| 分数阶灰色累减生成算子及其性质研究 |
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| 引用本文： | 孟伟.分数阶灰色累减生成算子及其性质研究[J].数学的实践与认识,2020(8):192-198. |
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| 作者姓名： | 孟伟 |
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| 作者单位： | 电子科技大学经济与管理学院;重庆工商大学商务策划学院 |
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| 基金项目： | 国家自然科学基金面上项目(71771033);中国博士后基金面上资助项目(2018M643442);重庆市自然科学基金项目(cstc2019jcyj-msxmX0767、cstc2019jcyj-msxmX0003);重庆市技术预见与制度创新项目(cstc2019jsyj-zzysbA0051);重庆市社科规划项目(2018YBJJ028);重庆市教委人文社科重点项目(19SKGH075);重庆市教委科学技术研究计划项目(KJQN201900801)。 |
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| 摘 要： | 给出了分数阶灰色累减生成算子的详细推导过程,并证明了分数阶灰色累减生成算子的不动点定理、信息优先原理、交换律与指数律,为分数阶灰色预测模型提供了理论基础.算例验证了分数阶灰色累减生成算子的特征,在灰色预测模型GM(1,1)中的应用证明了分数阶灰色累减生成算子的有效性.
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| 关 键 词： | 灰色系统理论 累减生成算子 分数阶 |
Study on the Properties of Fractional Order Grey Reducing Generation Operator |
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| MENG Wei.Study on the Properties of Fractional Order Grey Reducing Generation Operator[J].Mathematics in Practice and Theory,2020(8):192-198. |
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| Authors: | MENG Wei |
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| Institution: | (School of Management and Economics,University of Electronic Science and Technology of China,Chengdu 611731,China;College of Business Planning,Chongqing Technology and Business University,Chongqing 400067,China) |
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| Abstract: | The detailed proof steps of the fractional order reducing generation operator are given.The properties of fractional grey reducing generation operator that satisfy fixed point theorem,information priority principle,exchange law and exponential law are proved.The results are helpful for the theory of fractional order generation operators and fractional order grey prediction model.The example verifies the characteristics of the fractional grey reducing generation operator.The applications in the grey prediction model proves the validity of the fractional grey reducing generation operator. |
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| Keywords: | grey system theory reducing generation operator fractional order |
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