【作者】 王琼；

【导师】 宋振明；

【作者基本信息】 西南交通大学 ， 应用数学， 2004， 硕士

【摘要】 自Zadeh于1965年提出模糊集概念以来，模糊控制技术作为现代工业与新产品开发的高新技术之一，受到国内外普遍重视，而且在应用领域取得了令人瞩目的成功。模糊推理是模糊控制的核心内容之一，而推理又基于逻辑。针对如今在控制领域中广泛应用的CRI等方法的缺陷，王国俊教授提出了一种更为合理、逻辑基础更强的推理算法——三Ⅰ算法。 蕴涵算子的选取与模糊推理的效果密切相关。目前在模糊控制中用得比较多的是R_O和R_L蕴涵算子，它们都是属于特殊的剩余蕴涵算子，具有许多良好的性质。因此研究剩余蕴涵算子对将模糊推理与模糊逻辑和模糊控制相结合具有重要而广泛的意义，进而为实现新型模糊控制器地某些性能指标提供必要的理论依据。本文的目的就是讨论基于剩余蕴涵算子分析讨论模糊推理三Ⅰ算法。 本文首先基于Zadeh提出的CRI等算法中的缺陷与不足，探讨模糊推理三Ⅰ理论，给出基于剩余蕴涵算子的三Ⅰ方法的FMP与FMT算法的计算公式，并考虑算法的还原性：其次，分析了三Ⅰ方法的支持度理论和约束度理论，给出了α—FMP与FMT的计算公式；并进一步讨论了基于剩余蕴涵算子的反向三Ⅰ算法，给出其计算公式；最后，通过在区间值模糊集上引进偏序关系，探讨基于剩余蕴涵算子的区间值模糊推理三Ⅰ算法。更多还原

【Abstract】 As one of the high and new techniques that develop modern industry and new products, fuzzy control technique has attracted so much attention and obtained the outstanding success in the applied areas, since Zadeh brought up the concept of fuzzy sets in 1965. Professor Wang Guojun set forth a new triple-I algorithm for the defect of CRI method applied extensively in control areas. This new method is more reasonable and has better logic foundation.The selection of implication has closely related with the result of fuzzy reasoning. Now R0 and Rl operators, which belong to special residual implication operator and have many fine properties, are used mostly in fuzzy control. So this research has important and extensive significance to combine fuzzy reasoning with fuzzy logic and fuzzy control. The textual purpose is to discuss the triple-I algorithm of fuzzy reasoning based on residual implication operator.Firstly, this text further develops the triple-I theory of fuzzy reasoning based on the defect of CRI algorithm, gives the formula of triple-I FMP and FMT based on residual implication operator and discusses their reducible properties. Secondly, the sustaining and restraining theories of triple-I method are discussed and the formula of a-FMP and FMT are provided. Then the reverse triple-I algorithm are discussed based on residual implication operator. Finally, because common fuzzy reasoning is special interval fuzzy reasoning, we set up the interval fuzzy reasoning based on residual implication operator by introducing the relation of partial order.更多还原