An Imbedding Approach to Additive Value Zero-One Problems
Existing approaches to the determination of the parameters for zero-one additive value functions can involve a large amount of work. This paper considers an alternative imbedding approach which allows the parameters to be determined to within an error range 1/K within K steps. In considering the method itself specific elements of theory are developed relating to the existence of additive values for imbedding sets X \cdot Y*, X \cdot Y\~ where X is a subset of zero-one vectors, Y* is a countable subset of numbers in the range -\infty < y < \infty , and Y\~ is a connected open interval of the range -\infty < y < \infty . In seeking further approximation methods, it is necessary to investigate properties of the component value, u(\cdot) over Y* and Y\~. The coefficients of the zero-one variables are shown to be unique for Y* once two values have been preset. Under certain circumstances it can be demonstrated that a continuous u(\cdot) over Y\~ exists, and that considerable variations in u(\cdot) may be compatible with the specified preference structures, although in special circumstances u(\cdot) is unique over Y\~.
Year of publication: |
1973
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Authors: | White, D. J. |
Published in: |
Management Science. - Institute for Operations Research and the Management Sciences - INFORMS, ISSN 0025-1909. - Vol. 20.1973, 1, p. 85-100
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Publisher: |
Institute for Operations Research and the Management Sciences - INFORMS |
Saved in:
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