Extended methodology for deriving formal concepts

Two methodologies for formal concepts derivation are considered: the classical one, which focuses on the posterior analysis of the object’s properties of the studied knowledge domain, and non-classical, the cornerstone of which is the a priori formation of the set of measured object’s properties and the determination of existential relations on this set. In the article, firstly, a position is fixed in the technological chain of the target transformation of the source data, where the difference between considered methodologies shows itself. Secondly, the commonality of these two approaches is established in the aspect of the unity of their hypothetical-deductive basis. In this case, the cognitive activity of the subject is expressed first in a priori and then in a posteriori conceptual scaling of the measured properties. The work demonstrates the need for the joint use of the considered methodologies at processing incomplete and inconsistent empirical data about studied knowledge domain. The intermediate consolidation of these methodologies is possible only on the basis of multi-valued logic.

A PARAMETERIZED ALGORITHM TO EXPLORE FORMAL CONTEXTS WITH A TAXONOMY

Formal Concept Analysis (FCA) is a natural framework to learn from examples. Indeed, learning from examples results in sets of frequent concepts whose extent contains mostly these examples. In terms of association rules, the above learning strategy can be seen as searching the premises of rules where the consequence is set. In its most classical setting, FCA considers attributes as a non-ordered set. When attributes of the context are partially ordered to form a taxonomy, Conceptual Scaling allows the taxonomy to be taken into account by producing a context completed with all attributes deduced from the taxonomy. The drawback, however, is that concept intents contain redundant information. In this article, we propose a parameterized algorithm, to learn rules in the presence of a taxonomy. It works on a non-completed context. The taxonomy is taken into account during the computation so as to remove all redundancies from intents. Simply changing one of its operations, this parameterized algorithm can compute various kinds of concept-based rules. We present instantiations of the parameterized algorithm to learn rules as well as to compute the set of frequent concepts.