Hypermatrix of the Brain

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

Publication date: Jan, 2001

Journal: Artificial Neural Nets and Genetic Algorithms
- Pages: 16-21

Abstract: Decision-making, a natural and fundamental process of the brain, involves the use of pairwise comparisons. They are represented by a matrix whose entries belong to a fundamental scale, and from which an eigenvector of priorities that belongs to a ratio scale is derived. A simple decision is represented by a hierarchic structure, more complex ones by a feedback network. The alternatives from which the choice is made belong to the bottom level of the hierarchy whose upper levels contain the criteria and objectives of the decision. The derived eigenvectors are successively used to synthesize the outcome priorities by weighting and adding. A simple example of choosing the best school for the author’s son is used to illustrate this process. When there is dependence and feedback in a decision, synthesis requires the use of a stochastic supermatrix whose entries are block matrices of column normalized eigenvectors derived from paired comparisons. Stochasticity is ensured by also comparing the influence of the components that give rise to the blocks.

Keywords: Pairwise comparison, Ratio Scale, Stochastic Matrix, Block Matrice