Antiideal theory in semigroups and its fuzzification

Madeleine Al Tahan; Sarka Hoskova-Mayerova; Bijan Davvaz; Panackal Harikrishnan

doi:10.1007/s00500-025-10918-z

Antiideal theory in semigroups and its fuzzification

Madeleine Al Tahan
, Sarka Hoskova-Mayerova^*
, Bijan Davvaz
, Panackal Harikrishnan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Algebraic systems are better understood through their subsets. On the other hand, fuzzy sets help in dealing with ambiguities. The combination of these concepts led to founding the theory of fuzzy algebraic structures. This paper studies semigroups through their antiideals and bi-antiideals and fuzzifies them. First, it investigates the properties of antiideals and bi-antiideals of semigroups. Then it fuzzifies these concepts to fuzzy antiideals and fuzzy bi-antiideals of semigroups. Finally, it studies these new concepts and establishes a relationship between them and antiideals (bi-antiideals) of semigroups through level sets.

Original language	English
Pages (from-to)	5465-5470
Number of pages	6
Journal	Soft Computing
Volume	29
Issue number	19-20
DOIs	https://doi.org/10.1007/s00500-025-10918-z
Publication status	Published - 10-2025

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Software
Geometry and Topology

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AU - Davvaz, Bijan

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N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

PY - 2025/10

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N2 - Algebraic systems are better understood through their subsets. On the other hand, fuzzy sets help in dealing with ambiguities. The combination of these concepts led to founding the theory of fuzzy algebraic structures. This paper studies semigroups through their antiideals and bi-antiideals and fuzzifies them. First, it investigates the properties of antiideals and bi-antiideals of semigroups. Then it fuzzifies these concepts to fuzzy antiideals and fuzzy bi-antiideals of semigroups. Finally, it studies these new concepts and establishes a relationship between them and antiideals (bi-antiideals) of semigroups through level sets.

AB - Algebraic systems are better understood through their subsets. On the other hand, fuzzy sets help in dealing with ambiguities. The combination of these concepts led to founding the theory of fuzzy algebraic structures. This paper studies semigroups through their antiideals and bi-antiideals and fuzzifies them. First, it investigates the properties of antiideals and bi-antiideals of semigroups. Then it fuzzifies these concepts to fuzzy antiideals and fuzzy bi-antiideals of semigroups. Finally, it studies these new concepts and establishes a relationship between them and antiideals (bi-antiideals) of semigroups through level sets.

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Antiideal theory in semigroups and its fuzzification

Abstract

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