FI代数的新型软滤子

A new type of soft filters of FI-algebras

为解决软集在代数结构上不足的问题,将软集的参数集赋予FI代数的滤子的代数结构,给出了FI代数的新型软滤子的概念.然后利用软集的交、且等运算,研究了FI代数的新型软滤子的基本性质,并运用对偶软集的方法给出了FI代数的新型软滤子的等价刻画;最后讨论了FI代数的新型软滤子的同态像和原像的性质.研究结论为进一步对软集代数进行研究奠定了基础.

In order to solve the problem on the algebraic structure of soft sets inadequate, this paper mtroaucea the concept of a new type of soft filters of FI -algebras by endowing a parameter sets with an algebra structure of filters of FI -algebras. Then by using the intersection and the AND operation of soft sets, this paper studied the basic properties of the new type of soft filters of FI -algebras. Besides, by applying the dual soft sets, this study also gave the equivalent characterizations of the new type of soft filters of FI -algebras. Finally, the properties of the homomorphism image and inverse image of the new type of soft filters of FI -algebras are investigated. The conclusion laid the foundation for further research on the soft set algebras.