关于软集的新认识

发布时间：2018-10-26 10:23

【摘要】：在软集中已经有了几种不同形式的并、交和补算子的定义。但对于为什么如此定义这些算子,它们之间为什么存在差异,在目前的文献中都无法找到解释。本文通过对软集进行深入的分析,给出了软集的两种不同理解方式,称之为弱软集和强软集。在两种解释下采用完全相同的方法构造并、交和补算子,事实证明得到的结果恰好对应现有的算子。此外,还提出将软集看做一个信息系统,将每个参数对应的子集看做一个信息粒子。为此在两种解释下定义了新的软包含关系,使得在两种解释下都能通过并、交运算实现信息粒子的泛化与细化。同时给出了并、交和补运算的性质,证明了每种解释中的并、交和补运算都满足De Morgan律。
[Abstract]:Several different forms of union, intersection and complement operators have been defined in soft sets. However, no explanation can be found in the current literature as to why these operators are so defined and why there are differences between them. In this paper, through the deep analysis of soft sets, two different ways of understanding soft sets are given, which are called weak soft sets and strong soft sets. By using the same method to construct and, intersection and complement operators under two interpretations, it is proved that the results are exactly corresponding to the existing operators. In addition, the soft set is regarded as an information system, and the subset corresponding to each parameter is regarded as an information particle. For this reason, a new soft inclusion relation is defined under two interpretations, so that the generalization and refinement of information particles can be realized through the operation of and intersecting in both interpretations. At the same time, the properties of union, intersection and complement operations are given, and it is proved that the union, intersection and complement operations in each interpretation satisfy the De Morgan law.
【作者单位】：辽宁工业大学理学院;
【基金】：辽宁省教育厅基金(L2012226) 国家自然科学基金(61473139)
【分类号】：O159

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