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EBOOK
Author Liu, Sifeng.
Title Grey systems : theory and applications / Sifeng Liu and Yi Lin.
Imprint Berlin ; Heidelberg : Springer, 2011.

LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
View online
Author Liu, Sifeng.
Series Springer complexity
Understanding complex systems
Springer complexity.
Understanding complex systems.
Subject System theory.
Alt Name Forrest, Jeffrey Yi-Lin, 1959-
LOCATION CALL # STATUS MESSAGE
 OHIOLINK SPRINGER EBOOKS    ONLINE  
View online
Author Liu, Sifeng.
Series Springer complexity
Understanding complex systems
Springer complexity.
Understanding complex systems.
Subject System theory.
Alt Name Forrest, Jeffrey Yi-Lin, 1959-
Description 1 online resource (xx, 379 pages).
polychrome rdacc
Bibliography Note Includes bibliographical references and index.
Contents Note continued: 3.2.3. Synthetic Degree of Grey Incidence -- 3.3. Grey Incidence Models Based on Similarity and Closeness -- 3.4. Grey Cluster Evaluations -- 3.4.1. Grey Incidence Clustering -- 3.4.2. Grey Variable Weight Clustering -- 3.4.3. Grey Fixed Weight Clustering -- 3.5. Grey Evaluation Using Triangular Whitenization Functions -- 3.5.1. Evaluation Model Using Endpoint Triangular Whitenization Functions -- 3.5.2. Evaluation Model Using Center-Point Triangular Whitenization Functions -- 3.5.3. Comparison between Evaluation Models of Triangular Whitenization Functions -- 3.6. Applications -- 3.6.1. Order of Grey Incidences -- 3.6.2. Preference Analysis -- 3.6.3. Practical Applications -- 4. Grey Systems Modeling -- 4.1. GM(1, 1) Model -- 4.1.1. Basic Form of GM(1, 1) Model -- 4.1.2. Expanded Forms of GM(1, 1) Model -- 4.2. Improvements on GM(1, 1) Models -- 4.2.1. Remnant GM(1, 1) Model -- 4.2.2. Groups of GM(1, 1) Models -- 4.3. Applicable Ranges of GM(1, 1) Models -- 4.4. GM(r, h) Models -- 4.4.1. GM(1, N) Model -- 4.4.2. GM(0, N) Model -- 4.4.3. GM(2, 1) and Verhulst Models -- 4.4.3.1. GM(2, 1) Model -- 4.4.3.2. VerhulstModel -- 4.4.4. GM(r, h) Models -- 4.5. Grey Systems Predictions -- 4.5.1. Sequence Predictions -- 4.5.2. Interval Predictions -- 4.5.3. Disaster Predictions -- 4.5.3.1. Grey Disaster Predictions -- 4.5.3.2. Seasonal Disaster Predictions -- 4.5.4. Stock-Market-Like Predictions -- 4.5.5. Systems Predictions -- 4.5.5.1. Thought of Five-Step Modeling -- 4.5.5.2. System of Prediction Models -- 5. Discrete Grey Prediction Models -- 5.1. Basics -- 5.1.1. Definitions on Discrete Grey Models -- 5.1.2. Relationship between Discrete Grey and GM(1, 1) Models -- 5.1.3. Prediction Analysis of Completely Exponential Growths -- 5.2. Generalization and Optimization of Discrete Grey Models.
Note continued: 5.2.1. Three Forms of Discrete Grey Models -- 5.2.2. Impacts of Initial Values on Iterations -- 5.2.3. Optimization of Discrete Grey Models -- 5.2.4. Recurrence Functions for Optimizing Discrete Grey Models -- 5.3. Approximately Nonhomogeneous Exponential Growth -- 5.4. Discrete Grey Models of Multi-variables -- 6. Combined Grey Models -- 6.1. Grey Econometrics Models -- 6.1.1. Determination of Variables Using Principles of Grey Incidence -- 6.1.2. Grey Econometrics Models -- 6.2. Combined Grey Linear Regression Models -- 6.3. Grey Cobb-Douglas Model -- 6.4. Grey Artificial Neural Network Models -- 6.4.1. BP Artificial Neural Model and Computational Schemes -- 6.4.2. Principle and Method for Grey BP Neural Network Modeling -- 6.5. Grey Markov Model -- 6.5.1. Grey Moving Probability Markov Model -- 6.5.2. Grey State Markov Model -- 6.6. Combined Grey-Rough Models -- 6.6.1. Rough Membership, Grey Membership and Grey Numbers -- 6.6.2. Grey Rough Approximation -- 6.6.3. Combined Grey Clustering and Rough Set Model -- 7. Grey Models for Decision Making -- 7.1. Different Approaches for Grey Decisions -- 7.1.1. Grey Target Decisions -- 7.1.2. Grey Incidence Decisions -- 7.1.3. Grey Development Decisions -- 7.1.4. Grey Cluster Decisions -- 7.2. Decision Makings with Synthesized Targets -- 7.3. Multi-attribute Intelligent Grey Target Decision Models -- 8. Grey Game Models -- 8.1. Strategic Game Models for Duopolies with Limited Rationality and Knowledge -- 8.1.1. Duopolistic Strategic Output-Making Models Based on Empirically Ideal Production and Optimal Decision Coefficients -- 8.1.2. Concession Equilibrium of the Later Decision-Maker under Nonstrategic Expansion Damping Conditions: Elimination from the Market.
