I.The Basic Information of the Course
Course Number：202012420021
The English Name of the Course：Analysis on Uncertainty Information
The Chinese Name of the Course：不确定性信息分析
In-class Hours and Allocation：Total class hours:32, classroom teaching: 26 class hours, classroom discussion: 6 class hours
Credit(s)：2
Semester：2
Applied Discipline(Professional Degree Category)：Science and Technology
Course Object Oriented：Academic Master, Academic Doctor
Evaluation Mode:Project or small thesis
Teaching Method:Blended Teaching
Course Opening Department:College of Mathematical Sciences
II.Prerequisite Course
Discrete Mathematics, Abstract Algebra, Linear Algebra, Probability theory and mathematical statistics
III. The Objectives and Requirements of the Course
Fuzzy set theory and fuzzy logic are important research tools for analysis of uncertainty information in information science and information technology. They are also important research directions in the field of information science. The purpose of learning this course is to let students more understand and master modern information science theories and methods. Through the study of this course, students are required to learn uncertain about the fuzziness, randomness and incomplete information of various phenomena. We should have a clear understanding on basic theory of modern information technology, find a breakthrough point in the combination of mathematical theory research and practical applications, and lay a good foundation for training high-quality mathematical application talents.
IV. The Content of the Course
With the development of social information and intelligence, people face to a variety of information, most of which are uncertain. As a kind of mathematical theory and method to express and analyze uncertain information, the course of uncertain information analysis provides excellent mathematical basic theory and solution to analysis of uncertain information such as fuzziness, randomness and incompleteness. It has been widely and successfully applied in pattern recognition, artificial intelligence, soft computing and other fields.
This course mainly introduces the theories and methods of accuracy and uncertainty, the concept, representation and operation of fuzzy set, decomposition theorem and extensional principle, operations of fuzzy relations and fuzzy graph, fuzzy logic operator, fuzzy system clustering and dynamic clustering, multi criteria fuzzy group decision analysis, rough set and feature selection from the perspective of data uncertainty. Strive to integrate the latest research topics of artificial intelligence and data science to carry out exploratory and heuristic teaching.
Chapter 1 Concept and classification of uncertainty(2 class hours)
The uncertainty principle is the philosophical basis of artificial intelligence. Accuracy and uncertainty concept; understanding the type, meaning, difference and connection of uncertainty; understanding the concept, representation and operation of fuzziness; expanding model of fuzzy set; heuristic discussion on the representation and description of uncertainty information.
Chapter 2 Connotation of fuzzy sets and operations between fuzzy sets(6 class hours)
To master decomposition theorem and extensional principle of fuzzy sets. Discussion on operations and related properties of fuzzy sets.
Chapter 3 Fuzzy relations and relational graph(6 class hours)
Concept, meaning and representation of fuzzy relation; operation and properties of fuzzy relation; composition and properties of fuzzy relation; closure concept and construction method of fuzzy relation.
Chapter 4 Uncertainty measures(6 class hours)
Introduction of Shannon entropy, information entropy, cross entropy, relative entropy, mutual information, etc. The measure of distance, similarity and closeness to describe the relationship between two or more fuzzy concepts.
Chapter 5 Clustering and decision making(4 class hours)
The concepts of system clustering and dynamic clustering. Clustering methods based on fuzzy equivalence relations and fuzzy similarity relations. Evaluation criteria of fuzzy clustering effect. Understand and master the basic methods of AHP and Fuzzy AHP. Master basic principles and methods of multi-attribute decision-making and multi criteria group decision-making. Heuristic discussion on the applications of uncertain information in decision analysis and the latest research and development in related fields at home and abroad.
Chapter 6 Fuzzy logical operators(4 class hours)
Concepts of fuzzy conjunction, fuzzy disjunction and fuzzy implication. Understand the concepts and relations of triangle norm and triangle conjugate norm. Learn the decomposition mechanism of triangle norm. Grasp relations and construction ways between fuzzy implication and triangle norms.
Chapter 7 Rough sets and feature selection(4 class hours)
Basic concepts of rough set and granular computing; knowledge classification ability and representation method; indistinguishability of objects and attribute reduction method based on indistinguishable matrix; approximate representation of sets; description of dependency and attribute importance; attribute reduction method based on attribute importance; latest research progress of heuristic research on granular computing and knowledge discovery.
During the courses of theoretical teaching, the ideological and political content and case analysis of the course are interspersed with teaching and discussion.
Case1The world's first quantum computer surpassing the early classical computer was born in China (May 3, 2017), laying a solid foundation for the ultimate realization of the goal of quantum computing beyond the classical computing ability (known as "quantum hegemony" in the international academic community). Quantum computation is based on the principle of quantum coherence superposition, which has the ability of super-fast paralleling computation and simulation. The computing power increases exponentially with the number of particles that can be manipulated, which can provide an effective solution for large-scale computing problems that cannot be solved by classical computers.
Case 2Pan Jianwei's team from China University of science and technology announced that Mozi, the world's first quantum science experiment satellite, successfully completed three major scientific experiment tasks (August 10, 2017): quantum entanglement distribution, quantum key distribution and quantum teleportation. Pan Jianwei, the chief scientist and academician of the Chinese Academy of Sciences of the "Beijing Shanghai trunk line" technology verification and application demonstration activity of quantum secure communication, said that at present, China's quantum communication technology is five years ahead of the relevant international technology level, and will continue to lead in the next 10 to 15 years.
V. Reference Books, Reference Literatures, and Reference Materials
A. Text Books, Monographs and References
1. Chengzhong Luo. Introduction to Fuzzy Sets. Press of Beijing Normal University,2005.
2. Lihong Li, Shang Li, Yan Li, Yafeng Yang. Fuzzy Sets and Rough Sets. Press of Tsinghua University, 2015.
3. Deyi Li, Yi Du. Uncertainty Artificial Intelligence(2ndversion). Defense Industry Press，2014.
4. H.T．Nguyen, E.A．Walker. A First Course in Fuzzy Logic. Boca Raton, Florida, Chapman & Hall/CRC, 1999．
B. Learning Resources
1.https://download.csdn.net/download/u013003382/9848344
2.https://www.sciencedirect.com/journal/fuzzy-sets-and-systems
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