Abstract
Our concern is with the problem of constructing decision functions to aid in making decision under uncertainty. We discuss the tradeoff that has to be made, when selecting a scale for representing our possible payoffs, between the power of the scale and the burden of the scale. We consider here the situation in which our basic scale is an ordinal scale, however we augment this scale by allowing an additional notion, a classification of payoffs as to whether they are acceptable or not. This allows us to have information such as A is preferred to B but both are acceptable. We indicate that this formally corresponds to an ordinal scale with a denoted element and call such a scale a Denoted Ordinal Scale (DOS). It is shown that this augmentation of the ordinal scale increases the power of the scale and therefore allows us to built more sophisticated decision models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Krantz, D. H., Luce, R. D., Suppes, P. and Tversky, A., Foundations of Measurement, Academic Press: New York, 1971.
Roberts, F. S., Measurement Theory, Addison-Wesley: Reading, MA, 1979.
Arrow, K. J., Social Choice and Individual Values, John Wiley & Sons: New York, 1951.
Zadeh, L. A., “From computing with numbers to computing with words-From manipulation of measurements to manipulations of perceptions,” IEEE Transactions on Circuits and Systems, (To Appear).
Zadeh, L. A., “Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic,” Fuzzy Sets and Systems 90, 111 - 127, 1997.
Yager, R. R., “On mean type aggregation,” IEEE Transactions on Systems, Man and Cybernetics 26, 209 - 221, 1996.
Yager, R. R. and Rybalov, A., “Full reinforcement operators in aggregation techniques,” IEEE Transactions on Systems, Man and Cybernetics 28, 757 - 769, 1998.
Kosko, B., Neural Networks and Fuzzy Systems, Prentice Hall: Englewood Cliffs, NJ, 1991.
Yager, R. R. and Filev, D. P., Essentials of Fuzzy Modeling and Control, John Wiley: New York, 1994.
Roubens, M. and Vincke, P., Preference Modeling, Springer-Verlag: Berlin, 1989.
Congress, Sao Paulo, Brazil, I: 313 - 316, 1995.
Yager, R. R., “On the analytic representation of the leximin ordering and its application to flexible constraint propagation,” European Journal of Operations Research 102, 176 - 192, 1997.
Arrow, K. J. and Hurwicz, L., “An optimality criterion for decision making under ignorance,” in Uncertainty and Expectations in Economics, edited by Carter, C. F. and Ford, J. L., Kelley: New Jersey, 1972.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Yager, R.R. (2002). Ordinal Decision Making with a Notion of Acceptable: Denoted Ordinal Scales. In: Lin, T.Y., Yao, Y.Y., Zadeh, L.A. (eds) Data Mining, Rough Sets and Granular Computing. Studies in Fuzziness and Soft Computing, vol 95. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1791-1_19
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1791-1_19
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2508-4
Online ISBN: 978-3-7908-1791-1
eBook Packages: Springer Book Archive