By Claude Brezinski
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Additional resources for Algorithmes d'acceleration de la convergence: etude numerique
6, and that married individuals constitute 65% and singles make up 35% of the extent. 13). Categorization is the process of arranging individuals into categories. , Males, Volvo, Make of car, Leigh’s credit card expenses, and so on). Since we have the concept (Males, Volvo, Leigh, ) and we have a way of finding its extent, it is easy to obtain the components of the category by its extent. Therefore, in practice, the question of how to categorize is transformed to the question of how to obtain the extent of the concept from the database.
Hence, whereas a concept is defined by an intent and an extent, it is modeled by an intent and a way of finding its extent by symbolic objects akin to the workings of our mind. Since it is quite impossible to obtain all the characteristic properties (the complete description d) and the complete extent of a concept, a symbolic object therefore is just an approximation of a concept. This raises the question of the quality, robustness, and reliability of this approximation; we return to this issue later.
Or, there may be a rule that says that two variables Y1 and Y2 must satisfy the relation Y1 + Y2 = (say), and so on. Such rules may exist because of an inherent interest in variable outcomes that match such dependencies. Another type of logical dependency is necessary to maintain data integrity. When aggregating individual values (which would typically be classical values at a first level of aggregation; but which can in fact be symbolic-valued variables) into the relevant symbolic-valued data that make up the categories dictating that aggregation, the very process of aggregation can produce symbolic data which perforce engage the adoption of rule(s) to maintain data integrity.