《模糊數學及應用》課程介紹
模糊數學是研究和處理模糊性現象的數學。模糊數學是對經典數學的發展和擴充，能有效解決經典數學難以解決的大系統的複雜性問題，以及在自然界和日常生活中普遍存在而無法解決的模糊性問題。自1965年美國著名控制論專家L.A.Zadeh建立模糊集合理論以來，模糊數學在諸多領域被成功應用，以模糊集合理論為基礎的應用學科，如模糊聚類分析、模糊模式識别、模糊綜合評判、模糊決策與模糊預測、模糊規劃、模糊控制、模糊信息處理等，已經在工業、農業、醫學、軍事、工程技術、信息科學、社會科學和自然科學等各個領域發揮重要作用。
本課程的教學目的是：1）掌握模糊集合理論的相關概念、運算規則以及基本定理；2）熟悉與隸屬函數相關的各種概率統計方法，并熟練應用常用的模糊分布；3）初步掌握模糊數學在模糊模式識别、模糊聚類、綜合評判等方面的應用；4）為在其他應用學科中用模糊數學解決問題奠定理論基礎。
通過本課程的學習，使學生掌握模糊數學的基本理論及應用，培養學生用模糊數學解決現實中應用問題的能力。
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.
