| 模糊BCH-代数与Ω-模糊BCH-代数 |
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| 引用本文： | 彭家寅.模糊BCH-代数与Ω-模糊BCH-代数[J].内江师范学院学报,2007,22(4):5-10. |
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| 作者姓名： | 彭家寅 |
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| 作者单位： | 内江师范学院,数学系,四川,内江,641112;四川省高等学校数值仿真重点实验室,四川,内江,641112 |
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| 基金项目： | 四川省教育厅重点实验室专项基金(2006ZD050). |
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| 摘 要： | 引入了BCH-代数的模糊子代数与-模糊子代数的概念,给出了它们的恰当例子.利用模糊子代数描述了-模糊子代数.反之,利用-模糊子代数构造了模糊子代数.讨论了模糊子代数(Ω-模糊子代数)的同态象与同态原象能成为-模糊子代数(模糊子代数).最后,提出了Ω-模糊理想的概念,并研究了它的一些相关性质.
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| 关 键 词： | BCH-代数 模糊子集 模糊子代数 Ω-模糊子集 Ω-模糊子代数 Ω-模糊理想 |
| 文章编号： | 1671-1785（2007）04-0005-06 |
| 修稿时间： | 2006-12-18 |
Fuzzy BCH-algebras and Ω-fuzzy BCH-algebras |
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| PENG Jia-yin.Fuzzy BCH-algebras and Ω-fuzzy BCH-algebras[J].Journal of Neijiang Teachers College,2007,22(4):5-10. |
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| Authors: | PENG Jia-yin |
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| Institution: | 1. Department of Mathematics, Neijiang Teachers College, Neijiang, Sichuan 641112, China ; 2. Sichuan Provincal Key Laboratory of Numerical Simulation, Neijing Teachers College, Neijiang, Sichuan 641112, China |
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| Abstract: | The notions of fuzzy subalgebras and Ω-fuzzy subalgebras of BCH-algebras are introduced, and some appropriate examples are provided. Using fuzzy subalgebras, Ω-fuzzy subalgebras are described. Conversely,fuzzy subalgebras are constructed by using Ω-fuzzy subalgebras. It is stated that the homomorphic images and inverse images of fuzzy subalgebras (Ω-fuzzy subalgebras) become fuzzy subalgebras (Ω-fuzzy subalgebras).Finally, the notion of Ω-fuzzy ideals of BCH-algebras is put forward, and some related properties are investigated. |
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| Keywords: | BCH-algebra fuzzy set fuzzy subalgebra Ω-fuzzy set Ω-fuzzy subalgebras Ω-fuzzy ideal |
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