Conjoint measurement for MCDM. A brief introduction

[en] This paper offers a brief and nontechnical introduction to the use of conjoint measurement in multiple criteria decision making. The emphasis is on the, central, additive value function model. We outline its axiomatic foundations and present various possible assessment techniques to implement it. Some extensions of this model, e.g. nonadditive models or models tolerating intransitive preferences are then briefly reviewed.

Disciplines :

Mathematics

Author, co-author :

Bouyssou, D.

Pirlot, Marc ; Université de Mons > Faculté Polytechnique > Mathématique et Recherche opérationnelle

Language :

English

Title :

Conjoint measurement for MCDM. A brief introduction

Publication date :

01 January 2005

Main work title :

Multiple Criteria Decision Analysis: State of the Art Surveys

Pages :

73-130

Research unit :

F151 - Mathématique et Recherche opérationnelle

Commentary :

1045 p

Available on ORBi UMONS :

since 10 December 2010

Statistics

Number of views

6 (0 by UMONS)

Number of downloads

0 (0 by UMONS)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

Bibliography

E. W. Adams. Elements of a theory of inexact measurement. Philosophy of Science, 32:205-228, 1965.
E. W. Adams and R. F. Fagot. A model of riskless choice. Behavioral Science, 4:1-10, 1959.
L. Adelman, P. J. Sticha, and M. L. Donnell. An experimental investigation of the relative effectiveness of two techniques for structuring multiattributed hierarchies. Organizational Behavior and Human Decision Processes, 37:188-196, 1986.
F. Aleskerov and B. Monjardet. Utility Maximization, Choice and Preference, Springer Verlag, Heidelberg, 2002.
A. B. Atkinson. On the measurement of inequality. Journal of Economic Theory, 2:244-263, 1970.
C. A. Bana e Costa. The use of multi-criteria decision analysis to support the search for less conflicting policy options in a multi-actor context: Case study. Journal of Multi- Criteria Decision Analysis, 10(2): 111-125, 2001.
C. A. Bana e Costa, É. C. Corrêa, J.-M. De Corte, and J.-C. Vansnick. Facilitating bid evaluation in public call for tenders: A socio-technical approach. Omega, 30(3):227-242, April 2002.
C. A. Bana e Costa, M. L. Costa-Lobo, I. A. J. Ramos, and J.-C. Vansnick. Multicriteria approach for strategic town planning; The case of Barcelos. In D. Bouyssou, É. Jacquet-Lagrèze, P. Perny, D. Vanderpooten, and Ph. Vincke, editors, Aiding Decisions with Multiple Criteria: Essays in Honour of Bernard Roy, pages 429-456. Kluwer Academic Publishers, Dordrecht, 2002.
C. A. Bana e Costa, L. Ensslin, É. C. Corrêa, and J.-C. Vansnick. Decision support systems in action: Integrated application in a multicriteria decission aid process. European Journal of Operational Research, 113(2):315-335, March 1999.
C. A. Bana e Costa, F. Nunes da Silva, and J.-C. Vansnick. Conflict dissolution in the public sector: A case-study. European Journal of Operational Research, 130(2):388-401, 2001.
C. A. Bana e Costa and R. C. Oliveira. Assigning priorities for maintenance and repair and refurbishment in managing a municipal housing stock. European Journal of Operational Research, 138:380-91, 2002.
C. A. Bana e Costa and J.-C. Vansnick. MACBETH - An interactive path towards the construction of cardinal value functions. International Transactions in Operational Research, 1:489-500, 1994.
A. F. Beardon, J. C. Candeal, G. Herden, E. Induráin, and G. B. Mehta. The non-existence of a utility function and the structure of non-representatble preference relations. Journal of Mathematical Economics, 37:17-38, 2002.
