Affiliations: [a] Maria Curie-Skłodowska University, Department of Logic and Cognitive Science, Maria Curie-Skłodowska Sq. 4, 20-031 Lublin, Poland. [email protected] | [b] University of Białystok, Faculty of Mathematics and Informatics, Konstantego Ciołkowskiego 1M, 15-245 Białystok, Poland. [email protected]
Correspondence:
[†]
Address for correspondence: Maria Curie-Skłodowska University, Department of Logic and Cognitive Science, Maria Curie-Skłodowska Sq. 4, 20-031 Lublin, Poland
Note: [*] The paper is an extended and revised version of our talk which was presented at the international workshop Concurrency, Specification & Programming, held on 25 – 27 September 2017 in Warsaw.
Abstract: Pattern structures were introduced by Ganter and Kuznetsov in the framework of formal concept analysis (FCA) as a mean to direct analysis of objects having complex descriptions, e.g., descriptions presented in the form of graphs instead of a set of properties. Pattern structures actually generalise/replace the original FCA representation of the initial information about objects, that is, formal contexts (which form a special type of data tables); as a consequence, pattern structures are regarded in FCA as given (in some sense a priori to the analysis) rather than built (a posteriori) from data. The main goal of this paper is twofold: firstly, we would like to export the idea of pattern structures to and consistently with the framework/methodology of rough set theory (RST); secondly, we want to derive pattern structures from simple data tables rather than to regard them as the initial information about objects. To this end we present and discuss two methods of generating non-trivial pattern structures from simple information systems/tables. Both methods are inspired by near set theory, which is a methodology theoretically close to rough set theory, but developed in the topological settings of (descriptive) nearness of sets. Interestingly, these methods bear formal connections to other ideas from RST such as generalised decisions or symbolic value grouping.
Keywords: rough set theory, formal concept analysis, near set theory, pattern structures
