Rough Set Theory and Granular Computing

by Inuiguchi, Masahiro; Tsumoto, Shusaku; Hirano, Shoji

• ISBN13: 9783540005742
• ISBN10: 3540005749
• Format: Hardcover
• Copyright: 2003-07-01
• Publisher: Springer Verlag

Summary

This monograph presents novel approaches and new results in fundamentals and applications related to rough sets and granular computing. It includes the application of rough sets to real world problems, such as data mining, decision support and sensor fusion. The relationship of rough sets to other important methods of data analysis - Bayes theorem, neurocomputing and pattern recognition is thoroughly examined. Another issue is the rough set based data analysis, including the study of decision making in conflict situations. Recent engineering applications of rough set theory are given, including a processor architecture organization for fast implementation of basic rough set operations and results concerning advanced image processing for unmanned aerial vehicles. New emerging areas of study and applications are presented as well as a wide spectrum of on-going research, which makes the book valuable to all interested in the field of rough set theory and granular computing.

Table of Contents

Bayes' Theorem -- the Rough Set Perspective	1	(12)
Zdzislaw Pawlak
Introduction	1	(1)
Bayes' Theorem	2	(1)
Information Systems and Approximation of Sets	2	(2)
Decision Language	4	(1)
Decision Algorithms	5	(1)
Decision Rules in Information Systems	6	(1)
Properties of Decision Rules	7	(1)
Decision Tables and Flow Graphs	8	(1)
Illustrative Example	8	(3)
Conclusion	11	(2)
References	12	(1)
Approximation Spaces in Rough Neurocomputing	13	(10)
Andrzej Skowron
Introduction	13	(1)
Approximation Spaces in Rough Set Theory	14	(1)
Generalizations of Approximation Spaces	15	(1)
Information Granule Systems and Approximation Spaces	16	(2)
Classifiers as Information Granules	18	(1)
Approximation Spaces for Information Granules	19	(1)
Approximation Spaces in Rough-Neuro Computing	20	(1)
Conclusion	21	(2)
References	22	(1)
Soft Computing Pattern Recognition: Principles, Integrations and Data Mining	23	(14)
Sankar K. Pal
Introduction	23	(2)
Relevance of Fuzzy Set Theory in Pattern Recognition	25	(2)
Relevance of Neural Network Approaches	27	(1)
Genetic Algorithms for Pattern Recognition	28	(1)
Integration and Hybrid Systems	29	(1)
Evolutionary Rough Fuzzy MLP	30	(1)
Data mining and knowledge discovery	31	(6)
References	33	(4)
Part I. Generalizations and New Theories
Generalization of Rough Sets Using Weak Fuzzy Similarity Relations	37	(10)
Rolly Intan
Y. Y. Yao
Masao Mukaidono
Introduction	37	(1)
Weak Fuzzy Similarity Relations	38	(3)
Generalized Rough Set Approximations	41	(2)
Generalized Rough Membership Functions	43	(1)
An Illustrative Example	44	(2)
Conclusions	46	(1)
References	46	(1)
Two Directions toward Generalization of Rough Sets	47	(12)
Masahiro Inuiguchi
Tetsuzo Tanino
Introduction	47	(1)
The Original Rough Sets	48	(2)
Distinction among Positive, Negative and Boundary Elements	50	(4)
Approximations by Means of Elementary Sets	54	(2)
Concluding Remarks	56	(3)
References	56	(3)
Two Generalizations of Multisets	59	(10)
Sadaaki Miyamoto
Introduction	59	(1)
Preliminaries	60	(2)
Infinite Memberships	62	(2)
