Abstract
The concept of fuzzy set introduced by L.A. Zadeh was applied by Rosen Feld in 1971 to generalize some of the basic concept of groupoids and groups. The definitions of fuzzy sub groupoid and fuzzy groups where extended by him to cover other so-called non-deterministic structure which are similar to ordinary algebraic concepts like- Ideals- fuzzy ideals- homomorphism image fuzzy homomorphism image etc. But, some mathematical structure which seems to be “fuzzy” do not satisfied the definition of Rosen Feld. Hence it would be proper to modify these definitions. Anthony and Sherwood in 1979 observe that the use of minimum in the definition of fuzzy sub groupoid and fuzzy subgroup given by Rosen Feld restricts the notion rendering it not useful in various fuzzy situations, and hence they introduced t-norm place in of minimum and re-define fuzzy algebraic structure and have given independent proof of some theorems there in.
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