Notions of different types of fuzzy ideals are investigated in a semiring in the light of Tom Head’s metatheorem. Using Rep function, the classes of these fuzzy ideals are shown to be projection closed. The metatheorem was formulated to obtain fuzzy versions of classical outcomes. Tom Head’s metatheorem is also employed to present alternative proofs for various results related to fuzzy ideals, offering a non-computational approach. The proofs obtained by metatheorem are simple, shorter and calculation free. The metatheorem is utilized to characterize a semiring that is regular, intra-regular and weakly regular in terms of various types of fuzzy ideals.

semirings, fuzzy bi-ideal, fuzzy quasi-ideal, regular semiring, metatheorem, closed under projection, Rep function

Received: August 29, 2024; Revised: November 10, 2024; Accepted: December 18, 2024; Published: December 30, 2024

How to cite this article: Ravi Srivastava, Extending the ideals of semirings to fuzzy setting by metatheorem, Advances in Fuzzy Sets and Systems 29(2) (2024), 123-140. http://dx.doi.org/10.17654/0973421X24006

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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