摘要
设U是全集,R是U上的等价关系,(U,R)是相应的近似空间,则粗相等关系≈是幂集P(U)上的等价关系,其商集为P(U)/≈,而商集P(U)/≈是一个分配格,本文考虑两种特殊情况,使得在这两种特殊情况下粗糙度有类似于集合论的包容排斥原理,同时我们还把此结论推广到粗糙模糊集上。
Let U denote a finite and nonempty set called the universe, and P(U) a power set of U. Suppose that R is an equivalence relation on U. We proved that if X or Y is the definable set, then between the roughness measures of sets X,Y, X∩Y and X∪Y have a similar inclusion-exclusion principle for rough, sets. Consider the roughly equal relation which is an equivalence relation on P(U),the equivalence relation partitions the P(U) into disjoint subsets. The quotient set is denoted by F(U)/≈ We obtain a similar inclusion-exclusion principle on P(U)/≈.. We also extend these results to rough fuzzy sets.
出处
《计算机科学》
CSCD
北大核心
2004年第3期140-141,153,共3页
Computer Science
基金
教育部科学技术重点项目(01043)资助
关键词
粗糙集理论
粗糙度
数据处理
知识集合
Rough fuzzy set, Roughness measures, Lower approximation. Upper approximation
