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Grey systems : theory and applications

Author: Sifeng Liu; Jeffrey Yi-Lin Forrest
Publisher: Berlin ; Heidelberg : Springer, ©2011.
Series: Springer complexity.; Understanding complex systems.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sifeng Liu; Jeffrey Yi-Lin Forrest
ISBN: 9783642161582 3642161588
OCLC Number: 700200703
Description: 1 online resource (xx, 379 p.)
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.
Series Title: Springer complexity.; Understanding complex systems.
Responsibility: Sifeng Liu and Yi Lin.

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