| Heyting代数的模糊滤子格 |
| |
| 引用本文： | 刘春辉. Heyting代数的模糊滤子格[J]. 山东大学学报(自然科学版), 2013, 0(12): 57-60 |
| |
| 作者姓名： | 刘春辉 |
| |
| 作者单位： | [1]赤峰学院教务处,内蒙古赤峰024001 [2]赤峰学院数学与统计学院,内蒙古赤峰024001 |
| |
| 基金项目： | 国家自然科学基金资助项目（10371106,60774073） |
| |
| 摘 要： | 结合模糊集和滤子理论，对Heyting代数的模糊滤子概念作进一步研究。引入Heyting代数的由一个模糊集生成的模糊滤子的概念并获得了它的表示定理。在Heyting代数的全体模糊滤子之集上定义了格运算和蕴涵运算，证明了按此方式定义了格运算和蕴涵运算之后，全体模糊滤子之集形成一个完备Heyting代数的结论。
|
| 关 键 词： | 模糊逻辑 Heyting代数 模糊滤子 模糊滤子格 |
Lattice of fuzzy filter in a Heyting algebra |
| |
| LIU Chun-hui. Lattice of fuzzy filter in a Heyting algebra[J]. Journal of Shandong University(Natural Science Edition), 2013, 0(12): 57-60 |
| |
| Authors: | LIU Chun-hui |
| |
| Affiliation: | LIU Chun-hui ( 1. Office of Academic Affairs, Chifeng University, Chifeng 024001, Inner Mongolia, China; 2. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China) |
| |
| Abstract: | Combining fuzzy sets and filters theory, we further studied the concept of fuzzy filters in Heyting algebras. Reviewing the basic results of Heyting algebras and fuzzy filters, the concept of generated fuzzy filter by a fuzzy set in Heyting algebras is defined and its representation is obtained. Finally, the lattice operations and implication operation are defined on the set of all fuzzy filters in a Heyting algebra. It is proved that the fuzzy filters set with above operations form a complete Heyting algebra. |
| |
| Keywords: | fuzzy logic Heyting algebra fuzzy filter lattice of fuzzy filter |
| 本文献已被 维普 等数据库收录！ |
