TY - JOUR
T1 - Antiideal theory in semigroups and its fuzzification
AU - Tahan, Madeleine Al
AU - Hoskova-Mayerova, Sarka
AU - Davvaz, Bijan
AU - Harikrishnan, Panackal
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.
PY - 2025/10
Y1 - 2025/10
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.
UR - https://www.scopus.com/pages/publications/105017776141
UR - https://www.scopus.com/pages/publications/105017776141#tab=citedBy
U2 - 10.1007/s00500-025-10918-z
DO - 10.1007/s00500-025-10918-z
M3 - Article
AN - SCOPUS:105017776141
SN - 1432-7643
VL - 29
SP - 5465
EP - 5470
JO - Soft Computing
JF - Soft Computing
IS - 19-20
ER -