The Satisficing Process: A New Look

The satisficing process from the perspective of extended topology and, in particular, extended filters is explored. It is argued that the essence of the satisficing process is captured by the satisfaction relation, i.e., a relation between decisions and their corresponding satisfactory criterion sets. This relation leads directly to a characterization of the satisficing process in terms of isotonic spaces, extended topologies, and two special classes of filters, neighborhood-convergent systems. In this context it is possible to specify maximal product subrelations of the satisfaction relation, e.g., for a given criterion, set one can uniquely specify the largest set of decision elements which are satisfactory. These maximal product subrelations define filters on the decision set and criterion set which exhibit a fundamental property of the satisficing process-the balance principle. The satisfaction process is shown to be a generalization of optimization and other decisionmaking strategies. The filter systems on the decision and criterion sets form complete distributive lattices. Furthermore, the isotonic spaces associated with the satisfaction relation are closure spaces closely related to combinatorial geometrics, which are considered a generalization of vector spaces.