The concept of interval-valued intuitionistic fuzzy sets is intellectually stimulating and holds significant utility in the representation and analysis of real-world problems. The development of similarity measures within the class of interval-valued intuitionistic fuzzy sets possesses significant importance across various academic disciplines, particularly in the fields of decision-making and pattern recognition. The utilization of similarity measures is of utmost importance in the decision-making process when implementing interval-valued intuitionistic fuzzy sets. This is due to its inherent capability to quantitatively assess the level of resemblance or similarity between two interval-valued intuitionistic fuzzy sets. In this article, the drawbacks of the existing similarity measures in the context of an interval-valued intuitionistic fuzzy environment are addressed, and a novel similarity measure is presented. Many fundamental properties of this new interval-valued intuitionistic fuzzy similarity measure are also established, and the effectiveness of this similarity measure is illustrated by presenting a useful example. Moreover, a comparison is given to demonstrate the validity of the newly proposed similarity measure within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment. In addition, an algorithm is designed to solve multi-criteria decision making problems by means of the proposed measure in the interval-valued intuitionistic fuzzy setting. Furthermore, this newly defined similarity measure is successfully applied to select an optimal renewable energy source to reduce energy crises. Finally, we conduct a comparative study to showcase the authenticity of the recently defined technique within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment.
Hybrid nanofluids offer higher stability, synergistic effects, and better heat transfer compared to simple nanofluids. Their higher thermal conductivity, lower viscosity, and interaction with magnetic fields make them ideal for various applications, including materials science, transportation, medical technology, energy, and fundamental physics. The governing partial differential equations are numerically solved by employing a finite volume approach, and the effects of various parameters on the nanofluid flow and thermal characteristics are systematically examined from the simulations based on a self-developed MATLAB code. The parameters included magnetic field strength, the Reynolds number, the nanoparticle volume fraction, and the number and position of the strips in which the magnetic field is localized. It has been noted that the magnetized field induces the spinning of the tri-hybrid nanoparticles, which generates the intricate structure of vortices in the flow. The local skin friction (CfRe) and the Nusselt number (Nu) increase significantly when the magnetic field is intensified. Moreover, adding more nanoparticles in the flow enhances both Nu and CfRe, but with different effects for different nanoparticles. Silver (Ag) shows the highest increase in both Nu (52%) and CfRe (110%), indicating strong thermal-fluid coupling. Alumina (Al2O3) and Titanium Dioxide (TiO2) show lower increases in both Nu (43% and 34%) and CfRe (14% and 10%), indicating weaker coupling in the flow. Finally, compared with the localized one, the uniform magnetic field has a minor effect on the flow and temperature distributions.
