Solvability and approximate solvability of fuzzy relation equations*

Abstract

We give here a discussion of approximate solvability of a system of fuzzy relation equations. We demonstrate how problems of interpolation and approximation of fuzzy functions are connected with solvability of systems of fuzzy relation equations. First we explain the general framework, and later on we prove some particular results related to the problem of the best approximation.

Keywords:

• System of fuzzy relation equations
• Solvability and approximate solvability of a fuzzy relation equation system
• Fuzzy function
• Interpolation and approximation of fuzzy functions

Notes

^‡[email protected]

^*The work on this paper has been partially supported by Czech–German Scientific–Technical Cooperation CZE 01/022 and by Grant IAA1187301 of the GA AV ČR

Irina Perfilieva graduated from the Moscow State University named after M.V. Lomonosov, Department of Computer Mathematics and Cybernetics. At the same university she defended her Candidate Thesis and obtained the Degree of Candidate of Physical and Mathematical Sciences (PhD).

For a number of years she worked at the Moscow State Academy of Instrument-Making and Informatics as a professor and partially at the Moscow State University. In 1999, she moved to the Czech Republic, and since then she has worked in the University of Ostrava, Department of Mathematics and partially in the Institute for Research and Applications of Fuzzy Modeling.

In the Czech Republic she obtained full professorship in the Czech Technical University in Prague, awarded by the President of the Czech Republic. Her research activity is focused on many-valued logic, fuzzy set theory and applications, fuzzy logic, fuzzy approximation, fuzzy relation equations and neural networks.

She has published two books and more than 75 scientific papers, project reports and theses. She is a member of the board of the European Society for Fuzzy Logic and Technology (EUSFLAT) and also a member of the Editorial Board of the International Journal of Fuzzy Sets and Systems.

Siegfried Gottwald is the chair of the Institute of Logic and Theory of Science, Leipzig (Germany). Professor Gottwald graduated in mathematics from the Leipzig University and obtained his PhD in 1969. His research areas include many-valued logic and fuzzy logic, fuzzy sets, fuzzy relations and fuzzy control, and history of mathematics and logic. He is the author or editor of 11 books and more than 50 research papers in these areas. He is also a member of program committees and editorial boards of several international conferences and journals.