《模糊数学及应用》课程介绍

模糊数学是研究和处理模糊性现象的数学。模糊数学是对经典数学的发展和扩充，能有效解决经典数学难以解决的大系统的复杂性问题，以及在自然界和日常生活中普遍存在而无法解决的模糊性问题。自1965年美国著名控制论专家L.A.Zadeh建立模糊集合理论以来，模糊数学在诸多领域被成功应用，以模糊集合理论为基础的应用学科，如模糊聚类分析、模糊模式识别、模糊综合评判、模糊决策与模糊预测、模糊规划、模糊控制、模糊信息处理等，已经在工业、农业、医学、军事、工程技术、信息科学、社会科学和自然科学等各个领域发挥重要作用。

本课程的教学目的是：1）掌握模糊集合理论的相关概念、运算规则以及基本定理；2）熟悉与隶属函数相关的各种概率统计方法，并熟练应用常用的模糊分布；3）初步掌握模糊数学在模糊模式识别、模糊聚类、综合评判等方面的应用；4）为在其他应用学科中用模糊数学解决问题奠定理论基础。

通过本课程的学习，使学生掌握模糊数学的基本理论及应用，培养学生用模糊数学解决现实中应用问题的能力。

Introduction to the course: Fuzzy Mathematics and application

Fuzzy Mathematics is a branch of mathematics related to fuzzy set theory, which started in 1965 after the publication of Lotfi Asker Zadeh’s seminar work “Fuzzy sets”. Many applications based on fuzzy set theory, such as Fuzzy clustering, Fuzzy patter recognition, Fuzzy comprehensive evaluation, Fuzzy decision making and Fuzzy prediction, Fuzzy control, Fuzzy information processing, etc, have important impacts on industry, agriculture, medicine science, military field, engineering, information science, social science, and natural science.

The aims of this course are as follows: 1) To be familiar with the concepts, operation and principles of fuzzy sets; 2) to be familiar with the concept of fuzzy membership function and normal fuzzy distributions; 3) to know the application of fuzzy mathematics on Fuzzy patter recognition, fuzzy relation and fuzzy clustering, Fuzzy comprehensive evaluation; 4) to prepare for further study and research on fuzzy sets.

Study of this course makes students to grasp the basic theory and application, to improve ability to solve the real fuzzy problems.