Generalization of Membership Sequence	64	(3)
Conclusion	67	(2)
References	67	(2)
Interval Probability and Its Properties	69	(10)
Hideo Tanaka
Kazutomi Sugihara
Yutaka Maeda
Introduction	69	(1)
Interval Probability Functions	70	(4)
Combination and Conditional Rules for IPF	74	(1)
Numerical Example of Bayes' Formula	75	(2)
Concluding Remarks	77	(2)
References	77	(2)
On Fractal Dimension in Information Systems	79	(10)
Lech Polkowski
Introduction	79	(1)
Fractal Dimensions	80	(1)
Rough Sets and Topologies on Rough Sets	81	(3)
Fractals in Information Systems	84	(5)
References	86	(3)
A Remark on Granular Reasoning and Filtration	89	(8)
Tetsuya Murai
Michinori Nakata
Yoshiharu Sato
Introduction	89	(1)
Kripke Semantics and Filtration	90	(2)
Relative Filtration with Approximation	92	(2)
Relative Filtration and Granular Reasoning	94	(2)
Concluding Remarks	96	(1)
References	96	(1)
Towards Discovery of Relevant Patterns from Parameterized Schemes of Information Granule Construction	97	(12)
Andrzej Skowron
Jarostaw Stepaniuk
James F. Peters
Introduction	97	(2)
Approximation Granules	99	(2)
Rough--Fuzzy Granules	101	(2)
Granule Decomposition	103	(6)
References	106	(3)
Approximate Markov Boundaries and Bayesian Networks: Rough Set Approach	109	(16)
Dominik Slezak
Introduction	109	(1)
Data Based Probabilistic Models	110	(5)
Approximate Probabilistic Models	115	(5)
Conclusions	120	(5)
References	120	(5)
Part II. Data Mining and Rough Sets
Mining High Order Decision Rules	125	(12)
Y. Y. Yao
Introduction	125	(1)
Motivations	126	(2)
Mining High Order Decision Rules	128	(3)
Mining Ordering Rules: an Illustrative Example	131	(3)
Conclusion	134	(3)
References	134	(3)
Association Rules from a Point of View of Conditional Logic	137	(10)
Tetsuya Murai
Michinori Nakata
Yoshiharu Sato
Introduction	137	(1)
Preliminaries	137	(4)
Association Rules and Conditional Logic	141	(2)
Association Rules and Graded Conditional Logic	143	(2)
Concluding Remarks	145	(2)
References	145	(2)
Association Rules with Additional Semantics Modeled by Binary Relations	147	(10)
T. Y. Lin
Eric Louie
Introduction	147	(1)
Databases with Additional Semantics	148	(2)
Re-formulating Data Mining	150	(1)
Mining Semantically	151	(1)
Semantic Association Rules	152	(1)
Conclusion	153	(4)
References	155	(2)
A Knowledge-Oriented Clustering Method Based on Indiscernibility Degree of Objects	157	(10)
Shoji Hirano
Shusaku Tsumoto
Introduction	157	(1)
Clustering Procedure	158	(6)
Experimental Results	164	(2)
Conclusions	166	(1)
References	166	(1)
Some Effective Procedures for Data Dependencies in Information Systems	167	(10)
Hiroshi Sakai
Preliminary	167	(1)
Three Procedures for Dependencies	168	(5)
An Algorithm for Rule Extraction	173	(1)
Dependencies in Non-deterministic Information Systems	173	(3)
Concluding Remarks	176	(1)
References	176	(1)
Improving Rules Induced from Data Describing Self-Injurious Behaviors by Changing Truncation Cutoff and Strength	177	(10)
Jerzy W. Grzymala-Busse
Rachel L. Freeman
Introduction	177	(1)
Temporal Data	178	(3)
Rule Induction and Classification	181	(1)
Postprocessing of Rules	182	(1)
Experiments	182	(2)
Conclusions	184	(3)
References	184	(3)
The Variable Precision Rough Set Inductive Logic Programming Model and Future Test Cases in Web Usage Mining	187	(10)
