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Motivated by the concept of type-2 fuzzy sets, we introduce a novel framework known as trapezoidal type-2 Pythagorean fuzzy sets (TRT-2-PFSs), an extension of triangular fuzzy sets. Basic operations like addition and scalar multiplication of two TRT-2-Pythagorean fuzzy numbers (TRT-2-PFNs) are defined. We also explore comparative analysis and distance measurements between two TRT-2-PFNs. A methodology for evaluating unknown weight vectors and criteria weights is proposed. Building upon TRT-2-PFSs, an extension of the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method is developed to address intricate decision-making challenges. Ultimately, the newly introduced TRT-2-PFS-based TODIM technique is employed to tackle multicriteria decision-making (MCDM) problems. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating or computing the solution to one-dimensional partial fuzzy fractional order heat equation. In particular, one-dimensional fuzzy partial heat equation is hybridized into two equations by hybrid techniques along with the concept of parametric fuzzy number. For this investigation, a hybrid method of decomposition due to Adomian and Laplace transform is used. The considered techniques are presented for the computation of series of solutions of partial fractional order heat equation. The applied techniques have also provided the accuracy, simplicity and efficiency as compared to other existing methods. Finally, some illustrations are solved for the justification of our theoretical solution. [ABSTRACT FROM AUTHOR]

In this research work, we study the solidification of nanoparticles-enhanced phase change material (NEPCM) in a latent heat thermal energy storage system (LHTESS) in the existence of magnetic field through entropy optimization. The Finite element method (FEM) is applied for solving the developed equations. Koo–Kleinstreuer–Li model is used to model the nanoparticles characteristics. The impacts of varying strength of magnetic field and buoyancy forces on solidification are examined. It is obtained that the rising Lorentz force due to augmenting Hartmann number enhances the solidification rate of NEPCM, while the enhancing buoyancy forces mitigates this rate of solidification. The Bejan number (Be) augments with the higher Lorentz forces while drops with the augmenting Buoyancy forces. The entropy generations due to the frictional forces and the applied B -field augment with the rising buoyancy forces while depreciate with the rising Hartmann number. The agreement between our and already published work confirms the accuracy of the applied computational technique. The results of this research work have potential applications in modeling the efficient thermal energy transfer systems by using nanofluids. [ABSTRACT FROM AUTHOR]