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On equivalence of conceptual scaling and generalized one-sided concept lattices
Butka P., Pócs J., Pócsová J. Information Sciences259 57-70,2014.Type:Article
Date Reviewed: Jun 3 2014

A technical account with mathematical proofs, this paper shows that the methods of conceptual scaling and generalized one-sided concept lattices are equivalent.

The paper can be split into three parts. The first part recalls the specificities of conceptual scaling and one-sided concept lattices. The second part provides an outline of the proposed approach to prove that these two methods are equivalent. This section shows that “the closure systems on the set of objects induced by corresponding Galois connections are the same” after applying the two methods separately. It also describes the “transformation of a many-valued context to the framework of generalized one-sided concept lattices.” The third part demonstrates that the attributes in generalized one-sided concept lattices can be reduced, and that object reduction is also possible, thus producing isomorphic concept lattices with a smaller number of attributes and objects. The final observation in the paper’s conclusion deserves mention: the choice to apply generalized one-sided concept lattices can be “more convenient” because the set of attributes is the same as in the many-valued context.

With a well-argued claim and well-presented proofs, this paper demonstrates that the applications of conceptual scaling and generalized one-sided concept lattices are equivalent, and the latter “can be easily transformed into a binary one using the scaling method.” It is good reading for scholars and students interested in reasoning, mathematical proofs, and formal concept representation.

Reviewer:  Mariana Damova Review #: CR142349 (1409-0790)
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Concept Learning (I.2.6 ... )
 
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