Rough Sets and Formal Concept Analysis:
   Foundations and the Case Studies of Feature
    Subset Selection and Knowledge Structure
                    Formation

                                  Dominik Ślȩzak

                           Infobright Inc., Canada/Poland

Abstract. The theories of Rough Sets (RS) and Formal Concept Analysis (FCA) are
well-established from the point of view of both mathematical foundations and real-life
applications. The interest in searching for similarities and dissimilarities between RS
and FCA has been constantly growing, both with respect to pure theory, as well as with
an objective of developing hybrid techniques, better adjusted to practical problems.
In this talk, we outline introductory notions of RS and we draw basic lines of its
comparison with FCA. As the first case study, we consider the KDD-related problem of
feature subset selection and show how to model some new approaches to approximate
selection (a more flexible and more practically applicable extension of the classical
RS-based feature subset selection principles) in the FCA terminology. As the second
case study, we consider the latest Infobright’s open source data warehouse platform
(www.infobright.org) and we discuss possibilities of improving its performance by using
new RS-FCA-based knowledge structures automatically calculated from data.