| 模糊测度Shapley熵的完备化 |
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| 引用本文： | 王国俊,宋建社.模糊测度Shapley熵的完备化[J].陕西师范大学学报,2004,32(1):1-7. |
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| 作者姓名： | 王国俊 宋建社 |
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| 作者单位： | [1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]西安高技术研究所,陕西西安710025 |
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| 基金项目： | 国家自然科学基金资助项目(19831040，60272022) |
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| 摘 要： | 研究了模糊测度的Shapley熵的完备化问题．结果表明，具有完全不确定性的模糊测度虽然具有最大Shapley熵，但反之不真．通过例子表明具有最大Shapley熵的模糊测度可以远远不是完全不确定的；引入了与Shapley熵互为补充的分划熵，从而使Shapley熵得到了完备化，称二者之和为绝对熵，证明了模糊测度是完全确定的或完全不确定的，当且仅当它的绝对熵相应地取最小值或最大值；还研究了模糊测度的扩张问题，提出了可以保持F测度的基本性质的正则扩张理论．
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| 关 键 词： | 模糊测度 Shapley熵 完备化 分划熵 正则扩张理论 |
| 文章编号： | 1672-4291(2004)01-0001-07 |
| 修稿时间： | 2003年9月18日 |
Completion of Shapley entropy of fuzzy measures |
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| WANG Guo-jun,SONG Jian-she.Completion of Shapley entropy of fuzzy measures[J].Journal of Shaanxi Normal University: Nat Sci Ed,2004,32(1):1-7. |
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| Authors: | WANG Guo-jun SONG Jian-she |
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| Institution: | WANG Guo-jun~1,SONG Jian-she~2 |
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| Abstract: | The completion of Shapley entropy of fuzzy measures has been obtained. It is pointed out that the Shapley!entropy of fuzzy measure with complete uncertainty possesses the maximum value, but on the other hand, a counter example is provided which shows that fuzzy measures with maximum Shapley entropy may be far from complete uncertainty. A new entropy, called complemented entropy, has been introduced. It is proved that fuzzy measures have complete certainty or complete uncertainty if and only if the sum of their Shapley entropy and complemenued entropy takes minimum value or maximum value respectively. And regular extension theory of fuzzy measures has been proposed. |
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| Keywords: | fuzzy measure Shapley entropy completion |
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