Grey Systems Analysis: Methods, Models and Applications
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore
Springer Nature Singapore
2022
Singapore Springer |
| Series: | Series on Grey System
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXVIII, 365 Seiten |
| ISBN: | 9789811961625 |
| ISSN: | 2731-4944 |
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Record in the Search Index
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1 2 Introduction . 1,1 The Scientific Background of the Birth of Grey System Theory. 1 1.2 The Founder of Grey System Theory. 1.3 Development of Grey Systems Theory. 1.3.1 Building a Basic Team. 1.3.2 Establishment of Academic Organizations. 1.3.3 Journals and Book Series on Grey System Theory . 1.3.4 Grey System Theory Curriculums . 1.3.5 Researchers of Grey System Theory Are All Over the World. 6 1.3.6 Papers of Grey Systems Theory Are Growing Rapidly . 7 1.4 Elementary Concepts of Grey System Theory . 1.5 Fundamental Principles of Grey System Theory . 1.6 Main Contents of Grey System Theory . References . Characteristics of Grey System Theory. 2.1 A Kind of Poor Data Analysis Method with Strong Penetration . 17 2.2 Characteristics of Uncertain Systems and the
Simplicity Principle in Sciences. 18 2.2.1 Incomplete Information. 2.2.2 Inaccuracies in Data. 2.2.3 The Scientific Principle of Simplicity . 2.2.4 Precise Models Suffer from Inaccuracies . 2.3 Comparison of Several Uncertainty Methods . 2.4 Deep Applications of Grey System Theory in the Fields of Social Science, Natural Science and Engineering Technology. 24 1 2 3 3 4 5 6 10 11 13 14 17 18 19 20 21 23
Successful Application of Grey System Theory in the Field of Social Sciences . 2.4.2 Deep Application of Grey System Theory in the Field of Natural Science. 2.4.3 A Large Number of Applications of Grey System Theory in the Field of Engineering Technology . References . 2.4.1 3 4 Grey Numbers and Their Operations . 3.1 Grey Numbers . 3.2 The Whitenization of a Grey Number and Degree of Greyness . 3.3 Degree of Greyness Defined by Axioms . 3.4 The Operations of Interval Grey Numbers. 3.5 General Grey Numbers and Their Operations. 3.5.1 Reduced Form of Interval Grey Numbers. 3.5.2 General Grey Number and Its Reduced Form . 3.5.3 Synthesis of Degree of Greyness and Operations of General Grey Numbers. References . Sequence Operators and Grey Data Mining. Introduction . Systems Under Shocking Disturbances and Buffer Operators
. . 4.2.1 The Trap for Shocking Disturbed System Forecasting . 4.2.2 Axioms of Buffer Operators . 4.2.3 Properties of Buffer Operators . 4.3 Construction of Practically Useful Buffer Operators . 4.3.1 Weakening Buffer Operators . 4.3.2 Strengthening Buffer Operators . 4.3.3 The General Form of Buffer Operator. 4.4 Average Operator . 4.5 The Quasi-Smooth Sequence and Stepwise Ratio Operator . 4.6 Accumulating and Inverse Accumulating Operators . 4.7 Exponentiality of Accumulating Sequence . References . 4.1 4.2 5 Grey Relational Analysis Models . 5.1 Introduction . 5.2 Grey Relational Factors and Set of Grey Relational Operators . 5.3 Grey Relational Axioms and Deng’s Grey Relational Analysis Model . 5.4 Grey
Absolute Relational Degree .
