Further Study Of Fuzzy Ideals For Ordered Semigroups

The paper has two parts.The first part is about generalized fuzzy bi-ideal and generalized fuzzy quasi-ideal. Firstly ,we give the definition of generalized extension multiplication by using t-norm operator . The definitions of generalized fuzzy bi-ideal and generalized fuzzy quasi-ideal are given , then we get the sufficient and necessary conditions that a fuzzy set is a fuzzy ideal. Secondly , we depict normal quality of the two fuzzy ideals by using t-norm operator. At last, regular ordered semigroups are studied by the two fuzzy ideals .The second part is about fuzzy weak prime ideals and the extension of a fuzzy ideal . Firstly , we definite fuzzy weak prime ideals by fuzzy points , then study the relations of fuzzy prime left ideals , fuzzy quasi prime left ideals and fuzzy weak quasi prime left ideals . Secondly , when ordered semigroup is exchanged , we definite extension of a fuzzy ideal and fuzzy n-prime ideal . Then their relations are discussed and we get the conclusion that fuzzy n-prime ideal is equivalent to fuzzy n—1-prime ideal when the ordered semigroup S has unit element .