Knowledge discovery from decision tables by the use of multiple-valued logic
This paper describes how succinct rules, which reduce the size of decision tables, can be found by employing multiple-valued logic (MVL). Two multiple-valued algebras are described, one based on level detection, and the other on literal functions. Then a decision table which had also been reduced in size using rough set theory, is now reduced using both algebras and it is seen that all three approaches lead to reductions of comparable simplicity. The new methods require coding the values of each attribute as integers. Then an MVL function that maps the coding of the condition attributes to the coding of the decision attribute is found. As the coded table is sparse only some of the basis functions for each algebra are required. Then a simple approach requiring the reduction of a matrix to row echelon form is used to finding all suitable MVL functions. By decomposing a function in terms of its variables a complete set of rules can be found. The MVL function encodes the data in a very compact form and its decomposition into subfunctions reveals a good way to slice up the table into subtables. The structure of the subfunctions can then be used to simplify each subtable until compact sets of rules emerge. Alternatively, rules can be found by substitution into the MVL function. Encoding a decision table using MVL makes the data easy to manipulate and can uncover relationships that may not become apparent when using other methods.
knowledge discovery decision tables multiple-valued logic rough sets matrix algebra rule induction