Bck-algebras Of Generalized Fuzzy Implication Ideals And Generalized Fuzzy Bck-filters

In this paper, by the use of the relations between fuzzy points and fuzzy subsets, first of all, the concept of (∈,∈)((∈,∈vq), (∈,∈∨q))-fuzzy implicative ideal of BCK-algebras is given. And then, the properties of (∈,∈)((∈,∈∨q), (∈,∈∨q))-fuzzy implicative ideal are investigated, some necessary and sufficient conditions that a fuzzy subset is a (∈,∈)((∈,∈vq), (∈,∈v q))- fuzzy implicative ideal of BCK-algebras are acquired. Moreover, the relations among (∈,∈)-fuzzy implicative ideals, fuzzy ideals and fuzzy subalgebras of BCK-algebras are described.To follow, by the use of the same way as the above, the notion of (a, P)((∈,∈∨q)) -fuzzy BCK-filters is given, and the properties of (a,β)-fuzzy BCK-filter are discussed, Afterwards, to go a step further, the definition of fuzzy BCK-filters in BCK-algebras is also generalized, the concept of (λ1,λ2)((∈,∈vq(λ1,λ2))-fuzzy BCK-filters in BCK-algebras is introduced,, and the relation of (λ1,λ2)-BCK-filter and (∈,∈∨q(λ1,λ2)-BCK-filter is investigated.