A theory of aggregation centred on the notion of betweenness

报告题目:A theory of aggregation centred on the notion of betweenness

报告人:Bernard De Baets 教授,比利时根特大学



摘 要:The study of aggregation functions (formerly called aggregation operators) is undeniably one of the most important spin-offs of the fuzzy set community, mainly driven by the need for appropriate logical connectives. In this ‘era of aggregation’, data aggregation has become a central problem in many fields of application, with needs extending largely beyond the setting of real numbers, such as 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. Several methods for constructing penalty functions using amonometric, which carries a more appropriate semantics than the more commonly used distance function (metric), are provided. 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.

简 介:Bernard De Baets is a senior full professor in applied mathematics at the Faculty of Bioscience Engineering of Ghent University, the top-ranked Belgian university. He is leading the research unit KERMIT and acts as head of the Department of Data Analysis and Mathematical Modelling. Furthermore, he is an affiliated professor at the Anton de Kom Universiteit (Suriname), an Honorary Professor of Budapest Tech (Hungary), a Doctor Honoris Causa of the University of Turku (Finland) and a Profesor Invitado of the Universidad Central “Marta Abreu” de las Villas (Cuba).

As a trained mathematician, computer scientist and knowledge engineer, Bernard has developed a passion for multi- and interdisciplinary research. He is a prolific writer, with a bibliography comprising close to 500 peer-reviewed journal papers, 60 book chapters and 300 contributions to conference proceedings, accumulating over 18000 Google Scholar citations (h-index 67). He is a Fellow of IFSA and in 2012, he was a nominee for the Ghent University Prometheus Award for Research. Bernard actively serves the research community, in particular as co-editor-in-chief of Fuzzy Sets and Systems and as member of the editorial board of several other journals, including the Internat. J. of Approximate Reasoning, Engineering Applications of Artificial Intelligence, and the Iranian J. of Fuzzy Systems. He is a member of the Administrative Board of the Belgian OR Society.