Irina Perfilieva

University of Ostrava, Czech Republic

Laplace Operators in Hilbert manifolds initiated by fuzzy partition

The goals are:

- Propose a manifold organization of space (universe) based on a system of local coordinates that arose from a fuzzy partition;

- Use the theory of Riemannian-Hilbert manifolds as a framework;

- Define Laplace operators using the Laplace-Beltrami approach;

- Characterize the Laplace spectrum

Short bio

Professor Irina Perfilieva, Ph.D., received the degrees of M.S. (1975) and Ph.D (1980) in Applied Mathematics from the Lomonosov State University in Moscow, Russia. At present, she is full professor in the University of Ostrava (CZ) and a Head of Theoretical Research Department in the Institute for Research and Applications of Fuzzy Modeling (IRAFM). She is: the author and co-author of six books on mathematical principles of fuzzy sets, fuzzy logic and their applications; area editor of International Journal of CIS (IJCIS), Soft Computing, editorial board member of the journals: Fuzzy Sets and Systems,  Journal of Uncertain Systems, IEEE Transaction on Fuzzy Systems, Advances in Artificial Intelligence and Machine Learning.

She works as a member of Program Committees of the most prestigious International Conferences and Congresses in the area of fuzzy and knowledge-based systems. She is an EUSFLAT Honorary Member, and the IFSA Fellow. She received a special price at the 2010 Seoul International Invention Fair and several awards for the best paper, IFSA 2019 as the last. She has two patents.

Her scientific interests lie in the area of applied mathematics and mathematical modeling where she successfully uses modern as well as classical approaches. For the past five years, she has been working in the field of fuzzy integro-differential equations, image processing, pattern recognition and the theoretical foundations of deep learning.