Abstract
We consider aggregation of multiple criteria evaluations expressed on qualitative ordinal scales, which means representation of multiple criteria preferences using finite sets of values, such as “bad”, “medium”, “good”, or “weak”, “normal”, “strong”. The evaluation scales regarding single criteria, as well as comprehensive evaluations, are qualitative. Moreover, the qualitative evaluations concern either single alternatives (e.g., x is “bad”, or “medium”, or “good”) or degrees of preference for pairs of alternatives (e.g., x is “indifferent” to y, or x is “weakly preferred” to y, or x is “strongly preferred” to y).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bana e Costa, C. & Vansnick, J. (1994). Macbeth – an interactive path towards the construction of cardinal value functions. International transactions in operational Research, 34, 489–500.
Bana e Costa, C., De Corte, J.-M., & Vansnick, J. (2005). On the mathematical foundation of macbeth. In J. Figueira, S. Greco, & M. Ehrgott (Eds.), Multicriteria Decision Analysis: State of the Art Surveys (pp. 409–442). New York: Springer.
Dyer, J. & Sarin, R. (1979). Measurable multiattribute value functions. Operations Research, 27, 810–822.
Figueira, J., Mousseau, V., & Roy, B. (2005a). Electre methods. In J. Figueira, S. Greco, & M. Ehrgott (Eds.), Multicriteria Decision Analysis: State of the Art Surveys (pp. 133–162). New York: Springer.
Figueira, J., Greco, S., & Ehrgott, M. (2005b). Multiple Criteria Decision Analysis: State of the Art Surveys, Vol. 78 of Springer’s International Series in Operations Research & Management Science. New York, NY: Springer.
Figueira, J., Greco, S., & Slowinski, R. (2009). Building a set of additive value functions representing a reference preorder and intensities of preference: Grip method. European Journal of Operational Research, 195, 460–486.
Fodor, J. (2000). Smooth associative operations on finite ordinal scales. IEEE Transactions on Fuzzy Systems, 8, 791–795.
Grabisch, M. (2006). Representation of preferences over a finite scale by a mean operator. Mathematical Social Sciences, 52, 131–151.
Greco, S., Matarazzo, B., & Slowinski, R. (2001). Rough sets theory for multicriteria decision analysis. European Journal of Operational Research, 129, 1–47.
Greco, S., Matarazzo, B., & Słowiński, R. (2005). Decision rule approach. In J. Figueira, S. Greco, & M. Ehrgott (Eds.), Multicriteria Decision Analysis: State of the Art Surveys (pp. 507–563). New York: Springer.
Greco, S., Mousseau, V., & Słowiński, R. (2008). Ordinal regression revisited: multiple criteria ranking with a set of additive value functions. European Journal of Operational Research, 191, 416436.
Green, P. & Rao, V. (1971). Conjoint measurement for quantifying judgmental data. Journal Of Marketing Research, 8, 355–363.
Jacquet-Lagrèze, J. & Siskos, Y. (1982). Assessing a set of additive utility functions for multicriteria decision making: the uta method. European Journal of Operational Research, 10, 151–164.
Krantz, D., Luce, R., Suppes, P., & Tversky, A. (1971). Foundations of measurement, Vol. 1: Additive and Polynomial Representations. New York: Academic.
Marichal, J.-L. & Mesiar, R. (2004). Aggregation on finite ordinal scales by scale independent functions. Order, 21, 155–180.
Marichal, J.-L., Mesiar, R., & Rückschlossová, T. (2005). A complete description of comparison meaningful functions. Aequationes Mathematicae, 69, 309–320.
Mas, M., Mayor, G., & Torrens, J. (1999). T-operators and uninorms on a finite totally ordered set. International Journal of Intelligent Systems, 14, 909–922.
Mas, M., Monserrat, M., & Torrens, J. (2003). On bisymmetric operators on a finite chain. IEEE Transactions on Fuzzy Systems, 11, 647–651.
Ovchinnikov, S. (1996). Means on ordered sets. Mathematical Social Sciences, 32, 39–56.
Roy, B. & Bouyssou, D. (1993). Aide Multicritère à la Décision: Méthodes et Cas. Paris: Economica.
Saaty, T. (1980). The Analytic Hierarchy Process. New York: McGraw Hill.
Saaty, T. (2005). The analytic hierarchy process and analytic network processes for the measurement of intangible criteria and for decision making. In J. Figueira, S. Greco, & M. Ehrgott (Eds.), Multicriteria Decision Analysis: State of the Art Surveys (pp. 345–407). New York: Springer.
Słowiński, R., Greco, S., & Matarazzo, B. (2005). Rough set based decision support. In E. Burke & G. Kendall (Eds.), Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques (pp. 475–527). New York: Springer.
Stevens, S. (1975). Psychophysics. New York: Wiley.
Acknowledgements
The third author wishes to acknowledge financial support from the Polish Ministry of Education and Science, grant no. N N519 314435.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Greco, S., Matarazzo, B., Słowiński, R. (2010). Ordinal Qualitative Scales. In: Ehrgott, M., Naujoks, B., Stewart, T., Wallenius, J. (eds) Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems. Lecture Notes in Economics and Mathematical Systems, vol 634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04045-0_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-04045-0_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04044-3
Online ISBN: 978-3-642-04045-0
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)