SOME RELATIONS AND APPLICATIONS OF FUZZY AUTOMATION SUB SEMI-GROUPS

Résumé

1,3] In this research paper, to showing that A, besides B, remain two sets. Formerly, a relative
ρ from A to B may be defined as a subset of A × B [1,3,8]. For each a ∈ A, we then define aρ in the obvious
way, to find the aρ = {b ∈ B | (a, b) ∈ ρ}. If S and T are two fuzzy semi-groups, then a subset μ ⊆ S × T is
known as a relational morphism from S to T , if the conditions are satisfied by the relations as follows: (RM1)
(∀a ∈ S) aμ̸ = ∅; (RM2) (∀a, b ∈ S) (aμ)(bμ) ⊆ (ab)μ. It is known as injective if, in addition: (RM3)
(∀a, b ∈ S) aμ ∩ bμ̸ = ∅ ⇒ aμ = bμ [7]. To showing every relational morphism is a fuzzy sub semi-group of
direct products S × T . We say that S divides T if there exists a fuzzy sub semi-group U of T and a morphism
ψ from U onto S. Thus, S is a quotient of a fuzzy sub semi-group of T . To shows that S divides T if as well
as only if U is a relation morphism injection originating S to T [7,6,4]