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【數學模組化】模糊數學模型詳解

占坑,後補

【Background Information】

  Ambiguity refers to “unclearness” or “also to the other” in the intermediate transition of objective differences. Such as tall and short, young and old, hot and cold water, serious and not serious environmental pollution. In the decision-making, there is also such a vague phenomenon, such as electing a good cadre, but what is a good cadre? There is no absolutely clear and fixed boundary between good cadres and bad cadres. These phenomena are difficult to describe with classical mathematics. 

  Fuzzy mathematics is the mathematics of mathematical methods to study and deal with fuzzy phenomena. As a new discipline, it is a new mathematics discipline developed after classical mathematics and statistical mathematics. After a brief silence and controversy, it developed rapidly and became more widely used. Today\'s application of fuzzy mathematics has spread throughout the fields of science, engineering, agriculture, medicine, and social sciences, fully demonstrating its powerful vitality and penetration. 

  Statistical mathematics is to expand the scope of application of mathematics from the field of certainty to the field of uncertainty, that is, from the inevitable phenomenon to the accidental phenomenon, while the fuzzy mathematics expands the scope of application of mathematics from the field of determination to the field of uncertainty, that is, from the precise The phenomenon is blurred.

【目錄】:

  1. 基本理論
    1. 模糊集和隸屬函數
    2. 模糊關系和模糊矩陣
    3. 運算[尤其是合成運算]
  2. 模糊模式識别
    1. 模糊集的貼近度
    2. 格貼近度
    3. 有用的性質和運算
    4. 模糊識别原則
    5. 模糊識别步驟
  3. 模糊聚類分析
    1. 與傳統聚類相比的優點
    2. 核心概念:模糊等價矩陣和模糊近似矩陣
    3. 模糊聚類分析的步驟
    4. 其他細節
    5. 應用模糊聚類的例子
  4. 模糊決策分析
    1. 單目标模糊綜合評價
    2. 多目标模糊綜合評價與決策
    3. 多層次模糊綜合評價與決策
    4. 多層次模糊評價與傳統多層次分析
    5. 多層次模糊綜合評價決策法模組化執行個體
    6. 其他關于模糊評價的細節
  5. 具體問題分析過程