Effective Convolutions of Vector Preference Relations in Decision Making Problems

Abstract

Scientific study of decision making problems are practised on a large scale. It comprises traditional psyco-physiological research, such new areas as modern theory of decision making,development of man machine procedures of decision making, decision support systems, expert systems. In this paper we are interested in formal presentation of decision making problems. It so happened that binary relations and functions of utility turned out to describe problems of decision making with most adequate manner. There is certain relationship between them. Moreover, it was the theory of decision making that began to study some classes of nonconventional binary relations. We shall consider some of them in this paper. Traditionally the problem of decision making is presented by the pare <X,R>, where X is some finite set of comperetive alternatives (decisions) and R ⊆ E is a binary relation,where E=X×X. In the theory of decision making there used a special class of binary relations making it possible to compare a pare of alternatives over some oriterium, e.g. bigger, better,more preferable, heavier, taller etc. Fishburn (11) called these binary relations preference relations.