多尺度单值中智系统中基于优势粗糙集模型的最优尺度选择与约简

多尺度单值中智系统中基于优势粗糙集模型的最优尺度选择与约简

王文珏, 黄兵

Optimal scale selection and reduction based on dominant rough set model in multi⁃scale single⁃valued neutrosophic systems

Wenjue Wang, Bing Huang

表1 多尺度优势单值中智决策系统

Table 1 Multi?scale dominant single?valued neutrosophic decision system

$U$	$a_{1}^{1}$	$a_{1}^{2}$	$a_{1}^{3}$	$a_{2}^{1}$	$a_{2}^{2}$	$a_{3}^{1}$	$a_{3}^{2}$	d
$x_{1}$	$〈0.4,0.5,0.3〉$	$〈0.5,0.4,0.3〉$	$〈0.5,0.3,0.2〉$	$〈0.4,0.5,0.4〉$	$〈0.5,0.4,0.2〉$	$〈0.8,0.2,0.3〉$	$〈0.8,0.1,0.2〉$	2
$x_{2}$	$〈0.3,0.4,0.3〉$	$〈0.5,0.4,0.3〉$	$〈0.5,0.3,0.2〉$	$〈0.4,0.5,0.4〉$	$〈0.5,0.4,0.1〉$	$〈0.6,0.1,0.3〉$	$〈0.7,0.1,0.2〉$	1
$x_{3}$	$〈0.3,0.4 . 0.4〉$	$〈0.5,0.4,0.2〉$	$〈0.5,0.3,0.2〉$	$〈0.4,0.4,0.4〉$	$〈0.5,0.4,0.1〉$	$〈0.8,0.1,0.2〉$	$〈0.8,0.1,0.2〉$	1
$x_{4}$	$〈0.7,0.3,0.2〉$	$〈0.7,0.2,0.2〉$	$〈0.8,0.1,0.1〉$	$〈0.4,0.5,0.2〉$	$〈0.5,0.4,0.2〉$	$〈0.9,0.1,0.2〉$	$〈0.9,0.1,0.2〉$	3
$x_{5}$	$〈0.4,0.6,0.3〉$	$〈0.5,0.4,0.2〉$	$〈0.5,0.3,0.2〉$	$〈0.7,0.3,0.3〉$	$〈0.8,0.2,0.2〉$	$〈0.9,0.1,0.2〉$	$〈0.9,0.1,0.2〉$	3
$x_{6}$	$〈0.7,0.3,0.2〉$	$〈0.7,0.2,0.2〉$	$〈0.8,0.1,0.1〉$	$〈0.7,0.3,0.2〉$	$〈0.8,0.2,0.1〉$	$〈0.8,0.1,0.2〉$	$〈0.8,0.1,0.2〉$	2
$x_{7}$	$〈0.4,0.5,0.3〉$	$〈0.5,0.4,0.2〉$	$〈0.5,0.3,0.2〉$	$〈0.4,0.5,0.3〉$	$〈0.5,0.4,0.2〉$	$〈0.8,0.2,0.3〉$	$〈0.8,0.1,0.2〉$	2
$x_{8}$	$〈0.3,0.6,0.4〉$	$〈0.4,0.4,0.3〉$	$〈0.5,0.3,0.2〉$	$〈0.4,0.6,0.3〉$	$〈0.5,0.5,0.2〉$	$〈0.7,0.2,0.2〉$	$〈0.8,0.1,0.2〉$	2
$x_{9}$	$〈0.1,0.8,0.5〉$	$〈0.3,0.6,0.3〉$	$〈0.4,0.5,0.1〉$	$〈0.1,0.8,0.4〉$	$〈0.2,0.7,0.3〉$	$〈0.4,0.5,0.3〉$	$〈0.5,0.5,0.2〉$	1
$x_{10}$	$〈0.4,0.6,0.3〉$	$〈0.5,0.4,0.2〉$	$〈0.5,0.3,0.2〉$	$〈0.7,0.3,0.2〉$	$〈0.8,0.2,0.1〉$	$〈0.9,0.1,0.2〉$	$〈0.9,0.1,0.2〉$	3