New Way For Extending Ideals of Ternary Semigroups to Fuzzy Setting
Keywords:
Ternary semigroups; fuzzy interior ideals; fuzzy quasi-ideals; metatheorem: projection closed.Abstract
Point-wise definitions of fuzzy interior ideals and fuzzy quasi-ideals in the context of ternary semigroups are systematically derived. Their eqivalence with the set-theoretic formulations is also established. Fuzzy left (lateral, right)ideals, fuzzy ideals, fuzzy bi-ideals, fuzzy interior ideals, and fuzzy quasi-ideals are explored within ternary semigroups under the framework of Tom Head's metatheorem. It is demonstrated that the classes of ternary fuzzy subsemigroups, along with various fuzzy ideals, are projection closed. Additionally, alternative proofs for several results are furnished using metatheorem-based approaches, which eliminate the need for explicit calculations. These proofs are more concise and straightforward, offering calculation-free solutions. Furthermore, regular, intra
regular, and completely regular semigroups are characterized in terms of different types of fuzzy ideals.
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