Characteristic of partition-circuit matroid through approximation number

TL;DR

This paper introduces partition-circuit matroids induced by partitions, exploring their properties through rough set theory and approximation numbers, thereby linking matroid theory with rough set concepts.

Contribution

It proposes a new class of matroids called partition-circuit matroids and studies their characteristics using rough set approximation numbers.

Findings

Partition-circuit matroids are induced by partitions satisfying circuit axioms.

Characteristics of these matroids are analyzed via upper and lower approximation numbers.

Dual matroids of partition-circuit matroids are also characterized using approximation numbers.

Abstract

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.