以下为句子列表：
英文: Based on intersection-representation theorems, the relationships between the intersection-representation theorem and the union-representation theorem of the both-branch fuzzy set are analyzed, and its operational property is discussed.
中文: 利用交－表现定理分析了双枝模糊集的运算性质，讨论了双枝模糊集并－表现定理与交－表现定理的关系。
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英文: Based on the concept of the both-branch fuzzy set, the intersection-representation theorem of the both-branch fuzzy set is put forward.
中文: 摘要利用双枝模糊集的概念，提出了双枝模糊集表现定理的对偶形式，即交－表现定理。
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英文: The results indicate that the intersection-representation theorem of the both-branch fuzzy set is the general form of the intersection-representation theorem of the Zadeh fuzzy set, and the intersection-representation theorem of the Zadeh fuzzy set is the
中文: 通过分析得到：双枝模糊集交－表现定理是单枝模糊集交－表现定理的一般形式，单枝模糊集交－表现定理是双枝模糊集交－表现定理的特例。
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英文: In 97 , Kac and Siegert offered a representation theorem without proof for the response of a second order Volterra system due to a stationary Gaussian excitation.
中文: 97年,Neal根据Kac和Siegert的思想,给出了一个在电子工程、海洋工程、建筑工程、航空工程、自动控制的随机振动中有重要应用的二阶Volterra非线性系统对平稳正态输入的统计响应的表示定理. 98年,Naess对此定理又给出了一个数学证明.
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