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<p>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.</p>

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Antiideal theory in semigroups and its fuzzification

  • 期刊论文

  • 发表日期：

    2025年9月23日

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

摘要

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.