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.
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We are very thankful to the reviewers for careful detailed reading and helpful comments/suggestions that improve the overall presentation of this paper.
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Communicated by Rosana Sueli da Motta Jafelice.
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Mahboob, A., Davvaz, B. & Khan, N.M. Fuzzy (m, n)-ideals in semigroups. Comp. Appl. Math. 38, 189 (2019). https://doi.org/10.1007/s40314-019-0930-5
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DOI: https://doi.org/10.1007/s40314-019-0930-5