模糊拟阵的导出集合函数  

The Induced Set Function from Fuzzy Matroids

作　　者：吴德垠[1] WU De-yin(College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China)

机构地区：[1]重庆大学数学与统计学院,重庆401331

出　　处：《模糊系统与数学》2019年第1期1-11,共11页Fuzzy Systems and Mathematics

摘　　要：本文从改进模糊拟阵的独立模糊壳概念出发,提出"导出集合函数"概念;然后详细讨论了导出集合函数的值域、与独立模糊壳的关系和与基本序列的关系等。并且详细研究了利用导出拟阵列和基本序列来计算导出集合函数值的办法;接着,利用导出集合函数找到了描述独立模糊集和模糊基的充要条件;最后,通过这些充要条件,得到了闭模糊拟阵、准模糊图拟阵和闭正规模糊拟阵这三类模糊拟阵的充要条件。这些结论既丰富了模糊拟阵理论,同时,也提示了研究模糊拟阵的一种可能的新方法。Starting from improving 44 independent fuzzy shell”,the paper has defined u induced set function". Then, we have discussed value fields of induced set functions, a relation between induced set functions and independent fuzzy shells, another relation between induced set functions and fundamental sequences in detail. With help of induced matroid sequences and fundamental sequences, we have researched the method of calculating values about induced set functions. We also have found out the necessary and sufficient condition of independent fuzzy sets and fuzzy bases by induced set functions. Finally, we have used these necessary and sufficient conditions to get necessary and sufficient conditions of three type fuzzy matriods including closed fuzzy matroids, quasi-fuzzy graph matriods and closed regular fuzzy matroids. These conclusions have enriched the theory of fuzzy matroids, and too proposed a possible method about researching fuzzy matriods.

关 键 词：模糊拟阵 闭模糊拟阵 准模糊图拟阵 闭正规模糊拟阵 导出集合函数 独立模糊壳 

分 类 号：O157[理学—数学] O159[理学—基础数学]