ASSOCIATIONS OF FUZZY-SETS

The concept of hierarchical models of associations of fuzzy sets (linguistic labels) is introduced and studied. Three basic levels of hierarchy (relational, set-theoretic, and scalar) facilitate to handle a variety of relationships between fuzzy sets. Learning mechanisms capable of discovering parameters of the introduced models are also studied. The inverse problem in models of associations is formulated along with a construction of diverse forms of matching achieved there (such as complete, borderline and excluded matching). An illustrative numerical example in pattern classification is also provided.