Compositions of fuzzy relations with hedges

We present extensions of ordinary compositions of fuzzy relations. The extensions consist in parameterizing the ordinary compositions by means of particular unary functions on the scales of truth degrees. The approach is inspired by our previous work on formal concept analysis of data with fuzzy attributes where such parameterization of one particular type of fuzzy relational composition was used to control the number of clusters extracted from data. We present definitions and basic properties of the parameterized compositions, examples, and implications for several domains of application of fuzzy relational compositions.