Partial Covers, Reducts and Decision Rules in Rough Sets: Theory and Applications

ISBN-13: 9783540690276 / Angielski / Twarda / 2009 / 152 str.

Mikhail Ju Moshkov; Marcin Piliszczuk; Beata Zielosko

Opis

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Spis treści

Partial Covers, Reducts and Decision Rules.- Partial Covers, Reducts and Decision Rules with Weights.- Construction of All Irreducible Partial Covers, All Partial Reducts and All Irreducible Partial Decision Rules.- Experiments with Real-Life Decision Tables.- Universal Attribute Reduction Problem.

Blurb

This monograph is devoted to theoretical and experimental study of partial reducts and partial decision rules on the basis of the study of partial covers. The use of partial (approximate) reducts and decision rules instead of exact ones allows us to obtain more compact description of knowledge contained in decision tables, and to design more precise classifiers. Algorithms for construction of partial reducts and partial decision rules, bounds on minimal complexity of partial reducts and decision rules, and algorithms for construction of the set of all partial reducts and the set of all irreducible partial decision rules are considered. The book includes a discussion on the 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 discovery both for knowledge representation and for prediction.

The results obtained in the monograph can be useful for researchers in such areas as machine learning, data mining and knowledge discovery, especially for those who are working in rough set theory, test theory and LAD (Logical Analysis of Data). The monograph can be used under the creation of courses for graduate students and for Ph.D. studies.