Studies in Computational Intelligence

2 primary works

Partial Covers, Reducts and Decision Rules in Rough Sets

by Mikhail Ju. Moshkov, Marcin Piliszczuk, and Beata Zielosko

Published 12 February 2009

This monograph is devoted to theoretical and experimental study of partial reductsandpartialdecisionrulesonthebasisofthestudyofpartialcovers. The use of partial (approximate) reducts and decision rules instead of exact ones allowsustoobtainmorecompactdescriptionofknowledgecontainedindecision tables,andtodesignmorepreciseclassi?ers. Weconsideralgorithmsforconstructionofpartialreductsandpartialdecision rules,boundsonminimalcomplexityofpartialreductsanddecisionrules,and algorithms for construction of the set of all partial reducts and the set of all irreducible partial decision rules. We discuss results of numerous experiments with randomly generated and real-life decision tables. These results show that partial reducts and decision rules can be used in data mining and knowledge discoverybothforknowledgerepresentationandforprediction. Theresultsobtainedinthe monographcanbe usefulforresearchersinsuch areasasmachinelearning,dataminingandknowledgediscovery,especiallyfor thosewhoareworkinginroughsettheory,testtheoryandLAD(LogicalAnalysis ofData). The monographcan be usedunder the creationofcoursesforgraduates- dentsandforPh. D. studies.
An essential part of software used in experiments will be accessible soon in RSES-RoughSetExplorationSystem(InstituteofMathematics,WarsawU- versity,headofproject-ProfessorAndrzejSkowron). We are greatly indebted to Professor Andrzej Skowron for stimulated d- cussionsand varioussupportof ourwork. We aregratefulto ProfessorJanusz Kacprzykforhelpfulsuggestions. Sosnowiec,Poland MikhailJu. Moshkov April2008 MarcinPiliszczuk BeataZielosko Contents Introduction...1 1 PartialCovers,ReductsandDecisionRules ...7 1. 1 PartialCovers...8 1. 1. 1 MainNotions...8 1. 1. 2 Known Results...9 1. 1. 3 PolynomialApproximateAlgorithms...10 1. 1. 4 Bounds on C (?)Based on Information about min GreedyAlgorithm Work...13 1. 1. 5 UpperBoundon C (?)...17 greedy 1. 1. 6 Covers fortheMostPartofSetCoverProblems...18 1. 2 PartialTests and Reducts...22 1. 2. 1 MainNotions...22 1. 2. 2Relationships betweenPartialCovers and Partial Tests...23 1. 2. 3 PrecisionofGreedyAlgorithm...24 1. 2. 4 PolynomialApproximateAlgorithms...25 1. 2. 5 Bounds on R (?)Based on Information about min GreedyAlgorithm Work...26 1. 2. 6 UpperBoundon R (?)...28 greedy 1. 2. 7 Tests fortheMostPartofBinaryDecisionTables...29 1.
3 PartialDecision Rules...

Combinatorial Machine Learning

by Mikhail Moshkov and Beata Zielosko

Published 29 June 2011

Decision trees and decision rule systems are widely used in different applications

as algorithms for problem solving, as predictors, and as a way for

knowledge representation. Reducts play key role in the problem of attribute

(feature) selection. The aims of this book are (i) the consideration of the sets

of decision trees, rules and reducts; (ii) study of relationships among these

objects; (iii) design of algorithms for construction of trees, rules and reducts;

and (iv) obtaining bounds on their complexity. Applications for supervised

machine learning, discrete optimization, analysis of acyclic programs, fault

diagnosis, and pattern recognition are considered also. This is a mixture of

research monograph and lecture notes. It contains many unpublished results.

However, proofs are carefully selected to be understandable for students.

The results considered in this book can be useful for researchers in machine

learning, data mining and knowledge discovery, especially for those who are

working in rough set theory, test theory and logical analysis of data. The book

can be used in the creation of courses for graduate students.