Global function of sets in the theory of alternative selection

A language for description of selection of alternatives is described which employs selection functions which associate the set of alternatives with its subset. A family of so-called piecewise adder functions is introduced. Each function of this family is univalently defined by specifying a totality of set-parameters. The family includes both functions satisfying the condition that the choice is independent of the rejected alternatives and functions recognizing significant dependence of the choice on the context. All the functions explicitly recognize the possibility of rejecting a choice (empty choice). The properties of the functions introduced and the relations between them are described.