D. E. Bell. Multilinear representations for ordinal utility functions. Journal of Mathematical Psychology, 31:44-59, 1987.
V. Belton, F. Ackermann, and I. Shepherd. Integrated support from problem structuring through alternative evaluation using COPE and Journal of Multi-Criteria Decision Analysis, 6:115-130, 1997.
V. Belton and T. Stewart. Multiple Criteria Decision Analysis: An Integrated Approach. Kluwer Academic Publishers, Dordrecht, 2001.
E. Ben-Porath and I. Gilboa. Linear measures, the Gini index and the income-equality tradeoff. Journal of Economic Theory, 64:443-467, 1994.
E. Ben-Porath, I. Gilboa, and D. Schmeidler. On the measurement of inequality under uncertainty. Journal of Economic Theory, 75:194-204, 1997.
M. Beuthe and G. Scannella. Applications comparées des méthodes d’analyse multicritère UTA. RAIRO Recherche Opérationnelle / Operations Research, 30(3):293-315, 1996.
M. Beuthe and G. Scannella. Comparative analysis of UTA multicriteria methods. European Journal of Operational Research, 130(2):246-262, 2001.
C. Blackorby, D. Primont, and R. Russell. Duality, Separability, and Functional Structure: Theory and Economic Applications. North-Holland, New York, 1978.
D. Bouyssou. Some remarks on the notion of compensation in MCDM. European Journal of Operational Research, 26:150-160, 1986.
D. Bouyssou. Modelling inaccurate determination, uncertainty, imprecision using multiple criteria. In A. G. Lockett and G. Islei, editors, Improving Decision Making in Organisations, pages 78-87. Springer Verlag, Heidelberg, 1989.
D. Bouyssou. Builing criteria: A prerequisite for MCDA. In C. A. Bana e Costa, editor, Readings in Multiple Criteria Decision Aid, pages 58-81, Berlin, 1990. Springer Verlag.
D. Bouyssou. Outranking methods. In C. A. Floudas and P. M. Pardalos, editors, Encyclopedia of Optimization, volume 4, pages 249-255. Kluwer Academic Publishers, Dordrecht, 2001.
D. Bouyssou, S. Greco, B. Matarazzo, M. Pirlot, and Characterization of ‘max’, ‘min’ and ‘order statistics’ multicriteria aggregation functions. Communication to IFORS’2002, 8-12 July, 2002, Edinburgh, U.K., July 2002.
D. Bouyssou, Th. Marchant, M. Pirlot, P. Perny, A. Tsoukiàs, and Ph. Vincke. Evaluation and Decision Models: A Critical Perspective. Kluwer Academic Publishers, Dordrecht, 2000.
D. Bouyssou and M. Pirlot. A characterization of strict concordance relations. In D. Bouyssou, É. Jacquet-Lagrèze, P. Perny, D. Vanderpooten, and Ph. Vincke, editors, Aiding Decisions with Multiple Criteria: Essays in Honour of Bernard Roy, pages 121-145. Kluwer Academic Publishers, Dordrecht, 2002.
D. Bouyssou and M. Pirlot. Nontransitive decomposable conjoint measurement. Journal of Mathematical Psychology, 46:677-703, 2002.
D. Bouyssou and M. Pirlot. Preferences for multiattributed alternatives: Traces, dominance, and numerical representations. www.lamsade.dauphine.fr/~bouyssou, 2002. Working Paper, LAMSADE, Université Paris-Dauphine, submitted.
D. Bouyssou and M. Pirlot. ‘Additive difference’ models without additivity and subtractivity. www.lamsade.dauphine.fr/~bouyssou, 2003. Working Paper, LAMSADE, Université Paris-Dauphine.
D. Bouyssou and M. Pirlot. A characterization of concordance relations. www.lamsade.dauphine.fr/~bouyssou, 2003. Working Paper, LAMSADE, Université Paris-Dauphine.
D. Bouyssou and J.-C. Vansnick. Noncompensatory and generalized noncompensatory preference structures. Theory and Decision, 21:251-266, 1986.
D. S. Briges and G. B. Mehta. Representations of Preference Orderings. Springer Verlag, Berlin, 1995.
J. D. Carroll and P. E. Green. Psychometric methods in marketing research. Part 1. Conjoint analysis. Journal of Marketing Research, 32:385-391, 1995.
