基于M-模糊化P-闭集族刻画M-模糊化拟阵  

Characterization of M-fuzzifying Matroids by M-fuzzifying Family of P-closed Sets

作　　者：王岚[1] 魏赟鹏[2] 

机构地区：[1]牡丹江师范学院数学科学学院,黑龙江牡丹江157011 [2]牡丹江医学院卫生经济管理学院,黑龙江牡丹江157011

出　　处：《数学的实践与认识》2017年第4期234-240,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11371002);黑龙江省自然科学基金(A201209);黑龙江省教育厅青年学术骨干项目(1251G063);黑龙江省教育厅资助项目(1351MSYYB010;1351MSYYB015);牡丹江师范学院科研项目(GY201204;GP2017001)

摘　　要：在已有M-模糊化拟阵的研究基础上,引入了M-模糊化秩函数及M-模糊化P-闭包算子的定义,研究了M-模糊化P-闭包算子的性质,并定义了M-模糊化P-闭集族及研究了它的基本性质,同时借助于M-模糊化拟阵的层拟阵结构,得到M-模糊化拟阵可由M-模糊化P-闭集族等价刻画这一结论.In this paper, based on existing research of M-fuzzifying matroids, by the defi- nitions of M-fuzzifying rank function and M-fuzzifying P-closure operators, some properties of M-fuzzifying P-closure operators are shown, and the notion of M-fuzzifying family of P- closed sets is defined, then its properties are found. By the cuts of M-fuzzifying matroid, it is proved that M-fuzzifying matroid can be expressed by M-fuzzifying family of P-closed sets. In short, it is a true that there is one-to-one corresponding between M-fuzzifying matroid and M-fuzzifying P-closure operators or M-fuzzifying family of P-closed sets.

关 键 词：M-模糊化拟阵 M-模糊化秩函数 M-模糊化P-闭包算子 M-模糊化 P-闭集族 

分 类 号：O159[理学—数学]