Rules and Apriori Algorithm in Non-deterministic Information Systems

Automatic Extraction of Decision Rules from Non-deterministic Data Systems: Theoretical Foundations and SQL-Based Implementation

“…In particular, we show that the abovementioned NIS-related approximations of rules' parameters are fully expressible in SQL. It proves that the methodology established in [14,15] can be reimplemented within a database framework, which is important especially for the analysis of NISs with large amounts of objects and attributes, using such technologies as, e.g., Infobright Community Edition (ICE) [7,18]. Indeed, it is an ongoing research direction how to redesign the data mining tasks to work basing on intermediate results of dynamically generated SQL aggregations instead of extraction of large amounts of raw data to be processed outside a database.…”

“…For example, if someone wants to search for decision rules, such that support and accuracy are good enough no matter what the actual values in the given NIS might turn out to be, Definition 2 should be rewritten as follows: Obviously, it would be extremely difficult to solve such problems, if we had to operate explicitly on multiple DISs derived from the given NIS. In [15], it was shown that the quantities of minsup(τ ) and minacc(τ ) (or maxsup(τ ) and maxacc(τ )) can be computed over the same derived DIS, denoted as DIS τ worst (or DIS τ best ). Such results help in understanding the complexity of the problem.…”

“…In [15], several methods for computing the above quantities directly from NISs were reported. Because of a lack of space, let us describe just one of them.…”

“…Analogously, we can introduce the quantities of τ con all , τ dec all , τ con som and τ dec som . The following equations, proved as valid in [15], enable us to compute the quantities of minsup(τ ) and minsup(τ ) that are considered in Definition 4:…”

“…In this paper, we continue our research on defining and generating IF-THEN rules from NISs [14,15]. Unlike in other approaches, wherein the phase of rule generation is preceded by various statistical, heuristic procedures of completing data/information, we derive the rules directly from non-deterministic data.…”