Contents -5 Э' Grey Relative and Synthetic Relational Degree . 5 5.1 Relative Grey Relational Degree . 91 91 5 5.2 Grey Synthetic Relational Degree . Grey Similarity, Closeness and Three-Dimensional Relational Degree . 95 5.6.1 Grey Relational Analysis Models Based on Similarity and Closeness . 5.6.2 Grey Three-Dimension Degree of Relational Degree . 99 5 7 Negative Grey Relational Analysis Models. 5.8 Superiority Analysis . 5.9 Practical Application . References . 94 56 6 7 95 101 109 115 123 Grey Clustering Evaluation Models . 6.1 Introduction . 6.2 Grey Relational Clustering Model . 6.3 Common Possibility Functions . 6.4 Variable Weight Grey Clustering Model . 6.5 Fixed Weight Grey Clustering Model. 6.6
Grey Clustering Evaluation Models Based on Mixed Possibility Functions. 140 6.6.1 Grey Clustering Evaluation Model Based on End-Point Mixed Possibility Functions . 6.6.2 Grey Clustering Evaluation Model Based on Center-Point Mixed Possibility Functions. 142 6.7 Practical Applications. References . 144 150 Series of GM Models . 7.1 Introduction . 7.2 The Four Basic Forms of GM(1,1) . 7.2.1 The Basic Forms of Model GM( 1,1) . 7.2.2 Properties and Characteristics of the Basic Model . 7.3 Suitable Ranges of Different GM( 1,1) . 7.3.1 Suitable Sequences of Different GM( 1,1). 7.3.2 Applicable Ranges of EGM . 7.4 Remnant GM( 1,1) Model. 7.5 Group of GM( 1,1) Models. 7.6 The Fractional Grey Model . 7.7 The Models of GM(r,h) .
7.7.1 The Model of GM(O,N) . 7.7.2 The Model of GM(1,V) . 7.7.3 The Grey Verhulst Model . 7.7.4 The Self-memory Grey Model . 7.7.5 The Models of GM(r,h). 153 153 154 154 156 161 161 169 172 177 180 183 183 185 187 190 192 125 125 126 130 132 136 140
7.8 Practical Applications. 194 References . 201· Combined Grey Models. 8.1 Grey Econometrics Models . 8.1.1 Determination of Variables Using the Grey Relational Principles . 203 8.1.2 Grey Econometrics Models. 8.2 Combined Grey Linear Regression Models. 8.3 Grey Cobb-Douglas Model . 8.4 Grey Artificial Neural Network Models. 8.4.1 BP Artificial Neural Model and Computational Schemes. 211 8.4.2 Steps in Grey BP Neural Network Modeling . 8.5 Grey Markov Model . 8.5.1 Grey Moving Probability Markov Model . 8.5.2 Grey State Markov Model. 8.6 Combined Grey-Rough Model . 8.6.1 Rough Membership, Grey Membership and Grey Numbers . 217 8.6.2 Grey Rough Approximation . 8.6.3 Combined Grey
Clustering and Rough Set Model . 8.7 Practical Applications. References . 203 203 Techniques for Grey Systems Forecasting. 9.1 Introduction . 9.2 Interval Forecasting. 9.3 Grey Distortion Forecasting. 9.4 Wave Form Forecasting . 9.5 System Forecasting . 9.5.1 The Five-Step Modeling Process . 9.5.2 System Models for Prediction . 9.6 Practical Applications. References . 229 229 231 235 238 240 240 242 243 245 10 Grey Models for Decision-Making . 10.1 Introduction . 10.2 Grey Target Decisions . 10.3 Other Approaches to Grey
Decision. 10.3.1 Grey Relational Decision . 10.3.2 Grey Development Decision. 10.3.3 Grey Clustering Decision . 10.4 Multi-attribute Intelligent Grey Target Decision Model . 10.4.1 The Uniform Effect Measure . 10.4.2 The Weighted Synthetic Effect Measure. 247 247 249 254 254 258 260 261 262 264 8 9 204 207 210 211 212 214 214 215 217 219 222 223 228
On Paradox of Rule of Maximum Value and Its Solution . 10.5.1 The Weight Vector Group with Kernel . 10.5.2 The Weighted Comprehensive Clustering Coefficient Vector. 10.5.3 Several Functional Weight Vector Groups with Kernel . 271 10.6 Practical Applications. References . 10 5 267 268 270 272 274 11 Grey Control Systems . Ц.1 Introduction . 11.2 Controllability and Observability of Grey System . 11.3 Transfer Functions of Grey System . 11.3.1 Grey Transfer Function . 11.3.2 Transfer Functions of Typical Links . 11.3.3 Matrices of Grey Transfer Functions. 11.4 Robust Stability of Grey System. 11.4.1 Robust Stability of Grey Linear Systems . 11.4.2 Robust Stability of Grey Linear Time-Delay Systems . 288 11.4.3 Robust Stability of Grey Stochastic Linear Time-Delay System
. 291 11.5 Several Typical Grey Control Models . 11.5.1 Control of Redundancy Removal. 11.5.2 Grey Relational Control . 11.5.3 Control of Grey Prediction . References . 277 277 278 280 280 281 285 286 286 12 Spectrum Analysis of Sequence Operators. 12.1 Introduction . 12.2 Spectrum Analysis of Time Series Data. 12.3 Filtering Effect of Mean Operator and Accumulation Operator . 308 12.3.1 Filtering Effect of Mean Operator . 12.3.2 Filtering Effect of Accumulation Operator. 12.3.3 Filtering Effectof Series Operator. 12.4 Spectrum Analysisof Buffer Operator. References . 305 305 306 Appendix: Introduction to Grey Systems Modeling Software . 315 Memorabilia of the Establishment and Development of Grey System Theory (1982-2021)
