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This basic book has been used at the middle schools in Shanghai, China for more than 10 years. The book presents carefully-selected contents in order to achieve the roles of enlightenment and popularization. It mainly includes: Chapter 1: Human Brains, Computers and Fuzzy Mathematics; Chapter 2: Matrix, Fuzzy Relations and Fuzzy Matrix; Chapter 3: Fuzzy Control; Chapter 4: Fuzzy Statistics and Fuzzy Probability and Chapter 5: Fuzzy Linear Programming. It includes at the end of each chapter concise, interesting and profound reading and thinking materials, and a certain amount of exercises so as to make it an informative and interesting textbook. This book can be used not only as a textbook in senior middle schools, and in vocational colleges, but also as a primer for individually learning fuzzy mathematics.
List of contents
Introduction.- Human Brain, Computers and Fuzzy Mathematics.- Matrix. Fuzzy Relations and Fuzzy Matrix.- Fuzzy Contol.- Fuzzy Statistics and Fuzzy Probability.- Fuzzy Linear Programming.
About the author
Hao-ran Lin, male, graduated from the Department of Mathematics, Shanghai Normal University in 1968, has long been engaged teaching in middle school mathematics . Since 1997, by using teaching materials, he tried fuzzy mathematics enlightenment and popularization work first in ordinary middle schools and published twenty papers in the "Mathematical Bulletin", "People's Education", "Shanghai Education" and other core journals in mathematics education in China. He propagandized enlightenment to secondary school students by popularization of fuzzy mathematics necessary and possible.In 2003 he was named the top ten annual figures in Shanghai education. In 2005, he asked Professor of L.A. Zadeh , the founder of fuzzy mathematics, of University of California, whether the English version of this textbook could be published, which has formed the book today. Bing-yuan Cao, male, professor, doctoral and postdoctoral supervisor in School of Mathematics and Information Science, Guangzhou University,Second-level Chair Professor of Lingnan, Foshan University,dean and professor, School of Finance and Economics, Guangzhou Vocational College of Science and Technology, China. Former President of Fuzzy Information & Engineering Society in Operations Research Society of China,present Operations Research Society of Guangdong Province,and Operations Research Society of Guangdong, HongKong and Macao. President of China science and education press. He developed fuzzy geometric programming, published 7 books and 10 proceedings in Springer etc. He has published more than 180 papers (SCI index 40). He serves as the editor-in-chief of the 3 international magazine, and 5 deputy editors or member of the editorial board of magazine. He has won 15 Honors and Awards, and has been in charge of 12 scientific research projects, training more than 30 doctoral, postdoctoral and master's degree students home and aboard.
Yun-zhang Liao,male, a professor and doctoral supervisor at School of Mathematics & Information Science, Guangzhou University, Guangzhou, China. His research interest is related to mathematics curriculum and teaching theory, In particular, he is interested in the cognitive psychology of mathematical application problems solving, international mathematics curriculum comparison, Mathematical assessment, mathematics teacher education and other fields. His work has been published in various research journals, more than 80 papers were published, including Curriculum teaching materials, teaching methods, Journal of mathematics education. He has presided over multiple national, provincial and other kinds of research projects. In 2014, The middle school mathematics teaching theory and practice of problem driving was awarded the second prize of national teaching achievements.
Summary
Introduction to Fuzzy Set Theory
Analyzes the relationship between computers, human brains and fuzzy mathematics
Introduces fuzzy relations, fuzzy matrices and fuzzy control and discusses fuzzy probability statistics and fuzzy linear programming
Shows that Fuzzy Set Theory can be an answer to the following questions: What can be done when computers have limitations? And what should be done when traditional mathematics can't solve ambiguous problems in our real world?
Additional text
“This book ... is aimed to give basic knowledge about the theoretical background of some parts of fuzzy mathematics, and sketches several possible applications. ... This book also provides several simple exercises to support the presented ideas. The presentation of new non-standard ideas (without going to superfluously deep results out of the understanding of middle-school students) makes this book a useful starting literature, also for any researcher aiming to understand the philosophy of fuzzy mathematics.” (Radko Mesiar, zbMath 1412.03001, 2019)
Report
"This book ... is aimed to give basic knowledge about the theoretical background of some parts of fuzzy mathematics, and sketches several possible applications. ... This book also provides several simple exercises to support the presented ideas. The presentation of new non-standard ideas (without going to superfluously deep results out of the understanding of middle-school students) makes this book a useful starting literature, also for any researcher aiming to understand the philosophy of fuzzy mathematics." (Radko Mesiar, zbMath 1412.03001, 2019)
