On the Structure of Some Families of Fuzzy Measures

The generation of fuzzy measures is an important question arising in the practical use of these operators. In this paper, we deal with the problem of developing a random generator of fuzzy measures. More concretely, we study some of the properties that any random generator should satisfy. These properties lead to some theoretical problems concerning the group of isometries that we tackle in this paper for some subfamilies of fuzzy measures.