The Semiring Properties of Fuzzy Algebras

The relationship between fuzzy algebras and semirings is explored with fuzzy algebra operators replacing the arithmetic operators of semirings. A new class of fuzzy structures which are similar to semirings is defined. Results of partial ordering on fuzzy algebras are shown. The zero-sum free property of semirings on fuzzy structures is shown. The semiring property of homomorphism is mapped to fuzzy structures and results like order- and operator-preservation are described.