| 半群的R-模糊理想 |
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| 引用本文： | 朱晓英,廖祖华,郝翠芸,田超超.半群的R-模糊理想[J].江南大学学报(自然科学版),2011,10(5):612-616. |
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| 作者姓名： | 朱晓英 廖祖华 郝翠芸 田超超 |
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| 作者单位： | 江南大学理学院,江苏无锡,214122 |
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| 基金项目： | 国家自然科学基金项目(11001109); 江苏省教育科学“十一五”规划基金项目(D/2006/01/171); 江苏省教育厅基金项目(2009-598); 江南大学大学生创新训练计划项目(2010-596) |
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| 摘 要： | R-蕴涵算子与半群的模糊理想相结合引入半群的R-模糊理想的定义,得到了当R(x,y)对变量x递减时,两个半群的R-模糊理想的交仍是半群的R-模糊理想,当R(xy,)对变量x递增时,两个半群的R-模糊理想的并仍是半群的R-模糊理想的相关定理及推论。基于半群同态的定义,研究了R-模糊理想的满同态像及同态原像的相关性质,推出半群的R-模糊理想的满同态像及同态原像仍是半群的R-模糊理想;最后给出半群的R-模糊理想在8个蕴涵算子上的特征刻画。
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| 关 键 词： | 半群的R-模糊理想 R-蕴涵算子 半群同态 满同态像 同态原像 |
R-Fuzzy Ideals of Semigroups |
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| ZHU Xiao-ying,LIAO Zu-hua,HAO Cui-yun,TIAN Chao-chao.R-Fuzzy Ideals of Semigroups[J].Journal of Southern Yangtze University:Natural Science Edition,2011,10(5):612-616. |
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| Authors: | ZHU Xiao-ying LIAO Zu-hua HAO Cui-yun TIAN Chao-chao |
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| Institution: | ZHU Xiao-ying,LIAO Zu-hua,HAO Cui-yun,TIAN Chao-chao(School of Science,Jiangnan University,Wuxi 214122,China) |
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| Abstract: | The definition of R-fuzzy ideals of semigroups is introduced by combining R-implication operations and fuzzy ideals of semigroups.And we obtain the related theories and deductions that the intersection of two R-fuzzy ideals of semigroups is still a R-fuzzy ideal of semigroups when R(x,y) is decreasing on the variable x and the union of two R-fuzzy ideals of semigroups is still a R-fuzzy ideal of semigroups when R(x,y) is increasing on the variable x.Based on the definition of semigroup homomorphism,we study... |
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| Keywords: | R-fuzzy ideals of semigroups R-implication operations semigroup homomorphism full homomorphic image homomorphic preimage |
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