Erich Klement, Radko Mesiar, Endre Pap,
"On the order of triangular norms - comments on "A triangular norm hierarchy" by E. Cretu"
, in Fuzzy Sets and Systems, Vol. 131, Seite(n) 409-413, 2002, ISSN: 0165-0114
Original Titel:
On the order of triangular norms - comments on "A triangular norm hierarchy" by E. Cretu
Sprache des Titels:
Englisch
Englische Kurzfassung:
In Cretu (Fuzzy Sets and Systems 120 (2001) 371), the members of the families of Frank, Dubois-Prade, Yager, and
Hamacher t-norms, respectively, are compared (in a pointwise way) with the minimum, the product, and the Lukasiewicz t-norm. All these results are well-known and trivial. Moreover, these families of t-norms cannot only be compared with the three basic t-norms above, but all these families are monotone with respect to their index, a fact which is also well known and straightforward to prove (with the exception of the family of Frank t-norms whose monotonicity has been first proven in Butnariu and Klement, Triangular Norm-Based Measures and Games with Fuzzy Coalitions, Kluwer, Dordrecht, 1993).
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