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In this paper, we define almost (m, n)-ideals of semigroups by using the concepts of (m, n)-ideals and almost ideals of semigroups. An almost (m, n)-ideal is a generalization of (m, n)-ideals and a generalization of almost one-sided ideals. We investigate properties of almost (m, n)-ideals of semigroups. Moreover, we define fuzzy almost (m, n)-ideals of semigroups and give relationships between almost (m, n)-ideals and fuzzy almost (m, n)-ideals.

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