Research Papers

We will be including abstracts of research papers and papers that are of interest to the AHP/ANP community in our authors database. For example, we plan to include early works by Thomas L. Saaty, Ernest Forman, Luis Vargas, Patrick Harker and others that lay out the basic concepts of the AHP/ANP. Note that the papers in our authors' database will be submitted by the authors themselves, who will retain the copyright to each paper. An author will be in control of any of his or her papers that are submitted and can replace it with a changed version or remove the paper entirely, perhaps giving a reference or a hyperlink to a Journal that insists on an exclusive copyright.

In this section we plan to give brief reports on interesting on-going research or books in progress, with links when we can to any supporting documents, models or other materials such as powerpoint slides.

ANP and Fractals

Claudio Garuti of Fulcrum, Inc., and Isabel Spencer of IBM in Santiago, Chile, (e-mail: fulcrum@bellsouth) report on their work about the similarities between the ANP and Fractals. They will be presenting it at the XXXII Brasilian Operative Research Simposium (SOBRAPO), 18-20 of October, 2000, in Brazil.

The objective of our work is to show the parallels and analogies that exist in establishing measurements for processes with dependence and feedback that exist in physical systems as well as in decision making processes. We need to compare things with different scales of measurement in both the physical world (using geometry) and in the world of the human brain with its internal processes of decision-making. We start by exploring the basic concepts of interpretation of measures and quantification using measures and their development in human history (some examples are Euclidean, Cartesian and Fractal geometry). The axioms of metrics are examined along with their interpretations in the physical world, and we point out the analogies to be found with the processes of decision making. There are mathematical parallels in how the two systems, ANP and Fractals, represent reality in their modeling processes. We examine how the two systems use limits, eigenvectors and points of accumulation, how they handle errors and consistencies, and their physical interpretations. All this is shown in an intuitive way, supported by figures and graph, that make it easy and interesting to follow.