發(fā)布時間：2018-10-26 10:23

【摘要】：在軟集中已經(jīng)有了幾種不同形式的并、交和補算子的定義。但對于為什么如此定義這些算子,它們之間為什么存在差異,在目前的文獻中都無法找到解釋。本文通過對軟集進行深入的分析,給出了軟集的兩種不同理解方式,稱之為弱軟集和強軟集。在兩種解釋下采用完全相同的方法構造并、交和補算子,事實證明得到的結果恰好對應現(xiàn)有的算子。此外,還提出將軟集看做一個信息系統(tǒng),將每個參數(shù)對應的子集看做一個信息粒子。為此在兩種解釋下定義了新的軟包含關系,使得在兩種解釋下都能通過并、交運算實現(xiàn)信息粒子的泛化與細化。同時給出了并、交和補運算的性質(zhì),證明了每種解釋中的并、交和補運算都滿足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)大學理學院;
【基金】：遼寧省教育廳基金(L2012226) 國家自然科學基金(61473139)
【分類號】：O159

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1 冀燕釗;冀振川;;補集法應用探析[J];數(shù)學學習與研究;2011年13期

2 黃冠斌;;對集合中“補集”有關規(guī)定的質(zhì)疑[J];珠算與珠心算;2009年01期

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本文編號：2295408