreement between accomplished computational results and published ones. Numerical variations in drag coefficient and Nusselt number are elaborated through the tables. It has been perceived that the enhancement in Casson fluid parameter diminishes the velocity profile. Moreover, it is noted that the porosity parameter and Lorentz’s forces reinforce the resulting frictional factor at the inclined stretching surface.

The correlation coefficient between the two parameters plays a significant part in statistics. Furthermore, the exactness of the assessment of correlation depends upon information from the set of discourses. The data collected for various statistical studies are full of ambiguities. The idea of interval-valued intuitionistic fuzzy soft sets is an extension of intuitionistic fuzzy soft sets that is used to express insufficient evaluation, uncertainty, and anxiety in decision-making. Intuitionistic fuzzy soft sets consider two different types of information, such as membership degree and nonmembership degree. In this paper, the concepts and properties of the correlation coefficient and the weighted correlation coefficient of interval-valued intuitionistic fuzzy soft sets are proposed. A prioritization technique for order preference by similarity to the ideal solution based on interval-valued intuitionistic fuzzy soft sets of correlation coefficients and the weighted correlation coefficient is introduced. We also proposed interval-valued intuitionistic fuzzy soft weighted average and interval-valued intuitionistic fuzzy soft weighted geometric operators and developed decision-making techniques based on the proposed operators. By using the developed techniques, a method for solving decision-making problems is proposed. To ensure the applicability of the proposed methods, an illustrative example is given. Finally, we present a comparison of some existing methods with our proposed techniques.

The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow. The flow is initiated by the stretching of a sheet at an exponential rate in the upward vertical direction. The buoyancy effects in terms of temperature and concentration differences are inserted in the x -momentum equation. The aspects of heat and mass transfer are studied using dimensionless thermophoresis, Schmidt and Brownian motion parameters. The governing coupled partial differential system (PDEs) is remodeled into coupled non-similar nonlinear PDEs by introducing non-similar transformations. The numerical analysis for the dimensionless non-similar partial differential system is performed using a local non-similarity method via bvp4c. Finally, the quantitative effects of emerging dimensionless quantities on the non-dimensional velocity, temperature and mass concentration in the boundary layer are conferred graphically, and inferences are drawn that important quantities of interest are substantially affected by these parameters. It is concluded that non-similar modeling, in contrast to similar models, is more general and more accurate in convection studies in the presence of buoyancy effects for second-grade non-Newtonian fluids.