Visual decision-making:
Using treemaps for the Analytic Hierarchy Process

Toshiyuki Asahi*, David Turo and Ben Shneiderman

Human-Computer Interaction Laboratory,
Dept. of Computer Science &
Institute for Systems Research
University of Maryland, College Park, MD 20742 USA


The Analytic Hierarchy Process (AHP), a decision-making method based upon division of problem spaces into hierarchies, is visualized through the use of treemaps, which pack large amounts of hierarchical information into small screen spaces. Two direct manipulation tools, presented metaphorically as a ìpumpî and a ìhook,î were developed and applied to the treemap to support AHP sensitivity analysis. The problem of construction site selection is considered in this video. Apart from its traditional use for problem/ information space visualization, the treemap also serves as a potent visual tool for "what if" type analysis.


Visualization, treemap, analytic hierarchy process, AHP, decision support

* Current address: Kansai C&C Research Lab., NEC Corporation, 4-24, Shiromi 1-Chome, Chuo-Ku, Osaka 540, Japan, Tel: 81-6-945-3214, email:


Treemaps graphically represent hierarchical information via a two-dimensional rectangular map, providing compact visual representations of complex data spaces through both area and color [2-5]. Their efficiency for particular data searching tasks has been tested through controlled studies [4,5] with primary benefits seen for two types of tasks: location of outliers in mass hierarchies and identification of cause-effect relationships within hierarchies. By extending the treemap into a "read/write" graphic through direct manipulation tools, the user is given the capability to massage the data and perform the outlier and cause-effect tasks much more effectively. Analytic Hierarchy Process (AHP) [1], given its decision tree hierarchy and inherent need for large-scale data visualization and user manipulation, is an appropriate choice for treemap visualization.

AHP was developed to promote improved decision-making for a specific class of problems that involve prioritization of potential alternate solutions through evaluation of a set of criteria elements. These elements may be divided into sub-elements and so on, thus forming a hierarchical decision tree. Once the hierarchical problem definition has been established, these criteria are weighted individually at every level relative to each other; prioritization of the alternate solutions can then be obtained via evaluation of these weights.

The treemap can represent both hierarchical structure and each elementsí quantitative information simultaneously in a two-dimensional rectangular space; 100% of the designated screen area is utilized. Application arenas for treemaps have included computer directory browsing, stock market portfolio visualizations, an NBA player statistical browser, and a US budget viewer.

Treemaps are generated using a straightforward algorithm known as ìslice-and-dice.î The root node of a hierarchy is represented by the entire screen area. For the root nodeís children, the screen area is sliced (either horizontally or vertically) to create smaller rectangles with area dependent upon the value of a particular weighting attribute. Each node is then processed recursively, with the direction of the slicing switched by 90 degrees for each level.

Since the decision-making processes are represented by hierarchical trees in AHP, these trees translate directly to the treemap visualization method. Figure 1 is an example of a treemap generated with our prototype AHP application. A base rectangle representing the goal of decision-making is divided into small rectangular areas proportional to their relative importances. Users can identify any criterion by labels displayed in the offset areas (offset areas are also helpful for users to recognize the hierarchical structure). The hook and pump tools (upper right in Figure 1) enable users to adjust the size of areas by pulling on a boundary or by pumping up an area. Since areas represent preferences among the alternatives, the users can quickly grasp the relative impact of each component and understand which components most influence the outcome. On the bottom of the display, a horizontal histogram shows the aggregate result, and as users hook or pump areas the histogram changes within a few hundred milliseconds. This dynamic approach enables users to explore many alternatives in seconds as opposed the many minutes required to input a fresh set of preferences using the current keyboard entry approach. The treemap, which till now has been used as a way of displaying large amounts of data, now becomes a powerful input strategy.

A usability test was conducted with six business or management majors who were already familiar with the AHP. They performed five tasks and then rated the interface highly on all 12 criteria. Improvements were suggested, but the basic concept was strongly supported [6].


1. Saaty, T.L. The Analytic Hierarchy Process. McGraw-Hill, New York, 1980.

2. Shneiderman, B. Tree Visualization with Tree-maps: A 2-D space-filling approach. ACM Transactions on Graphics 11, 1 (Jan. 1992), pp. 92-99.

3. Turo, D. and Johnson, B. Improving the visualization with treemaps: Design issues and experimentation. Proceedings of Visualization ë92, IEEE Computer Society Press, 1992, pp. 124-131.

4. Turo, D. and Johnson, B. Improving the visualization with treemaps: Design issues and experimentation. Proceedings of Visualization ë92, IEEE Computer Society Press, 1992, pp. 124-131.

5. Turo, D., Enhancing treemap displays via distortion and animation: Algorithms and experimental evaluation, Unpublished Masters Thesis, Department of Computer Science, University of Maryland, 1993.

6. Asahi, T., Turo, D., and Shneiderman, B., Using treemaps to visualize the Analytic Hierarchy Process, University of Maryland Department of Computer Science Technical Report CS-TR-3293 (June 1994).

Figure 1: Screen design for treemap representation of Analytic Hierarchy Process

with user interface tools for adjusting the treemap.