Theory exploration is a term describing the development of a formal (i.e. with the help of an automated proof-assistant) approach to selected topic, usually within mathematics or computer science. This activity however usually doesn’t reflect the view of science considered as a whole, not as separated islands of knowledge. Merging theories essentially has its primary aim of bridging these gaps ...

The role of opposition in rough set theory is laid bare. There are two sources which generate oppositions in rough sets: approximations and relations. In the former case, we outline a hexagon and a cube of oppositions. In the second case, we define a classical square of oppositions and also a tetrahedron when considering the standpoint of two agents.

This paper summarizes various formulations of the standard rough set theory. It demonstrates how those formulations can be adopted to develop different generalized rough set theories. The relationships between rough set theory and other theories are discussed. 1 Formulations of Standard Rough Sets The theory of rough sets can be developed in at least two different manners, the constructive and ...

background: using primary tumor gene expression has been shown to have the ability of finding metastasis-driving gene markers for the prediction of breast cancer recurrence (bcr). however, there are some difficulties associated with the analysis of microarray data which led to poor predictive power and inconsistency of the previously introduced gene signatures. methods: in this study a hybrid m...

There exist two formulations of rough sets: the conceptual and computational one. The conceptual or semantical approach of rough set theory focuses on the meaning and interpretation of concepts, while algorithms to compute those concepts are studied in the computational formulation. However, the research on the former is rather limited. In this paper, we focus on a semantically sound approach o...

In this paper, we intend to study a connection between rough sets and lattice theory. We introduce the concepts of upper and lower rough ideals (filters) in a lattice. Then, we offer some of their properties with regard to prime ideals (filters), the set of all fixed points, compact elements, and homomorphisms. 2012 Elsevier Inc. All rights reserved.

The aim of this paper is to give the basic concepts of rough set theory.