A NOVEL STUDY ON FUZZY CONGRUENCES ON n-ARY SEMIGROUPS

In this paper, we introduce the concept of fuzzy congruences on n-ary semigroups and describe quotient n-ary semigroups by fuzzy congruences. Some isomorphism theorems about n-ary semigroups are established. Moreover, we discuss a special kind of n-ary semigroups. We also establish relationships between normal fuzzy ideals and fuzzy congruences. In particular, we prove that there exists a preserving inclusion injective mapping from the set of all normal fuzzy ideals of the special n-ary semigroups to the set of all fuzzy congruences in an n-ary semigroup with one zero. Finally, we obtain that there is a one-to-one correspondence between the set of all invariant fuzzy congruences on an n-ary semigroup and the set of all invariant fuzzy congruences on a quotient n-ary semigroup.