剩余格上的α-交软滤子

α-intersectional Soft Filters on Residuated Lattices

赋予剩余格作为参数集,提出了剩余格上的α-交软滤子的概念,给出一些刻画和软集交运算下的性质。进一步,剩余格上的α-交软同余关系和α-交软滤子的关系被研究。特别是,当X=α时,证明了SFil(L)(剩余格上交软滤子α-交软滤子的全体)和Scon(L)(剩余格上交软滤子α-交软同余关系的全体)是完备格同构的。最后,得到了剩余格上的α-交软滤子像与原像的性质。

Endowing a residuated lattice as a parameter set, the concepts of a-intersectional soft filters on a residuated lattice are introduced, and some characterization and intersectional operations of α-intersectional soft filters are discussed. Furthurmore, the relationship between a α-intersectional soft filters on a residuated lattice and α-intersectional soft congruence relations on a residuated lattice is given. In particular, it is proved that SFil（L）（the set of all α-intersectional soft filters on a residuated lattice） and Scan（L） （the set of all α-interseetional soft congruence relation on a residuated lattice） are complete lattices isomorphism. Finally, the concepts of image and preimage of a a-intersectional soft filters of residuated lattice and their properties are shown.