Semiring is one of the ring extensions by eliminating the inverse axiom in its first operation. The subset of a semiring is a non-empty subset of a semiring, and the same binary operation forms a semiring. In line with the times, research on semirings is not only on semi-ringed structures but has been combined with other concepts, one of which is the fuzzy set, known as the concept of subsemiring fuzzy. One of the characteristics of a semiring is that the Cartesian product of two semirings (subsemirings) is also a semiring. This characteristic raises the question, "Are the characteristics of the cartesian product owned by the semiring (subsemiring) possessed by the fuzzy subsemiring." This problem motivated this research to be carried out. This research introduces Cartesian products from fuzzy subsemiring, anti-fuzzy subsemiring, and fuzzy complement subsemiring. Furthermore, we will review the characteristics of the Cartesian product of two (more) fuzzy subsemirings and anti-fuzzy subsemirings associated with the zero-element membership value. The result of this study is a trait that states that the Cartesian product of two (more) fuzzy subsemirings (anti-fuzzy subsemirings, fuzzy complement subsemirings) is a fuzzy subsemiring (anti-fuzzy subsemirings, fuzzy complement subsemirings). Based on the resulting properties, further research can be continued related to the fuzzy subsemiring image (pre-image) under a semiring homomorphism.

Topics
Ring theory, Review
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