Error Systems: Concepts, Theory and Applications

Preface
Acknowledgements
Contents
1 Brief Introduction of Error Systems
	1.1 Concepts of Error System
		1.1.1 Definition of Error System
		1.1.2 Relationships and Operations Between Object Systems
		1.1.3 Categorization of Error Systems
		1.1.4 Relation Between Error System and Object System
	1.2 Relationships Between System, Subsystems, and Elements
		1.2.1 100% Error Produced by 1% Error
		1.2.2 Chaos
		1.2.3 Non-linearity
		1.2.4 Almost-There Phenomenon
		1.2.5 Concept of Error Systems
		1.2.6 Relationship Between Systems, Subsystems, and Elements
		1.2.7 Important Concepts of Error Subsystems
	1.3 Feature-Based System Optimization
		1.3.1 Background and Related Problems
		1.3.2 Relationship Between System Optimization and Subsystems Optimization
		1.3.3 Optimization of Feature-Additive Systems
2 Identification of Error
	2.1 Necessity of Studying the Rules for Judging Errors
		2.1.1 Objective Existence of Rules for Judging Errors
		2.1.2 Theoretical Foundations of Studying Rules for Judging Errors
	2.2 Properties of Rules for Judging Errors
		2.2.1 Changeability of Rules for Judging Errors
		2.2.2 The Hierarchy of Rules for Judging Errors
		2.2.3 Completeness of Rules for Judging Errors
		2.2.4 Scientificity of Rules for Judging Errors
		2.2.5 Fuzziness of Rules for Judging Errors
		2.2.6 Multi-objective Features of Rules for Judging Errors
		2.2.7 Non-contradiction of Rules for Judging Errors
		2.2.8 Unchangeability of Rules for Judging Errors Under Certain Conditions
		2.2.9 Parallelism of Rules for Judging Errors
		2.2.10 Acting Forces of Rules for Judging Errors
	2.3 Methods of Building Rules for Judging Errors
		2.3.1 Principles for Building Rules for Judging Errors
		2.3.2 Process of Building Rules of Judging Errors
		2.3.3 Steps for Building Rules of Judging Errors
	2.4 Relationship Between Rules for Judging Errors and the Object Being Judged
		2.4.1 Axioms
		2.4.2 Equivalence in the Rules for Judging Errors
		2.4.3 Correlation Between the Rules for Judging Errors
		2.4.4 Good and Bad Rules for Judging Errors
		2.4.5 Comparison Between Rules for Judging Errors
		2.4.6 Relationship Between Rules for Judging Errors and Object Being Judged
	2.5 Method for Identifying Errors
		2.5.1 Flow Chart Used for Identifying Errors
		2.5.2 Implementation Steps for Judging Errors
		2.5.3 Implementation Methods for Judging Errors
		2.5.4 Analysis on the Implementation Effectiveness in Judging Errors
	2.6 Case Analysis for Error Identification
		2.6.1 Addition of Binary Numbers
		2.6.2 Case in Identifying Trademark Error
3 Basic Structures of Systems
	3.1 System Structure
		3.1.1 Basic Structures of Systems
		3.1.2 Series Connections
		3.1.3 Parallel Connections
		3.1.4 Connections with Feedback
		3.1.5 Expanding and Shrinking Structure
		3.1.6 Inclusion Structure
4 Structures of Error Systems
	4.1 Basic Structures of Error System
		4.1.1 Hierarchical Structure of Error Systems
		4.1.2 Chain Structure of Error System
		4.1.3 Inclusion Structure of Errors
		4.1.4 Feedback Structure of Errors
		4.1.5 Changeable Structures of Error Systems
		4.1.6 Fuzzy Structures of Error Systems
		4.1.7 Stability of Error Systems
		4.1.8 Discussion
5 Structural Change of Error Systems
	5.1 Addition Transformation of Error System
		5.1.1 Types of Addition Transformation on Error System Structure
		5.1.2 Addition Transformation on Series Structure in Error Systems
		5.1.3 Addition Transformation on Parallel Structure in Error Systems
		5.1.4 Addition Transformation on Expanding and Shrinking Structure in Error Systems
		5.1.5 Addition Transformation on Inclusion Structure in Error Systems
		5.1.6 Addition Transformation on Feedback Structure in Error Systems
	5.2 Displacement Transformation on Error System Structures
		5.2.1 Types of Displacement Transformation on Error System Structures
		5.2.2 Displacement Transformation on Error System Structures
		5.2.3 Inverse Displacement Transformation on Error System Structures
	5.3 Similarity Transformation on Error System Structures
		5.3.1 Expression for Logical Proposition of Similarity Transformation on Error System Structure
		5.3.2 Types of Similarity Transformation on Error System Structures
	5.4 Decomposition Transformation on Error System Structures
		5.4.1 Expression for Logical Proposition of Decomposition Transformation on Error System Structure
