报告题目：A mathematical abstraction of the Three Kingdoms Wei-Shu-Wu
主讲人：Bernard De Baets Professor
Bernard De Baets received the M.Sc. degree in maths, the Postgraduate degree in knowledge technology, and the Ph.D. degree in maths, all summa cum laude from Ghent University, Belgium, where he is a Senior Full Professor in applied maths. His publications comprise more than 500 papers in international journals (Google Scholar h-index of 70). He serves on the Editorial Boards of various international journals, in particular as Co-Editor-in-Chief of Fuzzy Sets and Systems. He is a Government of Canada Award holder (1988), an Honorary Professor of Budapest Tech (2006), an IFSA Fellow (2011), a Doctor Honoris Causa of the University of Turku (2017), and a Professor Invitado of the Universidad Central “Marta Abreu” de las Villas (2017). In 2019, he received the EUSFLAT Scientific Excellence Award.
Reciprocal relations are an interesting generalization of complete relations covering both an important class of preference relations studied in fuzzy set theory, as well as the class of winning probability relations studied in probability theory. Due to their intrinsic nature, reciprocal relations that are not weakly transitive can be considered to be cyclical. Most attention so far has gone to cycles of lengths three, using the metaphor of the Rock-Paper-Scissors children game, triggered by evidence from nature and society. In this lecture, I will focus on winning probability relations associated with random vectors and point out the link with the underlying dependence structure. Interesting prototypical settings, such as dice games, mutual rank probability relations and graded stochastic dominance, will be discussed. I will also initiate the study of cycles of length four, introducing the Rock-Paper-Scissors-Lizard metaphor. Although the picture is still incomplete, it already offers some interesting insights.