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14. ABSTRACT Areas Covered In the Proceedings Includes: "Invited Talks" "Rough Computing" Foundations and Applications" "Rough Set Theory and Its Application" "Fuzzy Set Theory and Its Applications" "Non-classical Logic and Approximate Reasoning" "Information Granulation and Granular Computing" "Data Mining and Knowledge Discovery" "Machine Learning" "Intelligent Agents and Systems" 15. SUBJECT TERMS
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Lecture Notes in Artificial Intelligence Subseries of Lecture Notes in Computer Science Edited by J. G. Carbonell and J. Siekmann
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Ning Zhong Andrzej Skowron Setsuo Ohsuga (Eds.)
New Directions in Rough Sets, Data Mining, and Granular-Soft Computing 7th International Workshop, RSFDGrC'99 Yamaguchi, Japan, November 9-11, 1999 Proceedings
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Series Editors Jaime G. Carbonell, Carnegie Mellon University, Pittsburgh, PA, USA Jörg Siekmann, University of Saarland, Saarbrücken, Germany
Volume Editors Ning Zhong Yamaguchi University, Faculty of Engineering Department of Computer Science and Systems Engineering Tokiwa-Dai, 2557, Ube 755, Japan E-mail:
[email protected] Andrzej Skowron Warsaw University, Institute of Mathematics Banacha 2, 02-097 Warsaw, Poland E-mail:
[email protected] Setsuo Ohsuga Waseda University, School of Science and Engineering Department of Information and Computer Science 3-4-1 Okubo Shinjuku-ku, Tokyo 169, Japan E-mail:
[email protected] Cataloging-in-Publication data applied for Die Deutsche Bibliothek - CIP-Einheitsaufhahme New directions in rough sets, data mining, and granular soft computing: 7th international workshop; proceedings / RSFDGrC99, Yamaguchi, Japan, November 9 -11,1999. Ning Zhong... (ed.). - Berlin; Heidelberg; New York; Barcelona ; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer, 1999 (Lecture notes in computer science; Vol. 1711: Lecture notes in artificial intelligence) ISBN 3-540-66645-1 CR Subject Classification (1998): 1.2, F.4.1, H.3, H.2.4, F.l ISBN 3-540-66645-1 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1999 Printed in Germany Typesetting: Camera-ready by author SPIN 10705042 06/3142 - 5 4 3 2 1 0
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Preface This volume contains the papers selected for presentation at the Seventh International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and GranularSoft Computing (RSFDGrC'99) held in the Yamaguchi Resort Center, Ube, Yamaguchi, Japan, November 9-11, 1999. The workshop was organized by the International Rough Set Society, the BISC Special Interest Group on Granular Computing (GrC), the Polish- Japanese Institute of Information Technology, and Yamaguchi University. RSFDGrC'99 provided an international forum for sharing original research results and practical development experiences among experts in these emerging fields. An important feature of the workshop was to stress the role of the integration of intelligent information techniques. That is, to promote a deep fusion of these approaches to AI, soft computing, and database communities in order to solve real-world, large, complex problems concerned with uncertainty and fuzziness. In particular, rough and fuzzy set methods in data mining and granular computing were on display. The total of 89 papers coming from 21 countries and touching a wide spectrum of topics related to both theory and applications were submitted to RSFDGrC'99. Out of them 45 papers were selected for regular presentations and 15 for short presentations. Seven technical sessions were organized, namely: Rough Set Theory and Its Applications; Fuzzy Set Theory and Its Applications; Non-classical Logic and Approximate Reasoning; Information Granulation and Granular Computing; Data Mining and Knowledge Discovery; Machine Learning; Intelligent Agents and Systems. The RSFDGrC'99 program was enriched by four invited speakers: Zdzislaw Pawlak, Lotfi A. Zadeh, Philip Yu, and Setsuo Arikawa, from soft computing, database, and AI communities. A special session on Rough Computing: Foundations and Applications was organized by James F. Peters. An event like this can only succeed as a team effort. We would like to