Hybrid norm product and relation structures in hemirings

In fuzzy logic, the triangular norm ($t$-norm) is an operator that represents conjunctions. The concept of $t$-norm turned out to be a basic tool for probabilistic metric spaces, but also in several areas of mathematics, including fuzzy set theory, fuzzy decision making, probability and statistics, etc. In the study of hybrid structures, we noticed that hybrid ideals play an important role. By using $\mathfrak{T}_\Upsilon$-hybrid ideals in hemirings, the concepts of hybrid relations and the strongest $\mathfrak{T}_\Upsilon$-hybrid relations are investigated in this paper. The notion of hybrid $\mathfrak{T}_\Upsilon$-product and their relevant results are also discussed, and we prove that the direct $\mathfrak{T}_\Upsilon$-product of two $\mathfrak{T}_\Upsilon$-hybrid left $h$-ideals in hemiring is also a $\mathfrak{T}_\Upsilon$-hybrid left $h$-ideal.