Skip to main content
Log in

A descriptive-analytic approach to MCDA: the case of correspondence analysis

  • Original Paper
  • Published:
Operational Research Aims and scope Submit manuscript

Abstract

In this paper we introduce the method of correspondence analysis (CA) to a stochastic multicriteria problem in order to provide solutions that can support the descriptive problematic. These solutions are given in the form of new criteria-axes and the functions of factors. We interpret these functions in terms of the uniform conditional stochastic order. In case, where the first axis provides us with a significant percentage of information, we suggest a ranking of actions which approaches the usual stochastic order.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Arrow KJ, Hahn FH (1973) General competitive analysis, San Francisco, Holden Day, pp 83–87

  • Benzecri J-P (1973) L’ Analyse des Donnees, Tome II: L’ analyse des Correspondances. Dunod, Paris

    Google Scholar 

  • Brans JP, Mareschal B (1990) The PROMETHEE methods for MCDM; The PROMCALC, GAIA and BANKADVISER software. In: Bana e Costa CA (ed) Readings in multiple criteria decision aid. Springer, Berlin, pp 216–251

    Google Scholar 

  • Cailliez F, Pages J-P (1976) Introduction a l’ analyse des donnees. Smash, Paris

    Google Scholar 

  • Cheung Y-L (1989) Correspondence analysis: a descriptive technique to simplify the structure of the problems, Working Paper series. School of business, Hong Kong

    Google Scholar 

  • Cheung Y-L (1991a) Correspondence analysis as an aid to multicriteria decision making. OMEGA 19(2/3):149–155

    Article  Google Scholar 

  • Cheung Y-L (1991b) Categorical criteria values: correspondence analysis. OMEGA 22(4):371–380

    Article  Google Scholar 

  • Clark D, Rivett BHP (1976) A structural mapping to complex decision-making. J Oper Res Soc 29(2):113–128

    Article  Google Scholar 

  • D’ Avignon GR, Vincke Ph (1988) An outranking method under uncertainty. Eur J Oper Res 36:311–321

    Article  Google Scholar 

  • Dobson R, Golob TF, Gustafson RL (1974) Multidimensional scaling of consumer preferences for a public transportation system: an application of two approaches. Soc Econ Plan 8:28–36

    Google Scholar 

  • Gifi A (1990) Nonlinear multivariate analysis. Wiley, New York

    Google Scholar 

  • Gilula Z, Krieger A, Ritov Y (1988) Ordinal association in contingency tables: some interpretive aspects. J Am Stat Assoc 83(402):540–545

    Article  Google Scholar 

  • Glustoff E (1975) On continuous utility: The Euclidean distance approach. Q J Econom 512–517

  • Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic Press, London

    Google Scholar 

  • Heiser WJ (2004) Geometric representation of association between categories. Psychometrica 69(4):513–545

    Article  Google Scholar 

  • Heiser WJ, Meulman (1983)Analyzing rectangular tables by joint and constrained multidimensional scaling. J Econom 22:139–167

    Article  Google Scholar 

  • Hill MO (1974) Correspondence analysis: a neglected multivariate method. Appl Stat 23(3):340–354

    Article  Google Scholar 

  • Keeney RL, Raiffa H (1976) Decision with multiple objectives. Wiley, New York

    Google Scholar 

  • Krantz D (1967) Rational distance functions for multidimensional scaling. J Math Psychol 4:226–245

    Article  Google Scholar 

  • Lebart L, Fenelon JP (1979) Informatique et statistique appliqués. Dunod, Paris

    Google Scholar 

  • Loukas D, Papadimitriou I (2005) Introduction of correspondence analysis to the MCDA process. Data Anal Bull 6:62–75

    Google Scholar 

  • Matsatsinis NF, Avgerinopoylos E, Baourakis G (1995) Data analysis methods applied to agricultural marketing. In: Janssen J, Skiadas CH, Zopounidis C (eds) Advances in stochastic modeling and data analysis. Kluwer, Dordecht

    Google Scholar 

  • Mood AM, Graybill FA (1963) Introduction to the theory of statistics. Mc Craw-Hill, New York

    Google Scholar 

  • Muller A, Stoyan D (2002) Comparison models for stochastic models and risks. Wiley, Chichester

    Google Scholar 

  • Ritov Y, Gilula Z (1993) Analysis of contingency tables by correspondence analysis models subject to order constraint. J Am Stat Assoc 88(424):1380–1387

    Article  Google Scholar 

  • Roy B (1996) Multicriteria methodology for decision aiding. Kluwer, Dordrecht

    Google Scholar 

  • Shaked M, Schantikumar JG (1994) Stochastic orders and their applications. Academic press, New York

    Google Scholar 

  • Siskos Y, Grigoroudis E, Matsatsinis NF, Baourakis GH (1995) Comparative behavioral analysis of European oil consumers. In: Janssen J, Skiadas CH, Zopounidis C (eds) Advances in stochastic modelling and data analysis. Kluwer, Dordecht

    Google Scholar 

  • Stewart TJ (1981) A descriptive approach to multiple-criteria decision making. J Oper Res Soc 32:45–33

    Article  Google Scholar 

  • Stewart TJ (1992) A critical survey on the status of multiple-criteria decision making: theory and practice. OMEGA 20(5/6):569–586

    Article  Google Scholar 

  • Whitt W (1980) Uniform conditional stochastic order. J Appl Prob 17(1):112–123

    Article  Google Scholar 

  • Whitt W (1985) Uniform conditional variability ordering of probability distributions. J Appl Prob 22(3):619–633

    Article  Google Scholar 

  • Zeleny M (1974) A concept of the compromise solutions and the method of displaced ideal. Comp Ops Res 1:479–496

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dimos Loukas.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Loukas, D. A descriptive-analytic approach to MCDA: the case of correspondence analysis. Oper Res Int J 8, 141–152 (2008). https://doi.org/10.1007/s12351-008-0010-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12351-008-0010-x

Keywords

Navigation