acknowledge the contribution of the program committee members and thank the reviewers for their efforts. Many thanks to the honorary chairs Zdzislaw Pawlak and Lotfi A. Zadeh as well as the general chairs Setsuo Ohsuga and T.Y. Lin. Their involvement and support have added greatly to the quality of the workshop. Our sincere gratitude goes to all of the authors who submitted papers. We are grateful to our sponsors: Kayamori Foundation of Informational Science Advancement, United States Air Force Asian Office of Aerospace Research and Development, and Yamaguchi Industrial Technology Development Organizer, for their generous support. We wish to express our thanks to Alfred Hofmann of Springer-Verlag for his help and cooperation. November 1999
Ning Zhong Andrzej Skowron Setsuo Ohsuga
VI
RSFDGrC'99 Conference Committee
Honorary Chairs: Zdzislaw Pawlak L.A. Zadeh
Polish Academy of Sciences, Poland UC Berkeley, USA
General Chairs: Setsuo Ohsuga
T.Y. Lin
Waseda University, Japan San Jose State University, USA
Program Chairs: Andrzej Skowron Ning Zhong
Warsaw University, Poland Yamaguchi University, Japan
Advisory Board: Setsuo Arikawa Jerzy Grzymala-Busse Katsushi Inoue T.Y. Lin Masao Mukaidono Setsuo Ohsuga Zdzislaw Pawlak Lech Polkowski Zbigniew W. Ras Andrzej Skowron Roman Slowinski Hideo Tanaka Shusaku Tsumoto Yiyu Yao L.A. Zadeh Wojciech Ziarko Ning Zhong
Kyushu U., Japan U. Kansas, USA Yamaguchi U., Japan San Jose State U., USA Meiji U., Japan Waseda U., Japan Polish Academy of Sei., Poland Polish-Japanese Inst. Infor. Tech., Poland U. North Carolina, USA Warsaw U., Poland Poznan U. Tech., Poland Osaka Prefecture U., Japan Shimane Medical U., Japan U. Regina, Canada UC Berkeley, USA U. Regina, Canada Yamaguchi U., Japan
Program Committee
Rakesh Agrawal Shunichi Amari Mohua Banerjee Nick Cercone David Cheung Andrzej Czyzewski Honghua Dai Liya Ding Micheal Hadjimichael Koichi Hori Janusz Kacprzyk Willi Klosgen Wojciech Kowalczyk Bing Liu Chunnian Liu Jiming Liu Qing Liu Hongjun Lu Zbigniew Michalewicz Masoud Mohammadian Hiroshi Motoda Shinichi Nakasuka Hung Son Nguyen Sankar K. Pal James F. Peters Zdzislaw Piasta Gregory Piatetsky-Shapiro Mohamed Quafafou Vijay Raghavan Zhongzhi Shi Jerzy Stefanowski Jaroslaw Stepaniuk Einoshin Suzuki Shun'ichi Tano Takao Terano Hiroshi Tsukimoto Lipo Wang Paul P. Wang Anita Wasilewska Takashi Washio
IBM Almaden Research Center, USA RIKEN, Japan Indian Inst. of Tech. Kanpur, India U. Waterloo, Canada Hong Kong U., China Tech. U. Gdansk, Poland Deakin U., Australia National U. Singapore, Singapore Naval Research Lab., USA U. Tokyo, Japan Polish Academy of Sciences, Poland GMD, Germany Vrije U., The Netherlands National U. Singapore, Singapore Beijing Polytechnic U., China Hong Kong Baptist U., China Nan Chang U., China Hong Kong U. of Science and Tech., China U. North Carolina, USA U. Canberra, Australia Osaka U., Japan U. Tokyo, Japan Warsaw U., Poland Indian Statistical Inst., India U. Manitoba, Canada Kielce U. Tech., Poland Knowledge Stream, USA U. Nantes, France U. Southwestern, USA Chinese Academy of Sciences, China Poznan U. Tech., Poland Bialystok U. Tech., Poland Yokohama National U., Japan U. Electro-Communications, Japan U. Tsukuba, Japan Toshiba Corporation, Japan Nanyang Tech. U., Singapore Duke U., USA State U. New York, USA Osaka U., Japan
VIII
S.K. Michael Wong Xindong Wu Tetuya Yoshida Philip Yu Lizhu Zhou Jan M. Zytkow
U. Regina, Canada Colorado School of Mines, USA Osaka U., Japan IBM T.J. Watson Research Center, USA Tsinghua U, China U. North Carolina, USA
Contents Invited Talks Decision Rules, Bayes' Rule and Rough Sets Z. Pawlak A New Direction in System Analysis: From Computation with Measurements to Computation with Perceptions L. A. Zadeh
1
10
On Text Mining Techniques for Personalization C. C. Aggarwal, P. S. Yu
12
A Road to Discovery Science S. Arikawa
19
Rough Computing: Foundations and Applications Calculi of Granules Based on Rough Set Theory: Approximate Distributed Synthesis and Granular Semantics for Computing with Words L. Polkowski, A. Skowron
20
Discovery of Rules about Complications S. Tsumoto
29
Rough Genetic Algorithms P. Lingras, C. Davies
38
Classifying Faults in High Voltage Power Systems: A Rough-Fuzzy Neural Computational Approach L. Han, J. F. Peters, S. Ramanna, R. Zhai
