A computational procedure for variable selection preserving different initial conditions

ABSTRACT

The reduction of the set of attributes is an important preliminary challenge in order to obtain information from knowledge systems. Two remarkable formal tools for extracting such information are rough set theory (RST) and formal concept analysis (FCA). This work introduces a new method to reduce attributes in FCA considering the reduction philosophy given in RST. This method allows to carry out a deeper study of the relation between these two theories. Furthermore, several interesting properties of such a reduction have been proved and examples have been introduced to illustrate the mechanism.

KEYWORDS:

• Attributes reduction
• reduct
• formal concept analysis
• rough sets theory

2010 AMS SUBJECT CLASSIFICATIONS:

• 06Axx Ordered sets 06A15 Galoiscorrespondences
• closure operators

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Note that the discernibility matrix is symmetric due to the discernibility relation is symmetric, for that reason only the elements under the diagonal are written.

2 In order to simplify the notation, we will write ${(}^{{\uparrow }_1}{,}^{{\downarrow }^1})$ instead of ${(}^{{\uparrow }_{D_1}}{,}^{{\downarrow }^{D_1}})$ to denote the concept-forming operators in the reduced context given by $D_1$.

Additional information

Funding

Partially supported by the State Research Agency (AEI) and the European Regional Development Fund (FEDER) project TIN2016-76653-P.