On some extensions of the option choice theory (findamentals of the pseudocriterion theory)

The article is concerned with an external («input-output») description and study of operators which map a finite set of options and all its subsets onto a stretch of the numerical axis. Such operators are extensions of choice functions which have been extensively studied in the theory of choice in recent years. For the range of operators studied in the article a concept is introduced of characteristic properties which identify domains in the operator space; the graph mechanism of generating them is studied which is an extension of the graph-dominant mechanism from the theory of choice; and natural operations with such operators are introduced and studied. In particular, the set of operators generating membership functions in the vein of the fuzzy set theory and the probability generatin operators are subsets of the operator space.