Michal BACZYNSKI

Assistant professor at the University of Silesia, Institute of Mathematics ‘Habilitation’ in Computer Science, Systems Research Institute, Polish Academy of Sciences in Warsaw

Tuesday 19th – 9h00-10h00

Fuzzy Implications Functions: Recent Advances

Fuzzy implication functions generalize the classical implication and play a significant role in the development of fuzzy systems. The study of this class of operations has been extensively developed in the last 30 years from both theoretical and applicational points of view. Due to the importance and a constant growth of interest, it becomes a natural need to present a coherent knowledge about this class of functions.
In our talk we will firstly discuss some historical aspects of fuzzy implications. Next, we will describe main classes of implications functions, showing different methods of generating them from other connectives used in fuzzy logic or from unary functions defined on the unit interval. In this part we will present main characterizations and representations results and we will discuss also the problem of intersections of different classes of fuzzy implications. Finally, we will concentrate on recent topics connected with fuzzy implications. In particular we will show how knowledge of the solutions of certain functional equations can help in designing methods that increase the computing performance of different inference schemes used in approximate reasoning.