Maths Seminar Series: Radko Mesiar, STU in Bratislava – Aggregation functions: recent results and trends, links to fuzzy set theory

We bring an overview of some recent new concepts, results and trends in the aggregation theory. In particular, we focus on monotonicity issues in aggregation, including weak monotonicity, di- rectional monotonicity, etc. Next, we present several generalizations of additivity and maxitivity, such as k-additivity or k-maxitivity. Some note on implicitly given aggregation functions are also added. Based on Boolean functions, their link to fuzzy connectives is given, and extended Booelan functions and dualities are also discussed. Finally, some generalizations of subclasses of extended Boolean functions are given, and some recent trends in aggregation are sketched.

Prof. Radko Mesiar received the Graduate degree from the Faculty of Mathematics and Physics and the Ph.D. degree with the thesis ”Subadditive martingale processes” from Comenius University, Bratislava, Slovakia, in 1974 and 1979, respectively. In 1996, he received the D.Sc. degree from the Academy of Sciences of the Czech Republic, Prague, Czech Republic.

Since 1978, he has been a Member of the Faculty of Civil Engineering, Department of Mathematics, Slovak University of Technology (STU), Bratislava, where he is currently a Full Professor. In 1983, he became an Associate Professor and, in 1998,a full Professor. In 1995, he became a Fellow Member of the Czech Academy of Sciences, Institute of Information and Automation, Praha, Czech Republic, and of IRAFM, University of Ostrava, Ostrava, Czech Republic, in 2006.

He is the coauthor of two in􏰏luencial scienti􏰏ic monographs: Triangular Norms (Kluwer, Dordrecht, 2000) and Aggregation Functions (Cambridge,U.K.: Cambridge Univ. Press, 2009), and seven edited vol- umes. He is the author of more than 300 papers in WOS journals. His research interests include aggrega- tion operators, measure and integral theory, uncertainty modelling, fuzzy sets and fuzzy logic, multicri- teria decision support, copulas, triangular norms, and intelligent computing.

Prof. Mesiar has been a Fellow of the International Fuzzy Systems Association since 2011. He is a Founder and Organizer of the FSTA, ISCAMI, ISAS, and AGOP conferences.