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
讲座人：
Bernard De Baets
形式：
校区：
兴庆校区
实践学分：
讲座内容：
报告题目：Aggregation Theory: A Shift from Order to Betweenness
报告时间：2019年10月21日，星期一，上午10：00-12：00
报告地点：数学楼112
报告人：Bernard De Baets
报告摘要：
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.
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