A. Charnes and W. W. Cooper. Management Models and Industrial Applications of Linear Programming. John Wiley & Sons, New York, 1961.
A. Chateauneuf and P. P. Wakker. From local to global additive representation. Journal of Mathematical Economics, 22(6):523-545, 1993.
J.-C. Cosset, Y. Siskos, and C. Zopounidis. The evaluation of country risk: A decision support approach. Global Finance Journal, 3:79-95, 1992.
M. A. Croon. The axiomatization of additive difference models for preference judgements. In E. Degreef and G. van Buggenhaut, editors, Trends in Mathematical Psychology, pages 193-227, Amsterdam, 1984. North-Holland.
V. Dahlstrand and H. Montgomery. Information search and evaluation processes in decision-making: A computer-based process tracking study. Acta Psychologica, 56:113-123, 1984.
P. de Donder, M. Le Breton, and M. Truchon. Choosing from a weighted tournament. Mathematical Social Sciences, 40:85-109, 2000.
G. Debreu. Representation of a preference ordering by a numerical function. In R. Thrall, C. H. Coombs, and R. Davies, editors, Decision Processes, pages 159-175, New York, 1954. John Wiley & Sons.
G. Debreu. Theory of Value: An Axiomatic Analysis of Economic Equilibrium. John Wiley & Sons, New York, 1959.
G. Debreu. Topological methods in cardinal utility theory. In K. J. Arrow, S. Karlin, and P. Suppes, editors, Mathematical Methods in the Social Sciences, pages 16-26. Stanford University Press, Stanford, 1960.
G. Debreu. Continuity properties of Paretian utility. International Economic Review, 5(3):285-293, September 1964.
Ph. Delquié. Inconsistent trade-offs between attributes: New evidence in preference assessment biases. Management Science, 39(11):1382-1395, 1993.
A. I. Dimitras, C. Zopounidis, and C. Hurson. Assessing financial risks using a multicriteria sorting procedure: The case of country risk assessment. Foundations of Computing and Decision Sciences, 29:97-109, 2001.
M. Doumpos, S. H. Zanakis, and C. Zopounidis. Multicriteria preference disaggregation for classification problems with an application to global investing risk. Decision Sciences, 32(2):333-385, 2001.
D. Dubois, J.-L. Marichal, H. Prade, M. Roubens, and R. Sabbadin. The use of the discrete Sugeno integral in decision-making: A survey. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9(5):539-561, 2001.
J. S. Dyer and R. K. Sarin. Measurable multiattribute value functions. Operations Research, 27:810-822, 1979.
W. Edwards. Social utilities. Engineering Economist, 6:119-129, 1971.
W. Edwards. How to use multiattribute utility measurement for social decision making. IEEE Transactions on Systems, Man and Cybernetics, 7(5):326-340, 1977.
W. Edwards and F. Hutton Barron. SMART and SMARTER: Improved simple methods for multiattribute utility measurement. Organizational Behavior and Human Decision Processes, 60:306-325, 1994.
J.-C. Falmagne. On a class of probabilistic conjoint measurement models: Some diagnostic properties. Journal of Mathematical Psychology, 19(2):73-88, 1979.
H. Fargier and P. Perny. Modélisation des préférences par une règle de concordance généralisée. In A. Colorni, M. Paruccini, and B. Roy, editors, A-MCD-A, Aide Multicritère à la Décision/Multiple Criteria Decision Aid, pages 99-115. European Commission, Joint Research Centre, 2001.
Final report of the British Association for the Advancement of Science. 2:331-349, 1940.
P. C. Fishburn. Intransitive indifference in preference theory: A survey. Operations Research, 18(2):207-228, 1970.
P. C. Fishburn. Utility Theory for Decision-Making. John Wiley & Sons, New York, 1970.
