Algebraic properties of intuitionistic $$L-$$fuzzy multiset finite automata

Algebraic properties and structures of intuitionistic $$L-$$ fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly, we put forward the notion compatible relation, monoid associated with relation can be effectively constructed, construct two monoids different congruence relations given ILFMA, then prove that they isomorphic. Furthermore, using quotient structure algebraic transformation discussed. According to admissible homomorphism show there is bijective correspondence between an ILFMA another ILFMA.