Note continued: 8.1.3. Damping Equilibrium of the Advanced Decision-Maker under Strategic Expansion Damping Conditions: Giving Up Some Market Share -- 8.1.4. Damping Loss and Total Damping Cost for the First Decision-Making Oligopoly to Completely Control the Market -- 8.2. New Situational Forward Induction Model -- 8.2.1. Weaknesses of Backward Induction, Central Mehod of Equilibrium Analysis for Dynamic Games -- 8.2.2. Backward Derivation of Multi-Stage Dynamic Games' Profits -- 8.2.3. Termination of Forward Induction of Multi-Stage Dynamic Games and Guide Nash Equilibrium Analysis -- 8.3. Chain Structure Model of Evolutionary Games of Industrial Agglomerations and Its Stability -- 8.3.1. Chained Evolutionary Game Model for the Development of Industrial Agglomerations -- 8.3.2. Duplicated Dynamic Simulation for the Development Process of Industrial Agglomerations -- 8.3.3. Stability Analysis for the Formation and Development of Industrial Agglomerations -- 9. Grey Control Systems -- 9.1. Controllability and Observability of Grey Systems -- 9.2. Transfer Functions of Grey Systems -- 9.2.1. Grey Transfer Functions -- 9.2.2. Transfer Functions of Typical Links -- 9.2.3. Matrices of Grey Transfer Functions -- 9.3. Robust Stability of Grey Systems -- 9.3.1. Robust Stability of Grey Linear Systems -- 9.3.2. Robust Stability of Grey Linear Time-Delay Systems -- 9.3.3. Robust Stability of Grey Stochastic Linear Time-Delay Systems -- 9.4. Several Typical Grey Controls -- 9.4.1. Control with Abandonment -- 9.4.2. Control of Grey Incidences -- 9.4.3. Control of Grey Predictions -- 10. Introduction to Grey Systems Modeling Software -- 10.1. Features and Functions -- 10.2. Main Components -- 10.3. Operation Guide -- 10.3.1. Confirmation System -- 10.3.2. Using the Software Package -- 10.3.2.1. Entering Data -- 10.3.2.2. Model Computations.
Note continued: A. Interval Analysis and Grey Systems Theory -- A.1. Brief Historical Account of Interval Analysis -- A.2. Main Blocks of Interval Analysis -- A.2.1. Interval Number System and Arithmetic -- A.2.2. Interval Functions, Sequences and Matrices -- A.2.3. Interval Newton Methods -- A.2.4. Integration of Interval Functions -- References -- B. Approaches of Uncertainty -- B.1. Foundation for a Unified Information Theory -- B.1.1. Grey Uncertainties -- B.1.2. Stochastic Uncertainties -- B.1.3. Unascertainties -- B.1.4. Fuzzy Uncertainties -- B.1.5. Rough Uncertainties -- B.1.6. Soros Reflexive Uncertainties -- B.2. Relevant Practical Uncertainties -- B.3. Some Final Words and Open Questions -- References -- C. How Uncertainties Appear: A General Systems Approach -- C.1. Evolutionary Transitions -- C.1.1. Blown-Ups: Old Structures Replaced by New Ones -- C.1.2. Mathematical Properties of Blown-Ups -- C.1.3. Problem of Quantitative Infinity -- C.1.4. Eddy Motions of the General Dynamic System -- C.1.5. Equal Quantitative Effects -- C.2. Systemic Yoyo Structure of General Systems -- C.2.1. Systemic Yoyo Model -- C.2.2. Justification Using Conservation Law of Informational Infrastructures -- C.2.3. Justification Using Readily Repeatable Experiments -- C.3. Laws on State of Motion of Systems -- C.3.1. Quark Structure of Systemic Yoyos -- C.3.2. Interactions between Systemic Yoyos -- C.3.3. Laws on State of Motion -- C.4. Uncertainties Everywhere -- C.4.1. Artificial and Physical Uncertainties -- C.4.2. Uncertainties That Exist in the System of Modern Mathematics -- C.4.2.1. Uncertainties of Mathematics -- C.4.2.2. Inconsistencies in the System of Mathematics -- C.5. Few Final Words -- References.
Summary Due to inherent limitations in human sensing organs, most data collected for various purposes contain uncertainties. Even at the rare occasions when accurate data are available, the truthful predictions derived on the data tend to create chaotic consequences. So, to effectively process and make sense out of available data, we need methods to deal with uncertainty inherently existing inside the data. The intent of this monograph is to explore the fundamental theory, methods, and techniques of practical application of grey systems theory, initiated by Professor Deng Julong in 1982. This volume presents most of the recent advances of the theory accomplished by scholars from around the world. From studying this book, the reader will not only acquire an overall knowledge of this new theory but also be able to follow the most current research activities. All examples presented are based on practical applications of the theory when urgent real-life problems had to be addressed. Last but not the least, this book concludes with three appendices. The first one compares grey systems theory and interval analysis while revealing the fact that interval analysis is a part of grey mathematics. The second appendix presents an array of different approaches of studying uncertainties. And, the last appendix shows how uncertainties appear using general systems approach.
Access License restrictions may limit access.
Note English.
Print version record.
ISBN 9783642161582 (electronic bk.)
3642161588 (electronic bk.)
9783642161575
364216157X
9783642161575
ISBN/ISSN 10.1007/978-3-642-16158-2
OCLC # 700200703
Additional Format Print version: Grey systems. Berlin : Springer, 2010 (DLC) 2010937345


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