47
Rough Set Theory and Its Applications Toward Spatial Reasoning in the Framework of Rough Mereology L. Polkowski An Algorithm for Finding Equivalence Relations from Tables with Non-deterministic Information H. Sakai, A. Okuma
55
64
X
On the Extension of Rough Sets under Incomplete Information J. Stefanowski, A. Tsoukiäs
73
On Rough Relations: An Alternative Formulation Y. Y. Yao, T. Wang
82
Formal Rough Concept Analysis J. Saquer, J. S. Deogun
91
Noise Reduction in Telecommunication Channels Using Rough Sets and Neural Networks R. Krolikowski, A. Czyzewski Rough Set Analysis of Electrostimulation Test Database for the Prediction of Post-Operative Profits in Cochlear Implanted Patients A. Czyzewski, H. Skarzynski, B. Kostek, R. Krolikowski A Rough Set-Based Approach to Text Classification A. Chouchoulas, Q. Shen Modular Rough Fuzzy MLP: Evolutionary Design P. Mitra, S. Mitra, S. K. Pal
100
109
118
128
Approximate Reducts and Association Rules: Correspondence and Complexity Results H. S. Nguyen, D. Sl§zak
137
Handling Missing Values in Rough Set Analysis of Multi-attribute and Multi-criteria Decision Problems S. Greco, B. Matarazzo, R. Slowinski
146
The Generic Rough Set Inductive Logic Programming Model and Motifs in Strings A. Siromoney, K. Inoue
158
Rough Problem Settings for Inductive Logic Programming C. Liu, N. Zhong
168
Using Rough Sets with Heuristics to Feature Selection J. Z. Dong, N. Zhong, S. Ohsuga
178
XI
The Discretization of Continuous Attributes Based on Compatibility Rough Set and Genetic Algorithm L. Sun, W. Gao
188
Fuzzy Set Theory and Its Applications Level Cut Conditioning Approach to the Necessity Measure Specification M. Inuiguchi, T. Tanino Four c-regression Methods and Classification Functions S. Miyamoto, K. Umayahara, T. Nemoto
193
203
Context-Free Fuzzy Sets in Data Mining Context S. Tsumoto, T. Y. Lin
212
Applying Fuzzy Hypothesis Testing to Medical Data M. Last, A. Schenker, A. Kandel
221
Generating a Macroeconomic Fuzzy Forecasting System Using Evolutionary Search R. Veliev, A. Rubinov, A. Stranieri
230
Fuzzy Control of Nonlinear Systems Using Nonlinearized Parameterization H. Han, H. Kawabata
239
Control of Chaotic Systems Using Fuzzy Model-Based Regulators K. Watanabe, L. Udawatta, K. Kiguchi, K. Izumi Fuzzy Behavior-Based Control for the Obstacle Avoidance of Multi-link Manipulators P. Dassanayake, K. Watanabe, K. Izumi
248
257
Fuzzy Future Value and Annual Cash Flow Analyses N. Cetin, C. Kahraman
266
Semi-Linear Equation with Fuzzy Parameters S. Melliani
271
XII
Non-classical Logic and Approximate Reasoning First Order Rough Logic-Revisited T. Y. Lin, Q. Liu
276
A Generalized Decision Logic in Interval-Set-Valued Information Tables .. 285 Y. Y. Yao, Q. Liu Many-Valued Dynamic Logic for Qualitative Decision Theory C.-J. Liau
294
Incorporating Fuzzy Set Theory and Matrix Logic in Multi-layer Logic H. Yamauchi, S. Ohsuga
304
Fuzzy Logic as Interfacing Media for Constraint Propagation Based on Theories of Chu Space and Information Flow K. Sato, T. Horiuchi, T. Hiraoka, H. Kawakami, 0. Katai
314
Pattern Reasoning: A New Solution for Knowledge Acquisition Problem .. 324 H. Tsukimoto Probabilistic Inference and Bayesian Theorem Based on Logical Implication Y. Yamauchi, M. Mukaidono Reasoning with Neural Logic Networks R. Yasdi The Resolution for Rough Propositional Logic with Lower (L) and Upper (H) Approximate Operators Q. Liu
334
343
352
Information Granulation and Granular Computing Information Granules in Distributed Environment A. Skowron, J. Stepaniuk Evolving Granules for Classification for Discovering Difference in the Usage of Words T. Yoshida, T. Hondo, S. Nishida Interval Evaluation by AHP with Rough Set Concept K. Sugihara, Y. Maeda, H. Tanaka
357
366
375
XIII
Interval Density Functions in Conflict Analysis Y. Maeda, K. Senoo, H. Tanaka
382
Incorporating Personal Databases by Granular Computing Y. Kakemoto
390
Data Mining and Knowledge Discovery Knowledge-Driven Discovery of Operational Definitions J. M. Zytkow
395
A Closest Fit Approach to Missing Attribute Values in Preterm Birth Data J. W. Grzymala-Busse, W. J. Grzymala-Busse, L. K. Goodwin
405
Visualizing Discovered Rule Sets with Visual Graphs Based on Compressed Entropy Density E. Suzuki, H. Ishihara
414
