Bipolar fuzzy Fourier transform for bipolar fuzzy solution of the bipolar fuzzy heat equation

This article presents the exact solution of a bipolar fuzzy heat equation based on bipolar fuzzy Fourier transform under generalized Hukuhara partial (gH-p) differentiability. A bipolar fuzzy Fourier transform is defined, and the related key propositions and fundamental characteristics are discussed. Further, a bipolar fuzzy heat equation model is constructed using gH-differentiability, and the analytical solution of a bipolar fuzzy heat equation with bipolar fuzzy Fourier transform approach is examined. Some illustrative examples are provided to check the suggested methodology’s liability and efficiency. The type of differentiability and the solution of the bipolar fuzzy heat equation are shown graphically, demonstrating the versatility of the proposedmethodology and elucidating the impact of differentiability types on the solution behavior of the bipolar fuzzy heat equation. Additionally, the impact of different parameters on the solution behavior is analyzed, revealing insights into the underlying dynamics.

کلیدواژه ها:

Bipolar fuzzy sets ، generalized Hukuhara differentiability ، Heat equation ، Fourier transform