Characterization of fuzzy measures constructed by means of triangular norms

AbstractFollowing the ideas presented by the author (E. P. Klement, J. Math. Anal. Appl. 85 (1982), 543–565) finite T-fuzzy measures are introduced, T being a measurable triangular norm. We show that a T-fuzzy measure is always a fuzzy measure, as considered earlier (E. P. Klement, J. Math. Anal. Appl. 25 (1980), 330–339). Then we study the relation to the integral with respect to some classical measure. Finally, for some special triangular norms T, we give precise characterizations of the corresponding classes of T-fuzzy measures