| 信息熵公理及其在决策分析中的应用 |
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| 引用本文： | 郭进利. 信息熵公理及其在决策分析中的应用[J]. 数学的实践与认识, 2012, 42(13): 105-116 |
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| 作者姓名： | 郭进利 |
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| 作者单位： | 上海理工大学管理学院工业工程研究所,上海,200093 |
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| 基金项目： | 国家自然科学基金，上海市重点学科建设资助项目 |
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| 摘 要： | 针对信息量是消息发生前的不确定性给出一个直观测量信息量公式.为了克服Shannon熵的局限性和分析信息度量本质,借鉴距离空间理论中度量公理定义的思路,通过非负性、对称性、次可加和极大性给出信息熵的公理化新定义.将Shannon熵、直观信息熵和β-熵等不同形式的信息度量统一在同一公理化结构下.应用直观信息熵公式仅采用四则运算进行决策树分析,避免了利用Shannon熵公式的对数运算.
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| 关 键 词： | Shannon熵 信息度量 信息熵 决策分析 |
Axioms of Information Entropy and Applications in Decision Analysis |
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| GUO Jin-Li. Axioms of Information Entropy and Applications in Decision Analysis[J]. Mathematics in Practice and Theory, 2012, 42(13): 105-116 |
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| Authors: | GUO Jin-Li |
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| Affiliation: | GUO Jin-Li (Business School,University of Shanghai for Science and Technology,Shanghai 200093,China) |
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| Abstract: | Based on which quantities of information are uncertainty before messages taking place,an intuitive quantity of measure information is given.In order to better overcome the limitation of the Shannon entropy and explain essence of information quantity,utilizing the idea of the metric axiom system,a new axiom system for the information metric is given by nonnegativity,symmetry,subadditive and maximum.Shannon entropy,the intuitive information entropy andβ-entropy are unified under the axiom system,and we also generalizes an information measure system with all discrete random variable with the infinity countable distribution.In decision analysis we use the intuitive information entropy,avoiding the logarithms operation of the formula of Shannon entropy. |
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| Keywords: | Shannon entropy information measure information entropy decision analysis |
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