【摘要】：在軟集中已經(jīng)有了幾種不同形式的并、交和補(bǔ)算子的定義。但對(duì)于為什么如此定義這些算子,它們之間為什么存在差異,在目前的文獻(xiàn)中都無(wú)法找到解釋。本文通過(guò)對(duì)軟集進(jìn)行深入的分析,給出了軟集的兩種不同理解方式,稱之為弱軟集和強(qiáng)軟集。在兩種解釋下采用完全相同的方法構(gòu)造并、交和補(bǔ)算子,事實(shí)證明得到的結(jié)果恰好對(duì)應(yīng)現(xiàn)有的算子。此外,還提出將軟集看做一個(gè)信息系統(tǒng),將每個(gè)參數(shù)對(duì)應(yīng)的子集看做一個(gè)信息粒子。為此在兩種解釋下定義了新的軟包含關(guān)系,使得在兩種解釋下都能通過(guò)并、交運(yùn)算實(shí)現(xiàn)信息粒子的泛化與細(xì)化。同時(shí)給出了并、交和補(bǔ)運(yùn)算的性質(zhì),證明了每種解釋中的并、交和補(bǔ)運(yùn)算都滿足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.
【作者單位】： 遼寧工業(yè)大學(xué)理學(xué)院;
【基金】：遼寧省教育廳基金(L2012226) 國(guó)家自然科學(xué)基金(61473139)
【分類號(hào)】：O159

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本文編號(hào)：2295408