V. Uma Maheswari
Arul Siromoney
K. M. Mehata
Introduction	187	(1)
The VPRS model and future test cases	188	(1)
The VPRSILP model and future test cases	189	(1)
A simple graph VPRSILP ESD system	190	(1)
VPRSILP and Web Usage Graphs	191	(1)
Experimental details	191	(4)
Conclusions	195	(2)
References	195	(2)
Rough Set and Genetic Programming	197	(14)
Yesser Hassan
Eiichiro Tazaki
Introduction	197	(1)
Rough Set Theory	198	(1)
Genetic Rough Induction (GRI)	199	(3)
Experiments and Results	202	(4)
Conclusions	206	(5)
References	207	(4)
Part III. Conflict Analysis and Data Analysis
Rough Set Approach to Conflict Analysis	211	(12)
Rafal Deja
Introduction	211	(1)
Conflict Model	212	(4)
System with Constraints	216	(1)
Analysis	216	(2)
Agents' Strategy Analysis	218	(2)
Conclusions	220	(3)
References	220	(3)
Criteria for Consensus Susceptibility in Conflicts Resolving	223	(10)
Ngoc Thanh Nguyen
Introduction	223	(1)
Consensus Choice Problem	224	(2)
Susceptibility to Consensus	226	(6)
Conclusions	232	(1)
References	232	(1)
L1-Space Based Models for Clustering and Regression	233	(10)
Sadaaki Miyamoto
Takatsugu Koga
Yoichi Nakayama
Introduction	233	(1)
Fuzzy c-means Based on L1-space	234	(2)
Mixture Density Model Based on L1-space	236	(1)
Regression Models Based on Absolute Deviations	237	(2)
Numerical Examples	239	(1)
Conclusion	239	(4)
References	240	(3)
Upper and Lower Possibility Distributions with Rough Set Concepts	243	(8)
Peijun Guo
Hideo Tanaka
The Concept of Upper and Lower Possibility Distributions	243	(2)
Comparison of dual possibility distributions with dual approximations in rough set theory	245	(1)
Identification of Upper and Lower Possibility Distributions	245	(3)
Numerical Example	248	(2)
Conclusions	250	(1)
References	250	(1)
Efficiency Values Based on Decision Maker's Interval Pairwise Comparisons	251	(12)
Tomoe Entani
Hidetomo Ichihashi
Hideo Tanaka
Introduction	251	(1)
Interval AHP with Interval Comparison Matrix	252	(2)
Choice of the Optimistic Weights and Efficiency Value by DEA	254	(3)
Numerical Example	257	(2)
Concluding Remarks	259	(4)
References	259	(4)
Part IV. Applications in Engineering
Rough Measures, Rough Integrals and Sensor Fusion	263	(10)
Z. Pawlak
J.F. Peters
A. Skowron
Z. Suraj
S. Ramanna
M. Borkowski
Introduction	263	(1)
Classical Additive Set Functions	264	(1)
Basic Concepts of Rough Sets	264	(1)
Rough Measures	265	(1)
Rough Integrals	265	(3)
Multi-Sensor Fusion	268	(2)
Conclusion	270	(3)
References	271	(2)
A Design of Architecture for Rough Set Processor	273	(8)
Akinori Kanasugi
Introduction	273	(1)
Outline of Rough Set Processor	273	(2)
Design of Architecture	275	(4)
Discussions	279	(1)
Conclusion	280	(1)
References	280	(1)
Identifying Adaptable Components - A Rough Sets Style Approach	281	(10)
Yoshiyuki Shinkawa
Masao J. Matsumoto
Introduction	281	(1)
Defining Adaptation of Software Components	281	(1)
Identifying One-to-one Component Adaptation	282	(6)
Identifying One-to-many Component Adaptation	288	(1)
Conclusions	289	(2)
References	290	(1)
Analysis of Image Sequences for the UAV	291	(9)
Marcin S. Szczuka
Nguyen Hung Son
Introduction	291	(1)
Basic Notions	292	(1)
The WITAS Project	293	(1)
Data Description	294	(1)
Tasks	295	(1)
Results	296	(3)
Conclusions	299	(1)
References	300