Abstract: The notions of union algebra of two weak-BCI-algebras, extended intersection of two soft sets on union algebra, soft translation of soft set and composite operation of two soft sets are proposed. Examples are given to illustrate the existence of union algebra and extended intersection on union algebra. It is proved that the extended intersection of two new type soft weak-BCI-algebras on union algebra is also the new type of soft weak-BCI-algebra under certain condition. The properties of soft translation and projection of the new type of soft weak-BCI-algebra are studied. Furthermore, by applying compositional operation, the level set of soft set and generalized characteristic function, the equivalent characteri-zations of the new type of soft weak-BCI-algebra are obtained respectively.

Key words: soft weak-BCI-algebra, soft set, union algebra, compositional operation, soft translation, projection

摘要： 提出了两个亚BCI-代数的并代数、两个软集在并代数上的扩展交、软集的软平移以及两个软集的合成运算等新概念。举例说明了并代数以及在并代数上扩展交的存在性。证明了两个新型软亚BCI-代数在一定的条件下在并代数上的扩展交仍然是新型软亚BCI-代数。研究了新型软亚BCI-代数的软平移及投影等的相关性质。另外，利用两个软集的合成运算、软集的水平集以及广义特征函数分别给出了新型软亚BCI-代数的等价刻画。

关键词: 软亚BCI-代数, 软集, 并代数, 合成运算, 软平移, 投影