EXTENDING THE IDEALS OF SEMIRINGS TO FUZZY SETTING BY METATHEOREM
Keywords:
Semirings, fuzzy bi-ideal, fuzzy quasi-ideal, regular semiring, metatheorem, projection closed, Rep functionDOI:
https://doi.org/10.17654/0973421X24006Abstract
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.
Received: August 29, 2024
Revised: November 10, 2024
Accepted: December 18, 2024
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