| 关于PFI-代数与剩余格 |
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| 引用本文： | 朱怡权,曹喜望.关于PFI-代数与剩余格[J].数学进展,2006,35(2):223-231. |
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| 作者姓名： | 朱怡权 曹喜望 |
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| 作者单位： | 1. 肇庆学院数学系,肇庆,广东,526061
2. 南京航空航天大学数学系,210016 |
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| 基金项目： | 广东省博士启动基金;广东省自然科学基金 |
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| 摘 要： | 本文提出了一种强FI代数-PFI代数,并且深入研究了它的性质,借此进一步揭示了FI-代数和剩余格之间更加密切的联系,进而以FI-代数为基本框架建立了R0-代数、正则剩余格等逻辑系统的结构特征(包括对隅结构)及其相互关系．这种以FI-代数为基础来统一处理剩余格和R0-代数的方法,同样适合于格蕴涵代数和MV代数等代数结构,而且从中更能清楚地看出它们之间的密切联系,也将有助于对相应形式逻辑系统与模糊推理的研究．
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| 关 键 词： | 多值逻辑 (正则)PFI-代数 (正则)剩余格 (弱)R0-代数 对偶结构 |
| 文章编号： | 1000-0917（2006）02-0223-09 |
| 收稿时间： | 2003-10-12 |
| 修稿时间： | 2003年10月12 |
On PFI-algebras and Residuated Lattices |
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| ZHU Yi-quan,CAO Xi-wang.On PFI-algebras and Residuated Lattices[J].Advances in Mathematics,2006,35(2):223-231. |
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| Authors: | ZHU Yi-quan CAO Xi-wang |
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| Institution: | 1. Dept. of Math., Zhaoqing University, Zhaoqing, Guangdong, 526061, P. R. China; 2. School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China |
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| Abstract: | In this paper, a new kind of the special fuzzy implication algebras-PFI-algebras are introduced, their fundamental properties are obtained, and the close connections between PFI-algebras and residuated lattices are established. Moreover, for (weak) R0-algebras and (strong) regular residuated lattices, their interrelation and the characterizations of interior structures (including dual structures) are established by the concept of the PFI-algebras. Those results will be useful for further studying the corresponding formal deductive systems and fuzzy reasoning. |
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| Keywords: | multiple-valued logic (regular)PFI-algebra (regular) residuated lattice (weak) R0-algebras dual structure |
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