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首页> 外文会议>International Conference on Soft Methods in Probability and Statistics(SMPS'2004); 200405; Oviedo(ES) >On Limit Theorems for Random Fuzzy Sets Including Large Deviation Principles
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On Limit Theorems for Random Fuzzy Sets Including Large Deviation Principles

机译：包含大偏差原理的随机模糊集的极限定理

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摘要

Study of random fuzzy sets or fuzzy set-valued random variables was initiated by Feron and Kwakernaak in late 70's, about ten years after the famous paper by Zadeh. A systematic treatment of them was done by Puri and Ralescu in the case when the underlying space is R~d. For the general underlying space, see Li and Ogura. In this paper, after a short survey on traditional limit theorems such as laws of large numbers, a Law of Iterated Logarithm and Central Limit Theorems for independent random fuzzy sets as well as martingale convergence theorems with respect to the uniform Hausdorff topology, we give large deviation principles for independent identically distributed random fuzzy sets taking values in n-dimensional Euclidean spaces. We give Cramer type LDPs with respect to graphic Hausdorff topology and cylindrical Hausdorff topology, and a Sanov type LDP for the empirical probability measures on the cylindrical σ-field with respect to τ-topology. A couple of simple examples will also be given.
机译：Feron和Kwakernaak在70年代后期（距Zadeh的著名论文约十年后）开始研究随机模糊集或模糊集值随机变量。当基础空间为Rd时，Puri和Ralescu对它们进行了系统的处理。有关一般的基础空间，请参见Li和Ogura。在对传统的极限定理（例如大数定律），独立对数模糊集的对数定律和中心极限定理以及mar一致Hausdorff拓扑的mar收敛定理进行简短调查之后，我们给出了n维欧氏空间中取值的独立同分布随机模糊集的偏差原理。对于图形Hausdorff拓扑和圆柱Hausdorff拓扑，我们给出了Cramer型LDP，对于圆柱σ场中关于τ拓扑的经验概率测度，给出了Sanov型LDP。还将给出几个简单的例子。

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