Hierarchical grouping to maximize payoff /
Joe H. Ward, Jr.

Description

Main Author

Ward, Joe H., Jr.

Related Names

Lackland Air Force Base (Tex.)
United States. Wright Air Development Division

Language(s)

English

Published

Lackland Air Force Base, Texas : Personnel Laboratory, Wright Air Development Division, Air Research and Development Command, United States Air Force :

Subjects

Hierarchies.
Group theory.
Functions.
Functions.
Group theory.
Hierarchies.

Summary

This report describes mathematically a general procedure for forming hierarchical groups of mutually exclusive sets in a manner which yields an optimum value for the functional relation, or objective function, that reflects the criterion chosen by the investigator. Given k sets, this technique permits their reduction to k - 1 mutually exclusive sets by considering the union of all possible pairs that can be formed and the selection of that union which has the highest payoff value with respect to the criterion chosen. This procedure can be repeated until only one set remains. Hence decisions on the number of groups to be used can be based on a knowledge of the "costs" of grouping at each stage in the entire hierarchical structure. A computer flow-chart and a numerical example of the grouping procedure are provided. An Appendix shows how to determine the number of possible ways of forming groups and the number of distinguishable unions possible.

Note

"March 1961."

Physical Description

v, 18 pages ; 27 cm.

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