Characterization of measures based on strict triangular norms

As a natural generalization of a measure space, Butnariu and Klement [4] introduced T-tribes of fuzzy sets with T-measures. They gave a complete characterization of T-measures for a Frank triangular norm T. Here we characterize T-measures with respect to non-Frank strict triangular norms. We show the specific roles of Frank triangular norms and a newly introduced family, nearly Frank triangular norms. (C) 1999 Academic Press.