基于非交换剩余格的模糊蕴涵滤子及其性质

J4 ›› 2010, Vol. 45 ›› Issue (10): 61-65.

基于非交换剩余格的模糊蕴涵滤子及其性质

郝加兴,吴洪博

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2009-06-15 出版日期:2010-10-16 发布日期:2010-10-19
作者简介:郝加兴(1983-),男,硕士研究生,研究方向为非经典数理逻辑.Email:jiaxinghao2008@126.com
基金资助:
国家自然科学基金资助项目(10871121)

Fuzzy implicative filters of non-commutative residuated lattices and their properties

HAO Jia-xing, WU Hong-bo

College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an 710062, Shaanxi, China

Received:2009-06-15 Online:2010-10-16 Published:2010-10-19

摘要/Abstract

摘要：

对非交换剩余格的结构作了进一步研究。结合模糊数学的思想和方法, 在非交换剩余格上引入了模糊滤子,讨论了模糊滤子与分明滤子之间的关系; 并且在模糊滤子的基础上引入了模糊蕴涵滤子和模糊正蕴涵滤子的概念, 并讨论其基本性质,给出了模糊蕴涵滤子和模糊正蕴涵滤子的等价刻画, 证明了模糊正蕴涵滤子一定是模糊蕴涵滤子, 模糊蕴涵滤子和模糊正蕴涵滤子在一定条件下是等价的。

关键词: 模糊逻辑;非交换剩余格;模糊滤子;模糊蕴涵滤子;模糊正蕴涵滤子

Abstract:

The structure of non-commutative residuated lattices is further studied.With the help of the thought and method of fuzzy mathematics, the concept of fuzzy filters is introduced, and the relations between fuzzy filters and crisp filters of non-commutative residuated lattices are discussed. On the basis of fuzzy filters, fuzzy implicative filters and fuzzy positive implicative filters of non-commutative residuated lattices are introduced. The basic properties of them are discussed, and then several equivalent characterizations for fuzzy implicative filters and fuzzy positive implicative filters are given.It is proved that fuzzy positive implicative filters must be fuzzy implicative filters. Under certain conditions, the equivalence of fuzzy implicative filters and fuzzy positive implicative filters is proved.

Key words: fuzzy logic; non-commutative residuated lattices; fuzzy filters; fuzzy implicative filters; fuzzy positive implicative filters

郝加兴,吴洪博. 基于非交换剩余格的模糊蕴涵滤子及其性质[J]. J4, 2010, 45(10): 61-65.

HAO Jia-xing, WU Hong-bo. Fuzzy implicative filters of non-commutative residuated lattices and their properties[J]. J4, 2010, 45(10): 61-65.

参考文献

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed