Algebraic properties of intuitionistic \(L\)-fuzzy multiset finite automata. (English) Zbl 1498.68143
Summary: 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 of the intuitionistic \(L\)-fuzzy compatible relation, the compatible monoid associated with the intuitionistic \(L\)-fuzzy compatible relation can be effectively constructed, and we construct two finite monoids through two different congruence relations on a given ILFMA, then we prove that they are isomorphic. Furthermore, using the quotient structure of ILFMA, algebraic properties of intuitionistic \(L\)-fuzzy multiset transformation semigroup are discussed. According to intuitionistic \(L\)-admissible relation and homomorphism of ILFMA, we show that there is a bijective correspondence between an ILFMA and the quotient structure of another ILFMA.
Keywords:
multiset; intuitionistic fuzzy multiset; congruence relation; quotient structure; monoid; homomorphismReferences:
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