计算机科学与探索2017，Vol.11Issue(11)：1860-1870,11.DOI:10.3778/j.issn.1673-9418.1608028
剩余格的犹豫模糊滤子理论
Hesitant Fuzzy Filter Theory of Residuated Lattices
摘要
Abstract
By applying hesitant fuzzy set to the filter theory of residuated lattices, this paper proposes the concepts of hesitant fuzzy filters, hesitant fuzzy implicative filters, hesitant fuzzy positive implicative filter, hesitant fuzzy MV-filters and hesitant fuzzy regular filters of residuated lattices, investigates their properties, discusses their rela-tions, and obtains some equivalent characterizations between them. Then, this paper gives the conditions for a hesi-tant fuzzy set translating into a hesitant fuzzy filter and for a hesitant fuzzy filter translating into a hesitant fuzzy (positive implicative, MV, regular) implicative filter. Finally, this paper studies the relations between kinds of filters and its corresponding level filters, and establishes the extension theorems of hesitant fuzzy Boolean filters and hesi-tant fuzzy regular filters of residuated lattices.关键词
剩余格/犹豫模糊集/犹豫模糊(蕴涵、正定蕴涵、MV、正规)滤子/犹豫模糊集的水平集Key words
residuated lattice/hesitant fuzzy set/hesitant fuzzy (implicative/positive implicative/MV/regular) filter/level sets of a hesitant fuzzy set分类
信息技术与安全科学引用本文复制引用
彭家寅..剩余格的犹豫模糊滤子理论[J].计算机科学与探索,2017,11(11):1860-1870,11.基金项目
The National Natural Science Foundation of China under Grant No. 11071178 (国家自然科学基金) （国家自然科学基金）
the Comprehensive Reform of Mathematics and Applied Mathematics of the Ministry of Education of China under Grant No. ZG0464 (教育部数学与应用数学专业综合改革). （教育部数学与应用数学专业综合改革）
