Aggregation Theory: A Shift from Order to Betweenness

讲座名称: Aggregation Theory: A Shift from Order to Betweenness
讲座时间 2019-10-21
讲座地点 数学楼112
讲座人 Bernard De Baets

报告题目:Aggregation Theory: A Shift from Order to Betweenness
报告人:Bernard De Baets
The study of aggregation functions is undeniably one of the most important spin-offs of the fuzzy set community, mainly driven by the need for appropriate logical connectives. The generated body of knowledge has also contributed to the fields of multi-criteria decision making (e.g. OWA operators) and dependence modelling (e.g. quasi-copulas and copulas). However, the focus has increasingly narrowed to the aggregation of real numbers in the unit interval.  In the latter setting, Yager’s penalty functions traditionally play an important role.
In this era of aggregation, data aggregation has become a central problem in many fields of application, requiring the aggregation of multidimensional data, compositional data, rankings, relations and strings. In this talk, we draw attention to the old notion of a betweenness relation and propose to replace the currently-required property of quasi-convexity of a penalty function by the compatibility with a betweenness relation.  In this way, we are able to model aggregation processes on any set of objects equipped with a betweenness relation, thus considerably expanding the scope of the theory of aggregation.


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. 

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