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Rough approximations induced by orthocomplementations in formal contexts. (English) Zbl 1398.68546

Flores, Víctor (ed.) et al., Rough sets. International joint conference, IJCRS 2016, Santiago de Chile, Chile, October 7–11, 2016. Proceedings. Cham: Springer (ISBN 978-3-319-47159-4/pbk; 978-3-319-47160-0/ebook). Lecture Notes in Computer Science 9920. Lecture Notes in Artificial Intelligence, 97-106 (2016).
Summary: Formal contexts is a common framework for rough set theory and formal concept analysis, and some rough set models in formal contexts have been proposed. In this paper, based on the theory of abstract approximation spaces presented by G. Cattaneo [in: Rough sets in knowledge discovery 1. Methodology and applications. Heidelberg: Physica-Verlag. 59–98 (1998; Zbl 0927.68087)], a Brouwer orthocomplementation on the set of objects of a formal context is presented, as a result, a pair of new lower and upper rough approximation operators is introduced. Comparison between the new approximation operators and the existing approximation operators is made, and two necessary and sufficient conditions about equivalence of the operators are obtained. Relationships and algebraic structures among the definable subsets of these approximation operators are investigated.
For the entire collection see [Zbl 1346.68009].

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
68T30 Knowledge representation

Citations:

Zbl 0927.68087
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