Regular Semigroups and Metatheorem

Regularity of a semigroup in terms of fuzzy left ideals, fuzzy right ideals, fuzzy ideals, fuzzy bi-ideals, fuzzy interior ideals, fuzzy semiprime ideals and fuzzy quasi-ideals of a semigroup is studied in the light of Tom Head's metatheorem. The classes of different types of fuzzy ideals are shown to be closed under projection. Tom Head's metatheorem is also used to provide proofs of several results pertaining to these fuzzy ideals which doesn't involve calculations. The proofs obtained by metatheorem are simple and shorter. Characterization of a semigroup that is regular, intra-regular, left regular, complete regular, quasi regular and weakly regular in terms of aforementioned fuzzy ideals by utilizing metatheorem is provided.