Decision and Inhibitory Rule Optimization for Decision Tables with Many-valued Decisions
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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Abstract‘If-then’ rule sets are one of the most expressive and human-readable knowledge representations. This thesis deals with optimization and analysis of decision and inhibitory rules for decision tables with many-valued decisions. The most important areas of applications are knowledge extraction and representation. The benefit of considering inhibitory rules is connected with the fact that in some situations they can describe more knowledge than the decision ones. Decision tables with many-valued decisions arise in combinatorial optimization, computational geometry, fault diagnosis, and especially under the processing of data sets. In this thesis, various examples of real-life problems are considered which help to understand the motivation of the investigation. We extend relatively simple results obtained earlier for decision rules over decision tables with many-valued decisions to the case of inhibitory rules. The behavior of Shannon functions (which characterize complexity of rule systems) is studied for finite and infinite information systems, for global and local approaches, and for decision and inhibitory rules. The extensions of dynamic programming for the study of decision rules over decision tables with single-valued decisions are generalized to the case of decision tables with many-valued decisions. These results are also extended to the case of inhibitory rules. As a result, we have algorithms (i) for multi-stage optimization of rules relative to such criteria as length or coverage, (ii) for counting the number of optimal rules, (iii) for construction of Pareto optimal points for bi-criteria optimization problems, (iv) for construction of graphs describing relationships between two cost functions, and (v) for construction of graphs describing relationships between cost and accuracy of rules. The applications of created tools include comparison (based on information about Pareto optimal points) of greedy heuristics for bi-criteria optimization of rules, and construction (based on multi-stage optimization of rules) of relatively short systems of rules that can be used for knowledge representation.
Showing items related by title, author, creator and subject.
Decision rules for decision tables with many-valued decisionsChikalov, Igor; Zielosko, Beata (Springer Science + Business Media, 2011)In the paper, authors presents a greedy algorithm for construction of exact and partial decision rules for decision tables with many-valued decisions. Exact decision rules can be 'over-fitted', so instead of exact decision rules with many attributes, it is more appropriate to work with partial decision rules with smaller number of attributes. Based on results for set cover problem authors study bounds on accuracy of greedy algorithm for exact and partial decision rule construction, and complexity of the problem of minimization of decision rule length. © 2011 Springer-Verlag.
Optimization of decision rule complexity for decision tables with many-valued decisionsAzad, Mohammad; Chikalov, Igor; Moshkov, Mikhail (Institute of Electrical and Electronics Engineers (IEEE), 2013-10)We describe new heuristics to construct decision rules for decision tables with many-valued decisions from the point of view of length and coverage which are enough good. We use statistical test to find leaders among the heuristics. After that, we compare our results with optimal result obtained by dynamic programming algorithms. The average percentage of relative difference between length (coverage) of constructed and optimal rules is at most 6.89% (15.89%, respectively) for leaders which seems to be a promising result. © 2013 IEEE.
Minimization of Decision Tree Average Depth for Decision Tables with Many-valued DecisionsAzad, Mohammad; Moshkov, Mikhail (Elsevier BV, 2014-09-13)The paper is devoted to the analysis of greedy algorithms for the minimization of average depth of decision trees for decision tables such that each row is labeled with a set of decisions. The goal is to find one decision from the set of decisions. When we compare with the optimal result obtained from dynamic programming algorithm, we found some greedy algorithms produces results which are close to the optimal result for the minimization of average depth of decision trees.