Summarizing and propagating uncertain information with triangular norms

Generated triangular norms

Cardinalities of fuzzy sets with triangular norms

This paper presents a variety of cardinality concepts offered by cardinality theory of triangular norm-based fuzzy sets, including the scalar and the "fuzzy" streams.

Pinchings and Norms of Scaled Triangular Matrices 1 Pinchings and Norms of Scaled Triangular Matrices

Suppose U is an upper-triangular matrix, and D a nonsingular diagonal matrix whose diagonal entries appear in nondescending order of magnitude down the diagonal. It is proved that kD UDk kUk for any matrix norm that is reduced by a pinching. In addition to known examples { weakly unitarily invariant norms { we show that any matrix norm de ned by kAk def = max x 6=0; y 6=0 Re (x Ay) (x) (y) ; wh...

Summarizing information

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k-Lipschitz strict triangular norms

This paper deals with Lipschitzian t-norms. A partial answer to an open problem of Alsina, Frank and Schweizer is given with regard to strict t-norms with smooth additive generators. A new notion of local Lipschitzianity for arbitrary tnorms is introduced. Some remarkable examples of non-Lipschitzian continuous triangular norms are provided.