International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 351-357

Quasi-homogeneous associative functions

Bruce R. Ebanks

Department of Mathematics, Marshall University, Huntington 25755, WV, USA

Received 15 July 1996; Revised 18 March 1997

Copyright © 1998 Bruce R. Ebanks. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A triangular norm is a special kind of associative function on the closed unit interval [0,1]. Triangular norms (or t-norms) were introduced in the context of probabilistic metric space theory, and they have found applications also in other areas, such as fuzzy set theory. We determine the explicit forms of all t-norms which satisfy a generalized homogeneity property called quasi-homogeneity.