Rough Sets: Theoretical Aspects of Reasoning about Data

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Springer Science & Business Media, Oct 31, 1991 - Computers - 231 pages
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To-date computers are supposed to store and exploit knowledge. At least that is one of the aims of research fields such as Artificial Intelligence and Information Systems. However, the problem is to understand what knowledge means, to find ways of representing knowledge, and to specify automated machineries that can extract useful information from stored knowledge. Knowledge is something people have in their mind, and which they can express through natural language. Knowl edge is acquired not only from books, but also from observations made during experiments; in other words, from data. Changing data into knowledge is not a straightforward task. A set of data is generally disorganized, contains useless details, although it can be incomplete. Knowledge is just the opposite: organized (e.g. laying bare dependencies, or classifications), but expressed by means of a poorer language, i.e. pervaded by imprecision or even vagueness, and assuming a level of granularity. One may say that knowledge is summarized and organized data - at least the kind of knowledge that computers can store.
 

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Contents

THEORETICAL FOUNDATIONS
1
12 Knowledge and Classification
2
14 Equivalence Generalization and Specialization of Knowledge
6
Exercises
7
IMPRECISE CATEGORIES APPROXIMATIONS AND ROUGH SETS
9
23 Approximations of Set
10
24 Properties of Approximations
11
25 Approximations and Membership Relation
15
73 Semantics of Decision Logic Language
83
74 Deduction in Decision Logic
85
75 Normal Forms
88
76 Decision Rules and Decision Algorithms
89
77 Truth and Indiscernibility
91
78 Dependency of Attributes
94
79 Reduction of Consistent Algorithms
95
710 Reduction of Inconsistent Algorithms
98

26 Numerical Characterization of Imprecision
16
27 Topological Characterization of Imprecision
17
28 Approximation of Classifications
22
29 Rough Equality of Sets
24
210 Rough Inclusion of Sets
27
Summary
29
References
30
REDUCTION OF KNOWLEDGE
33
33 Relative Reduct and Relative Core of Knowledge
35
34 Reduction of Categories
38
35 Relative Reduct and Core of Categories
41
Summary
42
References
43
DEPENDENCIES IN KNOWLEDGE BASE
45
43 Partial Dependency of Knowledge
47
Summary
48
Exercises
49
KNOWLEDGE REPRESENTATION
51
52 Examples
52
53 Formal Definition
55
54 Significance of Attributes
58
55 Discernibility Matrix
60
Summary
62
References
63
DECISION TABLES
68
63 Simplification of Decision Tables
71
Summary
77
Exercises
78
References
79
REASONING ABOUT KNOWLEDGE
81
72 Language of Decision Logic
82
711 Reduction of Decision Rules
101
712 Minimization of Decision Algorithms
106
Summary
110
References
111
APPLICATIONS
116
83 Simplification of Decision Table
119
84 Decision Algorithm
129
85 The Case of Incomplete Information
130
Exercises
131
DATA ANALYSIS
133
93 Derivation of Control Algorithms from Observation
138
94 Another Approach
146
95 The Case of Inconsistent Data
150
Summary
159
References
162
DISSIMILARITY ANALYSIS
164
103 Beauty Contest
172
104 Pattern Recognition
174
105 Buying a Car
180
Summary
187
SWITCHING CIRCUITS
188
113 MultipleOutput Switching Functions
196
Summary
202
References
203
MACHINE LEARNING
205
123 The Case of an Imperfect Teacher
212
124 Inductive Learning
215
Summary
219
INDEX
225
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