摘要
对MTL代数的模糊滤子理论作系统研究。在MTL代数中引入模糊NIMTL-滤子、模糊IMTL-滤子、模糊结合滤子和模糊强滤子四类新的模糊滤子概念,给出了它们的若干性质和等价刻画。系统讨论了这四类模糊滤子以及模糊Boolean滤子、模糊G-滤子和模糊MV-滤子间的相互关系,证明了一个模糊集为模糊Boolean滤子当且仅当它既是模糊G-滤子又是模糊NIMTL-滤子的结论。最后,将各类模糊滤子间的关系进行了总结梳理。
In this paper, the theory of fuzzy filters in MTL-algebras is studied systematically. Four types new notions of fuzzy NIMTL-filters, fuzzy IMTL-filters, fuzzy associative filters and fuzzy strong filters are introduced in MTL-algehras. Some properties and characterizations of them are given. Relations among these new fuzzy filters and fuzzy Boolean-filters, fuzzy G-filters fuzzy MV-filters are discussed systematically. It is proved that a fuzzy set is a fuzzy Boolean-filter if and only if it is both a fyzzy G-filter and a fuzzy NIMTL-filter. Finally, relations of all kinds fuzzy filters are summarized.
出处
《模糊系统与数学》
CSCD
北大核心
2015年第2期98-108,共11页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(10371106
60774073)
