Let $A \in \mathbb{R}^{(2n+1) \times (2n+1) \times n \times n}, B \in \mathbb{R}^{(2n+1)\times n}$. Define $C = A\bigoplus B, C \in \mathbb{R}^{(2n+1) \times (2n+1) \times n \times n}$.
And $C_{ijkl} = \textbf{min}_{m=0}^{2n}(A_{(i-m)jkl} + B_{mk}, A_{i(j-m)kl} + B_{ml})$.
The traditional min-plus algebra typically works with matrix or vectors. While the tensor operation is my interest. Is there any theory around doing this type of operation?