## Grey Systems: Theory and ApplicationsDue 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. |

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### Contents

Introduction to Grey Systems Theory | 1 |

Basic Building Blocks | 19 |

Grey Incidence and Evaluations | 51 |

Grey Systems Modeling | 106 |

Discrete Grey Prediction Models | 149 |

Combined Grey Models | 169 |

Grey Models for Decision Making | 197 |

Grey Game Models | 224 |

Grey Control Systems | 259 |

Introduction to Grey Systems Modeling Software | 287 |

Appendix A Interval Analysis and Grey Systems Theory | 303 |

Appendix B Approaches of Uncertainty | 314 |

A General Systems Approach | 325 |

351 | |

373 | |

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### Common terms and phrases

absolute degree applications Assume axioms backward induction behavior clustering coefficient computational concept criteria data sequence decision decision-making oligopoly defined degree of grey degree of incidence Deng discrete grey model duopolies dynamic game economic effect measures effect value employed equation error factor iX game theory given grey class grey clustering grey incidence grey number grey prediction grey systems modeling grey systems theory grey target greyness interval analysis interval vector Jiangsu Journal of Grey known Liu and Lin mathematics matrix membership functions method Nash equilibrium obtain optimization parameters player problem production output quarks referred relevant rough set satisfies sequence operator situation Step stochastic strategic expansion subgame system in equ Systems Engineering Table Theorem triangular whitenization weight uncertainty variables vector Wang weakening buffer operator whitenization weight functions Wuhan γ γ σ σ