A Distance-Based Clustering and Selection of Association Rules on Numeric Attributes X. Du, S. Suzuki, N. Ishii Knowledge Discovery for Protein Tertiary Substructures C.-w. K. Chen, D. Y. Y. Yun
423
433
Integrating Classification and Association Rule Mining: A Concept Lattice Framework K. Hu, Y. Lu, L. Zhou, C. Shi
443
Using Rough Genetic and Kohonen's Neural Network for Conceptual Cluster Discovery in Data Mining H. Kiem, D. Phuc
448
Towards Automated Optimal Equity Portfolios Discovery in a Knowledge Sharing Financial Data Warehouse Y.-C. Lu, H. Cheng Rule-Evolver: An Evolutionary Approach for Data Mining C. Lopes, M. Pacheco, M. Vellasco, E. Passos
453
458
XIV
Machine Learning Decision Making with Probabilistic Decision Tables W. Ziarko
463
The Iterated Version Space Learning J. J. Zhang, N. Cercone
472
An Empirical Study on Rule Quality Measures A. An, N. Cercone
482
Rules as Attributes in Classifier Construction M. S. Szczuka
492
An Algorithm to Find the Optimized Network Structure in an Incremental Learning J. C. Lee, W. D. Lee, M.S. Han Patterns in Numerical Data: Practical Approximations to Kolmogorov Complexity T. Y. Lin Performance Prediction for Classification Systems F. Sun
500
509
514
Intelligent Agents and Systems Flexible Optimization and Evolution of Underwater Autonomous Agents E. Eberbach, R. Brooks, S. Phoha
519
Ontology-Based Multi-agent Model of an Information Security System ... 528 V. I. Gorodetski, L. J. Popyack, I. V. Kotenko, V. A. Skormin Optimal Multi-scale Time Series Decomposition for Financial Forecasting Using Wavelet Thresholding Techniques T. Shin, I. Han Computerized Spelling Recognition of Words Expressed in the Sound Approach M. Higgins, W. Ziarko
533
543
An Adaptive Handwriting Recognition System G. Qian
551
Author Index
557
Decision Rules, Bayes' Rule and Rough Sets Zdzislaw Pawlak Institute of Theoretical and Applied Informatics Polish Academy of Sciences ul. Baltycka 5, 44 000 Gliwice, Poland e-mail:
[email protected] Abstract. This paper concerns a relationship between Bayes' inference rule and decision rules from the rough set perspective. In statistical inference based on the Bayes' rule it is assumed that some prior knowledge (prior probability) about some parameters without knowledge about the data is given first. Next the posterior probability is computed by employing the available data. The posterior probability is then used to verify the prior probability. In the rough set philosophy with every decision rule two conditional probabilities, called certainty and coverage factors, are associated. These two factors are closely related with the lower and the upper approximation of a set, basic notions of rough set theory. Besides, it is revealed that these two factors satisfy the Bayes' rule. That means that we can use to data analysis the Bayes' rule of inference without referring to Bayesian philosophy of prior and posterior probabilities. Key words: Bayes' rule, rough sets, decision rules, information system
1
Introduction
This paper is an extended version of the author's ideas presented in [5,6,7,8]. It concerns some relationships between probability, logic and rough sets and it refers to some concepts of Lukasiewicz presented in [3]. We will dwell in this paper upon the Bayesian philosophy of data analysis and that proposed by rough set theory. Statistical inference grounded on the Bayes' rule supposes that some prior knowledge (prior probability) about some parameters without knowledge about the data is given first. Next the posterior probability is computed when the data are available. The posterior probability is then used to verify the prior probability. In the rough set philosophy with every decision rule two conditional probabilities, called certainty and coverage factors, are associated. These two factors are closely related with the lower and the upper approximation of a set, basic concepts of rough set theory. Besides, it turned out that these two factors satisfy the Bayes' rule. That means that we can use to data analysis the Bayes' rule of inference without referring to Bayesian philosophy, i.e., to the prior and posterior probabilities. In other words, every data set with distinguished condition
and decision attributes satisfies the Bayes' rule. This property gives a new look on reasoning methods about data.
