Abstract
Data sets, described by decision tables, are incomplete when for some cases (examples, objects) the corresponding attribute values are missing, e.g., are lost or represent “do not care” conditions. This paper shows an extremely useful technique to work with incomplete decision tables using a block of an attribute-value pair. Incomplete decision tables are described by characteristic relations in the same way complete decision tables are described by indiscernibility relations. These characteristic relations are conveniently determined by blocks of attribute-value pairs. Three different kinds of lower and upper approximations for incomplete decision tables may be easily computed from characteristic relations. All three definitions are reduced to the same definition of the indiscernibility relation when the decision table is complete. This paper shows how to induce certain and possible rules for incomplete decision tables using MLEM2, an outgrow of the rule induction algorithm LEM2, again, using blocks of attribute-value pairs. Additionally, the MLEM2 may induce rules from incomplete decision tables with numerical attributes as well.
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Grzymala-Busse, J.W. (2004). Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B., Świniarski, R.W., Szczuka, M.S. (eds) Transactions on Rough Sets I. Lecture Notes in Computer Science, vol 3100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27794-1_3
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DOI: https://doi.org/10.1007/978-3-540-27794-1_3
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