2012/10/23 by Yanfang Liu, Liu, Yanfang, William Zhu +1
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #I.2.3 #I.2.4 #Rough Sets and Fuzzy Logic #cs.AI
paper · pdf · doi:10.48550/arxiv.1210.6209
12 pages
arxiv created 2012/10/23 · openalex publication_date 2012/10/23 · arxiv updated 2012/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence in vector spaces, and has a variety of applications in many fields. In this paper, we propose a new type of matroids, namely, partition-circuit matroids, which are induced by partitions. Firstly, a partition satisfies circuit axioms in matroid theory, then it can induce a matroid which is called a partition-circuit matroid. A partition and an equivalence relation on the same universe are one-to-one corresponding, then some characteristics of partition-circuit matroids are studied through rough sets. Secondly, similar to the upper approximation number which is proposed by Wang and Zhu, we define the lower approximation number. Some characteristics of partition-circuit matroids and the dual matroids of them are investigated through the lower approximation number and the upper approximation number.