2
Information System and Decision Table
Starting point of rough set based data analysis is a data set, called an information system. An information system is a data table, whose columns are labelled by attributes, rows are labelled by objects of interest and entries of the table are attribute values. Formally by an information system we will understand a pair S = (U, A), where U and A, are finite, nonempty sets called the universe, and the set of attributes, respectively. With every attribute oeiwe associate a set Va, of its values, called the domain of a. Any subset B of A determines a binary relation 1(B) on U, which will be called an indiscernibility relation, and is defined as follows: (x,y) € 1(B) if and only if a(x) = a(y) for every a € A, where a(x) denotes the value of attribute a for element x. Obviously 1(B) is an equivalence relation. The family of all equivalence classes of 1(B), i.e., partition determined by B, will be denoted by U11(B), or simple U/B; an equivalence class of 1(B), i.e., block of the partition U/B, containing x will be denoted by B(x). If (x,y) belongs to 1(B) we will say that x and y are B-indiscernible or indiscernible with respect to B. Equivalence classes of the relation 1(B) (or blocks of the partition U/B) are referred to as B-elementary sets or B-granules. If we distinguish in an information system two classes of attributes, called condition and decision attributes, respectively, then the system will be called a decision table. A simple, tutorial example of an information system (a decision table) is shown in Table 1.
Table 1. An example of a decision table Car F 1 med. 2 high 3 med. 4 low 5 high 6 med.
P med. med. low med. low low
M S med. poor large poor large poor med. good small poor large good
The table contains data about six cars, where F, P, S and M denote fuel consumption, selling price, size and marketability, respectively.
Attributes F,P and S are condition attributes, whereas M is the decision attribute. Each row of the decision table determines a decision obeyed when specified conditions are satisfied.
3
Approximations
Suppose we are given an information system (a datat set) S = (U, A), a subset X of the universe U, and subset of attributes B. Our task is to describe the set X in terms of attribute values from B. To this end we define two operations assigning to every X C U two sets B* (X) and B* (X) called the B-lower and the B-upper approximation of X, respectively, and defined as follows:
B.(X) = (J {B(x) : B{x) C X}, B*{X)= \J{B{x):B{x)nX?9). x€U
Hence, the .B-lower approximation of a set is the union of all B-granules that are included in the set, whereas the B-upper approximation of a set is the union of all ß-granules that have a nonempty intersection with the set. The set
BNB(X) = B*(X)-B.(X) will be referred to as the B-boundary region of X. If the boundary region of X is the empty set, i.e., BNB(X) = 0, then X is crisp (exact) with respect to B; in the opposite case, i.e., if BNB(X) ^ 0, X is referred to as rough (inexact) with respect to B. For example, let C = {F, P, S} be the set of all condition attributes. Then for the set X = {1,2,3,5} of cars with poor marketability we have C*(X) = {1,2,5}, C*(X) = {1,2,3,5,6} and BNC(X) = {3,6}.
4
Decision Rules
With every information system S = (U, A) we associate a formal language L(S), written L when S is understood. Expressions of the language L are logical formulas denoted by #, $ etc. built up from attributes and attribute-value pairs by means of logical connectives A (and), V (or), ~ (not) in the standard way. We will denote by ||#||s the set of all objects x € U satisfying # in S and refer to as the meaning of # in S. The meaning of # in S is defined inductively as follows: 1) ll(a>v)lls = {v£U : a(v) = U} for all a £ A and v € Va, 2) ||*Vtf||s = ||*||5U||!P||s, 3) ||*A#||s = ||*||sn||!P||s, 4) ||~#||s = tf-||#||s.
A formula # is true in S if ||^||s = U. A decision rule in L is an expression # -*
