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This work aims to focus on the study of natural convection heat transfer characteristics in a vertical wall embedded in a non-Darcy porous medium filled with nanofluids.

The governed partial differential equations are transformed into ordinary differential equations which are obtained by similarity solution and then have been solved through homotopy analysis method.

The results show that Cu-water as nanofluid enhances the local Nusselt number more than other nanofluids.

Nanoparticles and nanofluid enhance the local Nusselt number.

Conventional approaches such as Data Envelopment Analysis (DEA) and Fuzzy Data Envelopment Analysis (FDEA) cannot effectively account for uncertainty, which can lead to imprecise decision-making. Furthermore, these methods frequently rely on precise numbers, ignoring the inherent uncertainty of real-world data. To address this gap, the research question arises: How can we develop a methodology that combines Z-number theory and FDEA to provide a comprehensive assessment of residency preferences in European countries while accounting for uncertainty in information reliability? The proposed methodology aims to fill this gap by incorporating Z-number theory and FDEA.

The proposed study assesses residency preferences across 39 European countries, focusing on key factors like environment, sustainability, technology, education, and development, which significantly influence individuals' residency choices. Unlike conventional DEA and FDEA approaches, the proposed method introduces a novel consideration: dependability. This inclusion aims to refine decision-making precision by accounting for uncertainties related to data reliability. The proposed methodology utilizes an interval approach, specifically employing the a-cut approach with interval values in the second step. Unlike using crisp values, this interval programming resolves formulations to determine the efficiencies of decision-making units (DMUs).

The comprehensive findings provide valuable insights into the distinctive factors of European nations, aiding informed decision-making for residency choices. Malta (75.6%-76.1%-75.8%), Austria (78.2%-78%-76.1%), and the United Kingdom (79.3%-78.4%-77%) stand out with distinct characteristics at levels of a = 0-a = 0.5-a = 1, assuming the independence of variables of the overall evaluation. Individual consideration of each factor reveals various countries as prominent contenders, except for the environmental factor, which remains consistent across countries.

Traditional DEA models encounter challenges when dealing with uncertainties and inaccuracies, particularly in the evaluation of large systems. To overcome these limitations, we propose integrating Z-numbers—a powerful mathematical tool for modeling uncertainty—into the conventional DEA process. Our methodology not only assesses the effectiveness of countries across various socio-economic and environmental metrics but also explicitly addresses the inherent uncertainties associated with the data. By doing so, it aims to enhance the precision of decision-making and provide valuable insights for policymakers and stakeholders.

This paper aims to propose a composite form of the robust disturbance fuzzy control scheme. The proposed method uses the benefits of fuzzy system modeling and Lyapunov direct methods.

The effciency of the control technique was demonstrated with assistance of numerical simulation in control problems of unmanned aerial vehicle (UAV) simulation.

To evaluate the control performance, the comparison of the proposed controller was made with conventional control techniques. The Lyapunov stability theorem has been used to testify for asymptotic stability and convergence of the closed loop system.

Implementation of the control law in the real world environment can be easier due to significant reduction in the fuzzy rules, tuning parameters and computation stages.

Simulation results confirm that the proposed control scheme performs remarkably well in terms of the robustness and disturbance attenuation.