【数学建模】模糊数学模型详解

【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.

 

【目录】：

1. 基本理论
   1. 模糊集和隶属函数
   2. 模糊关系和模糊矩阵
   3. 运算[尤其是合成运算]
2. 模糊模式识别
   1. 模糊集的贴近度
   2. 格贴近度
   3. 有用的性质和运算
   4. 模糊识别原则
   5. 模糊识别步骤
3. 模糊聚类分析
1. 与传统聚类相比的优点
2. 核心概念：模糊等价矩阵和模糊近似矩阵
3. 模糊聚类分析的步骤
4. 其他细节
5. 应用模糊聚类的例子
4. 模糊决策分析
1. 单目标模糊综合评价
2. 多目标模糊综合评价与决策
3. 多层次模糊综合评价与决策
4. 多层次模糊评价与传统多层次分析
5. 多层次模糊综合评价决策法建模实例
6. 其他关于模糊评价的细节
5. 具体问题分析过程