Computer Engineering and Applications ›› 2018, Vol. 54 ›› Issue (24): 26-33.DOI: 10.3778/j.issn.1002-8331.1807-0051
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HUANG Fei1, LIAO Zuhua2
Online:
Published:
黄 飞1,廖祖华2
Abstract: This paper mainly deals with the measure of fuzzy (prime) filters on lattices in fuzzy algebra. Firstly, the new concept of the measure of fuzzy (prime) filters is given and measures of fuzzy (prime) filters are used to discuss that the fuzzy subset is the degree of fuzzy (prime) filters. Secondly, equivalently describe of the measures of fuzzy (prime) filters is gotten by using the (strong) level set of fuzzy sets. Finally, the fuzzy (prime) filters degree of the intersection and the direct product of fuzzy subsets is discussed. Meanwhile, the measures of fuzzy (prime) filters properties about the homomorphism image and inverse image of the fuzzy subset of lattices is obtained.
Key words: lattices, (prime)filter, fuzzy (prime) filter, R-implication, measures
摘要: 主要研究了模糊代数中格的模糊(素)滤子的度量。首先给出了模糊(素)滤子度的新概念,并利用模糊(素)滤子度讨论了格的模糊子集是模糊(素)滤子的程度。其次,利用格的模糊集的(强)水平集得到了模糊(素)滤子的等价刻画。最后,讨论了任意多个模糊子集的交、直积的模糊(素)滤子度以及格的模糊子集在同态映射下像与原像的模糊(素)滤子度的性质。
关键词: 格, (素)滤子, 模糊(素)滤子, R-蕴涵, 度量
HUANG Fei1, LIAO Zuhua2. Measure of fuzzy filters and fuzzy prime filters on lattices[J]. Computer Engineering and Applications, 2018, 54(24): 26-33.
黄 飞1,廖祖华2. 格的模糊滤子与模糊素滤子的度量[J]. 计算机工程与应用, 2018, 54(24): 26-33.
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URL: http://cea.ceaj.org/EN/10.3778/j.issn.1002-8331.1807-0051
http://cea.ceaj.org/EN/Y2018/V54/I24/26