| Fuzzy蕴涵代数的MP理想与正规MP理想 |
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| 引用本文： | 师涛,徐罗山. Fuzzy蕴涵代数的MP理想与正规MP理想[J]. 模糊系统与数学, 2009, 23(5) |
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| 作者姓名： | 师涛 徐罗山 |
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| 作者单位： | 无锡科技职业学院,基础部,江苏,无锡,214028;扬州大学,数学科学学院,江苏,扬州,225002;扬州大学,数学科学学院,江苏,扬州,225002 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 在Fuzzy蕴涵代数(简称FI代数)上引入了MP理想与正规MP理想的概念并给出了它们的等价刻画;探讨了FI代数的MP理想、偏序理想和正规MP理想间的多种关系, 证明了一个正则FI代数是可交换FI代数当且仅当它的每个MP理想都是正规理想,也当且仅当{0}是正规MP理想.
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| 关 键 词： | Fuzzy蕴涵代数 正则FI代数 MP理想 正规MP理想 |
MP-ideals and Normal MP-ideals in Fuzzy Implication Algebras |
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| Abstract: | In this paper, the concepts of MP-ideals and normal MP-ideals in Fuzzy implication algebras (in short, FI-algebras) are introduced. Characterizations of MP-ideals and normal MP-ideals are given. Relations of MP-ideals, partial ordering related ideals and normal MP-ideals are discussed. It is proved that an FI-algebra is commutative iff its MP-ideals are normal iff {0} is a normal MP-ideal. |
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| Keywords: | Fuzzy Implication Algebra Regular FI-algebra MP-ideal Normal MP-ideal |
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