质量函数的多分位分析
Chenhui Qiang1,2, Zhen Li3, Yong Deng4
1Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054 China.
概括
本研究引入了普斯特-沙弗理论中质量函数的泛化多分体维度,增强了尺度不变性,并提高了基于证据的系统中的分类准确性.
科学领域:
- 信息理论 信息理论
- 人工智能的人工智能
- 数学分析的数学分析
背景情况:
- 斯特-沙弗证据理论使用质量函数处理不确定性.
- 对于质量函数的现有碎形维度与Renyi信息维度不兼容.
- 信念的尺度不变性是探索的一个关键特征.
研究的目的:
- 通过引入一个参数来概括质量函数的碎形维度.
- 为质量函数提出一个包含尺度不变的多分形维度.
- 开发一种方法,使用修改的质量函数来提高分类准确性.
主要方法:
- 引入一个参数来概括现有的碎形维度,创建一个多碎形维度.
- 通过使用多分形光谱,探索信仰程度和焦点元素之间的关系.
- 开发用于质量函数修改的静态贴现系数方法.
主要成果:
- 拟议的多分体维度概括了现有的维度,并显示与Renyi维度的兼容性.
- 多分法谱揭示了信仰程度和焦点元素之间的关系.
- 静态贴现系数方法有效地提高了对三个数据集的分类准确性.
结论:
- 质量函数的多分形维度是分析德姆斯特-沙弗理论中分形特征的宝贵工具.
- 拟议的方法提供了一种新的方法来提高证据分类的准确性.
- 进一步的研究可以探索多分法分析在复杂系统中的应用.
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