# Decision Rule Mining in Rough Set Theory

**DOI:**https://doi.org/10.1007/978-1-4614-8265-9_563

## Synonyms

Classification rules; Decision rules; Rough computing; Rough set theory

## Definition of the Subject

Mathematically, a relation is a subset of a Cartesian product of sets, called attribute domains. In relational databases (RDB), however, we extend the concept of sets to bags that allow more than one occurrence of their elements [1]. In RDB, the main focus is on time-varying bag relations; in rough set theory (RST), they are interested in the instances of bag relations, called information tables (IT). An information table is called a decision table (DT), if the attributes are divided into two disjoint families, called conditional and decision attributes. A tuple in such a DT is called a decision rule. A sub-relation is called a value reduct, if it consists of a minimal subset of minimal length decision rules that has the same decision power as the original decision table. Value reducts of a DT are not necessary unique. The main theorem of RST is:

Reduct Theorem: *Every decision...*

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