Abstract
In this paper, we introduce the concept of a fuzzy (m, n)-ideal, fuzzy (m, 0)-ideal and fuzzy (0, n)-ideal of a semigroup S for any positive integers m and n. This generalizes the concept of a fuzzy bi-ideal, fuzzy right ideal and fuzzy left ideal. After that, some properties of a fuzzy (m, n)-ideal, fuzzy (m, 0)-ideal and fuzzy (0, n)-ideal have been investigated. We also characterize different classes of semigroups ((m, n)-regular, (m, 0)-regular, (0, n)-regular) in terms of its fuzzy (m, n)-ideals, fuzzy (m, 0)-ideals and fuzzy (0, n)-ideals, respectively.