Abstract :
A set function is a function whose domain is the power set of a set, which is
assumed to be finite in this paper. We treat a possibly nonadditive set function, i.e.,
a set function which does not satisfy necessarily additivity, w A.qw B.s
w AjB. for AlBsB, as an element of the linear space on the power set.
Then some of the famous classes of set functions are polyhedral in that linear
space, i.e., expressed by a finite number of linear inequalities. We specify
the sets of the coefficients of the linear inequalities for some classes of set
functions. Then we consider the following three problems: a. the domain
extension problem for nonadditive set functions, b. the sandwich problem for
nonadditive set functions, and c. the representation problem of a binary relation
by a nonadditive set function, i.e., the problem of nonadditive comparative
probabilities.
