Multicriterion decisions in systems with feedback

Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States

Publication date: Jan, 1984

Journal: Mathematical Modelling in Science and Technology
- Pages: 26-36

Abstract: The process of setting priorities in systems with a network structure is more complex than it is in a hierarchy which is essentially linear. The composition of priorities in a hierarchy is a special case of composition in a system. Simple examples of composition in hierarchies with cycles between adjacent levels and cyclic hierarchies called holarchies are given. More generally suppose we have a network whose nodes are components of a system. These components can interact in a designated manner according to a variety of criteria whose priorities derive from a separate hierarchy. The object is to compose priorities for the elements of a system with respect to each criterion by examining the reducibility and primitivity characteristics of a column stochastic matrix which represents the interactions of the components of the system and then synthesize the results obtained for each criterion over the entire set of criteria by appropriate weighting with the priorities of each.

Keywords: Feedback, Network, Hierarchies, Synthesis