Among the various multi-level formulations of mathematical models in decision making processes, this book focuses on the bi-level model. Being the most frequently used, the bi-level model addresses conflicts which exist in multi-level decision making processes. From the perspective of bi-level structure and uncertainty, this book takes real-life problems as the background, focuses on the so-called random-like uncertainty, and develops the general framework of random-like bi-level decision making problems. The random-like uncertainty considered in this book includes random phenomenon, random-overlapped random (Ra-Ra) phenomenon and fuzzy-overlapped random (Ra-Fu) phenomenon. Basic theory, models, algorithms and practical applications for different types of random-like bi-level decision making problems are also presented in this book.

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Jiuping Xu holds a Ph.D. in Applied Mathematics from Tsinghua University and a Ph.D. in Physical Chemistry from Sichuan University, where he became a professor in 1995. At present, he is the Associate Vice President of the Business School at Sichuan University, Chengdu, China, the Dean of the Business School at Sichuan University, Chengdu, China, a lifetime Academician of the International Academy for Systems and Cybernetic Sciences, an Academician of Mongolian National Academy of Sciences, an Academician of Lotfi Zadeh International Academy of Sciences, President of the International Society for Management Science and Engineering Management and General Chair of the International Conference on Management Science and Engineering Management. He has published more than 40 books in over 10 publishing houses, and over 600 papers in more than 150 international journals.
Zongmin Li obtained her Ph.D. in Management Science and Engineering from Sichuan University.Currently she is an assistant professor in Business School of Sichuan University, Chengdu, China. She was a visiting scholar in Drexel University, LeBow College of Business in 2012.9-2013.9. She is an active scholar in the areas of mathematical modeling, uncertain decision making, algorithm, multi-criteria decision analysis and applications. Her research outputs appear on some international journals such as Omega, Automation in Construction, Knowledge-Based Systems as well as some international conference proceedings.
Zhimiao Tao holds a Ph.D. in Management Science and Engineering from Sichuan University. Currently Dr. Tao is an associate professor in Business School of Sichuan University, Chengdu, China, and a visiting scholar in University of Washington, Seattle. He has published a book “Rough Multiple Objective Decision Making” in Taylor & Francis Press and many papers on international journals, such as Information Sciences, Mathematics and Computers in Simulation, Petroleum Science and Technology respectively. His research interests include rough set theory, bi-level programming and intelligent algorithm.

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