| 基于核和灰度的灰色异构数据代数运算法则及其应用 |
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| 引用本文： | 曾波,孟伟,熊遥.基于核和灰度的灰色异构数据代数运算法则及其应用[J].统计与信息论坛,2014(4):18-23. |
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| 作者姓名： | 曾波 孟伟 熊遥 |
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| 作者单位： | [1]重庆工商大学商务策划学院,重庆400067 [2]重庆工商大学电子商务及供应链系统重庆市重点实验室,重庆400067 [3]重庆工商大学长江上游经济研究中心,重庆400067 |
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| 基金项目： | 重庆工商大学青年博士基金项目《灰色多源异构数据预测模型构建研究》（1152003） |
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| 摘 要： | 为解决灰色异构数据的建模问题,应用"核和灰度"对灰色异构数据代数运算法则及其性质展开研究。将灰信息表征为"核和灰度",通过"核"将灰色异构数据代数运算转换为实数之间代数运算,根据灰度不减公理确定运算结果之灰度,在此基础上构建灰色异构数据的代数运算法则,并将该法则应用于灰色异构数据预测模型的构建及空气质量指数(AQI)的预测。研究成果对丰富与完善灰色系统基础理论具有积极意义。
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| 关 键 词： | 灰色理论 代数运算法则 灰色异构数据 核和灰度 |
Algebra Algorithm Rules of Grey Isomerism Data Based on Kernel and Grey Degree and Its Applications |
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| Institution: | ZENG Bo, MENG Wei, XIONG Ya (a. Strategical Planning College; b. Chongqing Key Laboratory of Electronic Commerce and Supply Chain System; c. Research Center of the Economy of the Upper Reaches of the Yangtze River, Chongqing Technology and Business University, Chongqing 400067, China) |
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| Abstract: | In order to solve the modeling problem of grey isomerism data, this paper applies ＂kernel and grey degree to study the algebra algorithm rules of grey isomerism data and its properties. Grey information is represented as kernel and grey degree, and the algebra algorithm is switched from grey isomerism data to real numbers through kernel. The grey degree of calculation result is defined by the axiom of grey degree not-reducing; on those basses the algebra algorithm rules of grey isomerism data is established. Finally, this paper employs the novel algorithm rules to build a prediction model of grey isomerism data sequence and forecast the air quality index （AQI）. The research findings have a positive significance for enriching and perfecting the basic theory of grey system. |
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| Keywords: | grey theory algebra algorithm rules grey isomerism data kernel and grey degree |
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