Analysis and Decision Making in Uncertain Systems

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Springer Science & Business Media, Jan 9, 2004 - Business & Economics - 371 pages
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Problems, methods and algorithms of decision making based on an uncertain knowledge now create a large and intensively developing area in the field of knowledge-based decision support systems. The main aim of this book is to present a unified, systematic description of analysis and decision problems in a wide class of uncertain systems described by traditional mathematical models and by relational knowledge representations. A part of the book is devoted to new original ideas introduced and developed by the author: the concept of uncertain variables and the idea of a learning process consisting in knowledge validation and updating. In a certain sense this work may be considered as an extension of the author's monograph Uncertain Logics, Variables and Systems (Springer-Verlag, 2002). In this book it has been shown how the different descriptions of uncertainty based on random, uncertain and fuzzy variables may be treated uniformly and applied as tools for general analysis and decision problems, and for specific uncertain systems and problems (dynamical control systems, operation systems, knowledge-based pattern recognition under uncertainty, task allocation in a set of multiprocessors with uncertain execution times, and decision making in an assembly system as an example of an uncertain manufacturing system). The topics and the organization of the text are presented in Chapter 1 (Sects 1. 1 and 1. 4). The material presented in the book is self-contained.
 

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Contents

Introduction to Uncertain Systems
1
12 Uncertain Variables
3
13 Basic Deterministic Problems
5
14 Structure of the Book
7
Relational Systems
11
22 Analysis and Decision Making for Relational Plants
14
23 Relational Plant with External Disturbances
18
24 Determinization
22
Parametric Optimization of Decision Systems
201
92 Uncertain Controller in a Closedloop System
206
93 Random Controller in a Closedloop System
210
94 Descriptive and Prescriptive Approaches
212
95 Fuzzy Controller in a Closedloop System
216
96 Quality of Decisions Based on Nonparametric Descriptions
220
Stability of Uncertain Dynamical Systems
225
102 Stability Conditions
227

25 Discrete Case
25
Application of Random Variables
29
32 Functional Plants with Random Parameters Continuous Case
32
33 Functional Plants with Random Parameters Discrete Case
39
34 Empirical interpretations
41
35 Relational Plants with Random Parameters
44
36 Determinization
48
37 Nonparametric Uncertainty Continuous Case
54
38 Nonparametric Uncertainty Discrete Case
58
Uncertain Logics and Variables
63
42 Other Versions of Uncertain Logic
67
43 Uncertain Variables
71
44 Additional Description of Uncertain Variables
76
45 Functions of Uncertain Variables
78
Application of Uncertain Variables
85
52 Decision Making Problem for a Functional Plant
86
53 External Disturbances
88
54 Analysis for Relational Plants with Uncertain Parameters
93
55 Decision Making for Relational Plants with Uncertain Parameters
98
56 Computational Aspects 35
103
57 Nonparametric Uncertainty
108
58 Nonparametric Problems for a Plant with External Disturbances
115
Fuzzy Variables Analogies and Soft Variables
123
62 Application of Fuzzy Variables in Analysis and Decision Problems
129
63 Plant with External Disturbances
134
64 Comparison of Uncertain Variables with Random and Fuzzy Variables
140
65 Comparisons and Analogies for Nonparametric Problems
143
66 Introduction to Soft Variables
149
67 Application of Soft Variables to Nonparametric Problems
151
68 Generalized Nonparametric Problems
153
Systems with Logical Knowledge Representation
155
72 Analysis and Decision Making Problems
157
73 Logicalgebraic Method
159
74 Analysis and Decision Making for a Plant with Random Parameters
162
75 Analysis and Decision Making for a Plant with Uncertain Parameters
164
76 Uncertain and Random Logical Decision Algorithms
165
Dynamical Systems
169
82 Analysis and Decision Making for Dynamical Plants with Uncertain Parameters
175
83 Analysis and Decision Making for Dynamical Plants with Random Parameters
182
84 Optimization of Random and Uncertain Multistage Decision Process
184
85 Applications of Uncertain Variables for a Class of Knowledgebased Assembly Systems
189
851 Knowledge Representation and Decision Problem
190
852 Assembly Process with Uncertain Parameters
193
86 Nonparametric Problems
196
103 Special Cases
230
1032 Multiplicative Uncertainty
235
104 Examples
238
105 An Approach Based on Random Variables
243
106 An Approach Based on Uncertain Variables
251
107 Stabilization
254
Learning Systems
259
1111 Knowledge Validation and Updating
260
1112 Learning Algorithm for Decision Making in a Closedloop System
262
112 Learning System Based on Knowledge of Decisions
263
1121 Knowledge Validation and Updating
264
1122 Learning Algorithm for Decision Making in a ClosedLoop System
266
113 Learning Algorithms for a Class of Dynamical Systems 36
269
1131 Knowledge Validation and Updating
270
1132 Learning Control System
273
1133 Example
274
114 Learning Algorithms for a Class of Knowledgebased Assembly Systems
278
1142 Learning Algorithm for Decision Making in a Closedloop System
281
Complex Problems and Systems
283
122 Other Formulations Threelevel Uncertainty
289
123 Complex Systems with Distributed Knowledge
292
1232 Complex System with Uncertain and Random Parameters
295
124 Knowledge Validation and Updating
297
1241 Validation and Updating of the Knowledge Concerning the System
298
1242 Validation and Updating of the Knowledge Concerning the Decision Making
299
125 Learning System
302
Complex of Operations
313
132 Application of Uncertain Variables 49 54
316
133 Special Cases and Examples
320
134 Decomposition and Twolevel Control
325
135 Application of Random Variables 131460
328
136 Application to Task Allocation in a Multiprocessor System 33 57
331
137 Learning Algorithms
335
Pattern Recognition
339
142 Application of the Logicalgebraic Method
341
143 Application of Uncertain Variables 54
344
144 Application of Random Variables
350
145 Nonparametric Problems
353
146 Learning Algorithms
355
Conclusions
361
References
363
Index
369
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About the author (2004)

Professor Zdzislaw Bubnicki died on 12th March 2006.