(α,β)-软BCK代数

(α,β)-Soft BCK Algebras

将软集的参数集赋予BCK代数的代数结构,给出了(α,β)-软BCK代数的概念,并验证了得到的(α,β)-软BCK代数是交软BCK代数和α-交软BCK代数的非平凡推广;得到了两个(α,β)-软BCK代数在软集的交、并、且等运算下仍然是(α,β)-软BCK代数的结论,并讨论了(α,β)-软BCK代数的同态像和原像的性质;最后运用对偶软集的方法给出了(α,β)-软BCK代数的等价刻画。

Firstly, by endowing a parameter set with the algebra structure of BCK algebras, this paper introduces the concept of (α,β)- soft BCK algebras, and verifies that the (α, β)- soft BCK algebras is a non-trivial generalization of the intersectional soft BCK algebras and the α - intersectional soft BCK algebras. Then this paper reaches the conclusions that two (α,β)- soft BCK algebras are still (α,β)- soft BCK algebras under the intersection, union and the AND operation of soft sets, and investigates the properties of the homomorphism image and inverse image of the (α,β)- soft BCK algebras. At last, by applying the dual soft sets, this paper gives the equivalent characterizations of the (α,β)-soft BCK algebras.