. 331 Farewell to Our Tutor. 335 295 296 296 297 302 308 309 311 312 314
Bibliography . 339 Index. 359
The book covers up-to-date theoretical and applied advances in grey systems theory from across the world and vividly presents the reader with the overall picture of this new theory and its frontier research. Many of the concepts, models and methods in the book are original by the authors, including simplified form of grey number, general grey number and the operations of grey numbers; the axiomatic system of buffer operators and a series of weakening and strengthening operators; a series of grey relational analysis models, including grey absolute, relative, synthetic, similarity, closeness, negative and three dimension degree, etc.; grey fixed weight clustering model, grey evaluation models based on center-point and end-point mixed possibility functions; original difference grey model (ODGM), even difference grey model (EDGM), discrete grey model (DGM), fractional grey models, self-memory grey models; multi attribute intelligent grey target decision models, weight vector group with kernel and the weighted comprehensive clustering coefficient vector, and spectrum analysis of sequence operators, etc. This book will be appropriate as a reference and/or professional book for courses of grey system theory for graduate students or high-level undergraduate students, majoring in areas of science, technology, agriculture, medicine, astronomy, earth science, economics, and management. It can also be utilized by researchers and practitioners in research institutions, business entities, and government agencies. |
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| spelling | Liu, Sifeng Verfasser (DE-588)139281495 aut Grey Systems Analysis Methods, Models and Applications Sifeng Liu, Yingjie Yang, Jeffrey Yi-Lin Forrest Singapore Springer Nature Singapore 2022 Singapore Springer XXVIII, 365 Seiten txt rdacontent n rdamedia nc rdacarrier Series on Grey System 2731-4944 Operations Research and Decision Theory Applied Statistics Operations Research, Management Science Operations research Statistics Management science Unvollkommene Information (DE-588)4140474-9 gnd rswk-swf Unvollkommene Information (DE-588)4140474-9 s DE-604 Yang, Yingjie aut Forrest, Jeffrey Yi-Lin aut Erscheint auch als Online-Ausgabe 978-981-19-6160-1 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034878835&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034878835&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Liu, Sifeng Yang, Yingjie Forrest, Jeffrey Yi-Lin Grey Systems Analysis Methods, Models and Applications Operations Research and Decision Theory Applied Statistics Operations Research, Management Science Operations research Statistics Management science Unvollkommene Information (DE-588)4140474-9 gnd |
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| title | Grey Systems Analysis Methods, Models and Applications |
| title_auth | Grey Systems Analysis Methods, Models and Applications |
| title_exact_search | Grey Systems Analysis Methods, Models and Applications |
| title_exact_search_txtP | Grey Systems Analysis Methods, Models and Applications |
| title_full | Grey Systems Analysis Methods, Models and Applications Sifeng Liu, Yingjie Yang, Jeffrey Yi-Lin Forrest |
| title_fullStr | Grey Systems Analysis Methods, Models and Applications Sifeng Liu, Yingjie Yang, Jeffrey Yi-Lin Forrest |
| title_full_unstemmed | Grey Systems Analysis Methods, Models and Applications Sifeng Liu, Yingjie Yang, Jeffrey Yi-Lin Forrest |
| title_short | Grey Systems Analysis |
| title_sort | grey systems analysis methods models and applications |
| title_sub | Methods, Models and Applications |
| topic | Operations Research and Decision Theory Applied Statistics Operations Research, Management Science Operations research Statistics Management science Unvollkommene Information (DE-588)4140474-9 gnd |
| topic_facet | Operations Research and Decision Theory Applied Statistics Operations Research, Management Science Operations research Statistics Management science Unvollkommene Information |
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