		5.4.2 Decomposition Transformation on Error System Structures
		5.4.3 Inverse Decomposition Transformation on Error System Structure-``Combination Transformation\'\'
	5.5 Destruction Transformation on Error System Structures
		5.5.1 Expression for Logical Proposition of Destruction Transformation on Error System Structure
		5.5.2 Destruction Transformation on Error System Structures
		5.5.3 Inverse Destruction Transformation on Error System Structure-``Generation Transformation\'\'
		5.5.4 Stable Structures of Error Systems
6 System Acting Forces and Their Applications to Error Systems
	6.1 Structural Acting Forces of System
		6.1.1 Background
		6.1.2 Basics Concepts
		6.1.3 Transformations on System Structural Acting Forces
		6.1.4 Relevant Research Regarding System Acting Forces
	6.2 Acting Forces of System Elements
		6.2.1 Motivation for Studying Acting Forces of System Elements
		6.2.2 Concept of Acting Forces of System Elements
		6.2.3 Transformations on Acting Forces of System Elements
		6.2.4 Relevant Research Regarding Acting Forces of System Elements
	6.3 Relationships Between Acting Forces of System Elements and System Features
		6.3.1 Motivation on the Investigation
		6.3.2 Relevant Concepts
		6.3.3 Critical and Important Elements in a System
		6.3.4 Function for Feature Acting Force of System Element
		6.3.5 Conclusion
7 Transformations on Universe of Discourse and Rules in Error Systems
	7.1 Transformations on Domain in Error Systems
		7.1.1 Concept of Transformations on Universe of Discourse
		7.1.2 Transformations on Universe of Discourse
		7.1.3 Theorem of Transformation on Universe of Discourse
	7.2 Transformations on Rules of Error Systems
		7.2.1 Necessity in Studying Rules for Judging Errors
		7.2.2 Properties of Rules for Judging Errors
		7.2.3 Transformations on Rules for Judging Errors in Error Systems
8 Error Function
	8.1 Concept of Error Function
		8.1.1 Definition for Error Function
		8.1.2 Categorization of Error Functions
	8.2 Forms of Error Functions
		8.2.1 Definitions of Error Function
		8.2.2 Scalar Error Functions
		8.2.3 Vector Type Error Function
	8.3 Relationships Between Error Function and Judging Rules for Errors
		8.3.1 Effects of Judging Rules on Error Function f
		8.3.2 Relationships Between Different Error Values Under Different Judging Rules
9 Applications of Error Systems Theory
	9.1 Preparation for Eliminating Errors
		9.1.1 Identifying Error by Analyzing Root Causes
		9.1.2 Principles for Eliminating Errors
		9.1.3 Transformations and Their Impacts
	9.2 Eliminating Errors in Systems Through Similarity Transformation
		9.2.1 Introduction
		9.2.2 Principles in Eliminating Errors Through Transformation
		9.2.3 Eliminating Error Through Similarity Transformation
		9.2.4 Examples Illustrating Error Elimination Through Similarity Transformation
	9.3 Eliminating Errors in Systems Through Displacement Transformation
		9.3.1 Starting Story
		9.3.2 Definition on Displacement Transformation
		9.3.3 Examples Illustrating Error Elimination Through Displacement Transformation
	9.4 Eliminating Errors in Systems Through Decomposition Transformation
		9.4.1 Starting Story
		9.4.2 Definition on Decomposition Transformation
		9.4.3 Types of Decomposition Transformations in Error Elimination
		9.4.4 Examples Illustrating Error Elimination Through Decomposition Transformation
	9.5 Eliminating Errors in Systems Through Addition Transformation
		9.5.1 Starting Story
		9.5.2 Definition on Addition Transformation
		9.5.3 Types of Addition Transformations in Error Elimination
		9.5.4 Examples Illustrating Error Elimination Through Addition Transformation
	9.6 Eliminating Errors in Systems Through Destruction Transformation
		9.6.1 Starting Story
		9.6.2 Definition on Destruction Transformation
		9.6.3 Types of Destruction Transformations in Error Elimination
		9.6.4 Examples Illustrating Error Elimination Through Destruction Transformation
	9.7 Case Study on Eliminating Errors in Enterprise Management
		9.7.1 Case Background
	9.8 Analyzing and Eliminating Four Typical Errors  in Parenting Children
		9.8.1 Four Principles Used in Parenting Children
		9.8.2 Four Examples in Parenting Children
	9.9 Applications of Error Theory
		9.9.1 Establishing Error System Model
		9.9.2 Practical Application of Error System Theory
Appendix  Glossary
Appendix  References