模糊转移系统的双模拟

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摘要翻译：
用模糊语言等价来比较模糊系统的行为已经有很长的历史，但这一层次的比较过于粗糙。最近，模糊有限自动机中引入了一种更精细的行为测度&双模拟。然而，所得结果仅适用于有限状态系统。本文通过将一般的模糊系统建模为模糊转移系统，研究了无穷状态或无穷事件的模糊系统的双模拟问题。为了帮助理解和检查双模拟，我们用三种方式来描述它，即枚举整个转换，比较单个转换，以及使用单调函数。此外，我们还讨论了模糊转移系统的合成运算、子系统、商和同态，并讨论了它们与双模拟有关的性质。本文给出的结果对于比较一般模糊系统的行为是有用的。特别是，这使得有可能将一个无限模糊系统与一个更容易分析的有限模糊系统联系起来，具有相同的行为。
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英文标题：
《Bisimulations for fuzzy transition systems》
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作者：
Yongzhi Cao, Guoqing Chen, and Etienne Kerre
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最新提交年份：
2010
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
  There has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems, but the comparison at this level is too coarse. Recently, a finer behavioral measure, bisimulation, has been introduced to fuzzy finite automata. However, the results obtained are applicable only to finite-state systems. In this paper, we consider bisimulation for general fuzzy systems which may be infinite-state or infinite-event, by modeling them as fuzzy transition systems. To help understand and check bisimulation, we characterize it in three ways by enumerating whole transitions, comparing individual transitions, and using a monotonic function. In addition, we address composition operations, subsystems, quotients, and homomorphisms of fuzzy transition systems and discuss their properties connected with bisimulation. The results presented here are useful for comparing the behavior of general fuzzy systems. In particular, this makes it possible to relate an infinite fuzzy system to a finite one, which is easier to analyze, with the same behavior.
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PDF链接：
https://arxiv.org/pdf/1012.2148

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