Associations of fuzzy sets

The concept of hierarchical models of associations of fuzzy sets (linguistic labels) is discussed. Three basic levels of hierarchy (relational, set-theoretic, and scalar) facilitate the handling of a variety of relationships between fuzzy sets. Learning mechanisms capable of discovering parameters of the models introduced are studied. The inverse problem in models of associations is formulated along with a construction of diverse forms of matching achieved there. An illustrative numerical example in pattern classification is also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>