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An Uncertainty Measure Based on Lower and Upper Approximations for Generalized Rough set Models

Wang Zhaohao, Yue Huifang, Deng Jianping

Fundamenta Informaticae

2019

Vol. 166, nr 3

273--296

Uncertainty measures are an important tool for analyzing data. There is the uncertainty of a rough set caused by its boundary region in rough set models. Thus the uncertainty measurement issue is also an important topic for rough set theory. Shannon entropy has been introduced into rough set theory. However, there are relatively few studies on the uncertainty measure in generalized rough set models. We know that the boundary region of a rough set is closely related to the upper and lower approximations in rough set models. In this paper, from the viewpoint of the upper and lower approximations, we propose new uncertainty measures, the upper rough entropy and the lower rough entropy, in generalized rough set models. Then we focus on the investigations of the upper rough entropy, and give the concepts of the upper joint entropy, the upper conditional entropy and the mutual information with respect to a general binary relation. Some important properties of these measures are obtained. The connections among these measures are given. Furthermore, comparing with the existing uncertainty measures, the upper rough entropy has high distinguishing degree. Theoretical analysis and experimental results show that the proposed entropy is better effective than some existing measures.

Topological Structure of Relation-based Generalized Rough Sets

Zhang Y.-L., Li J., Li C.

Fundamenta Informaticae

2016

Vol. 147, nr 4

477--491

Rough set theory is an important tool to deal with vagueness and granularity in information systems. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough set approximations is based on equivalence relations and has been extended to relation-based generalized rough set approximations. In this paper, properties of relation-based generalized rough set approximations are examined, and topological properties of relation-based generalized rough set approximations presents. Necessary and sufficient conditions for the relation-based generalized upper (lower) approximation operators to be topological closure (interior) operators are proposed.