On a Generalization of Fuzzy Filters of Ordered Semigroups

M. Al Tahan (), B. Davvaz (), A. Mahboob and N. M. Khan ()
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M. Al Tahan: Department of Mathematics and Statistics, Abu Dhabi University, Abu Dhabi, United Arab Emirates
B. Davvaz: Department of Mathematical Sciences, Yazd University, Iran
A. Mahboob: Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle 517325, India
N. M. Khan: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

New Mathematics and Natural Computation (NMNC), 2023, vol. 19, issue 02, 489-502

Abstract: The aim of this paper is to generalize the results related to fuzzy filters of ordered semigroups. In this regard, the concept of fuzzy (m,n)-filters of ordered semigroups is initiated, nontrivial examples are presented, and its properties are investigated. It is known that a fuzzy set of an ordered semigroup is a fuzzy filter if and only its complement is a fuzzy prime ideal. As a generalization of the latter result, it is proved that a fuzzy set of an ordered semigroup is a fuzzy (m,n)-filter if and only if its complement is a prime generalized fuzzy (m,n)-ideal. Furthermore, it is shown that in an (m,n)-regular semigroup, fuzzy (m,n)-filters and fuzzy bi-filters coincide.

Keywords: Ordered semigroup; fuzzy (m; n)-filter; generalized fuzzy (m; n)-ideal; fuzzy prime subset (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S1793005723500187

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