Rough Set Theory and Granular Computing,9783540005742

Rough Set Theory and Granular Computing

by ; ;
ISBN13: 9783540005742
ISBN10: 3540005749
Format: Hardcover
Pub. Date: 2003-07-01
Publisher(s): Springer Verlag
List Price: $216.07

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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

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