The Fuzzy Bi-ideals Of Semigroups

The semigroup theory is a younger branch of algebra that rised between the fifties andsixties of the last century,after several decades years devlop it has growed up to an importantresearch subject of algebra.In1965,American control theory proficient L.A.Zadeh publishedthe pioneering paper of Fuzzy Mathematics which under the title “Fuzzy Sets”,with thewidespread use of fuzzy theory lots of new science branches had emerged and grown up inthe following tens years,which include the study of fuzzy algebra theory.In1980,Kuroki firstcame up with the concept of fuzzy semigroup,which enriched the researching contents offuzzy algebra.Although the fuzzy semigroup theory is a new subject,there’s already lots ofresearch achivements about it in the30years its existence,the fuzzy semigroup theory hasalready emerged a strongly life force.In this paper,we introduced some kinds of fuzzy prime bi-ideals,we use the level cutset,characteristic function,fuzzy point and relationship between function values to give thenecessary and sufficient conditions which make a fuzzy set of a semigroup to be one of thosespecial fuzzy prime bi-ideals,what’s more we give the conditions for which the fuzzy bi-idealscan translate to another ones.The central contents of this paper will be the depictions of somespecial semigroups by using those fuzzy prime bi-ideals.