Fuzziness of n-ary Semigroups

Abstract

A nonempty set S together with an n-ary operation given by f: Sn→ S, where n ≥ 2, is called an n-ary groupoid and is denoted by (S, f). The following sequence of elements ¿, +1, ..., ; is denoted by x. In the case i > j, it is Ø. We call an n-ary groupoid (S, f) as (i, j)-associative if the following holds: n+i-1 2n-1 f(x, f(x+1), x) = f(x, f(x+1), x211) for every 1, 2,..., 2n-1 E S. The operation f is associative if the above identity holds for every 1 ≤ i ≤ j ≤ n, and (S, f) is called an n-ary semigroup.In this thesis, we study i-ideals and fuzzy i-ideals of n-ary semi- groups. Moreover, we study almost i-ideals and fuzzy almost i-ideals of n-ary semi- groups.