P. C. Fishburn. Lexicographic orders, utilities and decision rules: A survey. Management Science, 20(11):1442-1471, 1974.
P. C. Fishburn. Axioms for lexicographic preferences. Review of Economic Studies, 42:415-419, 1975.
P. C. Fishburn. Noncompensatory preferences. Synthese, 33:393-403, 1976.
P. C. Fishburn. Condorcet social choice functions. SIAM Journal on Applied Mathematics, 33:469-489, 1977.
P. C. Fishburn. A survey of multiattribute/multicriteria evaluation theories. In S. Zionts, editor, Multicriteria Problem Solving, pages 181-224. Springer Verlag, Berlin, 1978.
P. C. Fishburn. Lexicographic additive differences. Journal of Mathematical Psychology, 21:191-218, 1980.
P. C. Fishburn. Nontransitive measurable utility. Journal of Mathematical Psychology, 26:31-67, 1982.
P. C. Fishburn. Interval Orders and Intervals Graphs. John Wiley & Sons, New York, 1985.
P. C. Fishburn. Nonlinear Preference and Utility Theory. Johns Hopkins University Press, Baltimore, 1988.
P. C. Fishburn. Normative theories of decision making under risk and under uncertainty. In Nonconventional Preference Relations in Decision Making, pages 1-21. Springer Verlag, Berlin, 1988.
P. C. Fishburn. Additive non-transitive preferences. Economic Letters, 34:317-321, 1990.
P. C. Fishburn. Continuous nontransitive additive conjoint measurement. Mathematical Social Sciences, 20:165-193, 1990.
P. C. Fishburn. Skew symmetric additive utility with finite states. Mathematical Social Sciences, 19:103-115, 1990.
P. C. Fishburn. Nontransitive additive conjoint measurement. Journal of Mathematical Psychology, 35:1-40, 1991.
P. C. Fishburn. Nontransitive preferences in decision theory. Journal of Risk and Uncertainty, 4:113-134, 1991.
P. C. Fishburn. Additive differences and simple preference comparisons. Journal of Mathematical Psychology, 36:21-31, 1992.
P. C. Fishburn. A general axiomatization of additive measurement with applications. Naval Research Logistics, 39(6):741-755, 1992.
P. C. Fishburn. On nonstandard nontransitive additive utility. Journal of Economic Theory, 56:426-433, 1992.
P. C. Fishburn. Finite linear qualitative probability. Journal of Mathematical Psychology, 40:21-31, 1996.
P. C. Fishburn. Cancellation conditions for multiattribute preferences on finite sets. In M. H. Karwan, J. Spronk, and J. Wallenius, editors, Essays in Decision Making, pages 157-167. Springer Verlag, Berlin, 1997.
S. French. Decision Theory - An Introduction to the Mathematics of Rationality. Ellis Horwood, London, 1993.
D. G. Fryback and R. L. Keeney. Constructing a complex judgmental model: An index of trauma severity. Management Science, 29:869-883., 1983.
G. Furkhen and M. K. Richter. Additive utility. Economic Theory, 1:83-105, 1991.
G. Furkhen and M. K. Richter. Polynomial utility. Economic Theory, 1:231-249, 1991.
D. Gale. The Theory of Linear Economic Models. McGraw-Hill, New York, 1960.
I. Gilboa and R. Lapson. Aggregation of semiorders: Intransitive indifference makes a difference. Economic Theory, 5:109-126, 1995.
Ch. Gonzales. Additive utilities when some components are solvable and others not. Journal of Mathematical Psychology, 40:141-151, 1996.
Ch. Gonzales. Utilités additives: Existence et construction. Thèse de doctorat, Université Paris 6, Paris, France, 1996.
Ch. Gonzales. Two factor additive conjoint measurement with one solvable component. Journal of Mathematical Psychology, 44:285-309, 2000.
Ch. Gonzales. Additive utility without restricted solvavibility on every component. Journal of Mathematical Psychology, 47:47-65, 2003.
W. M. Gorman. The structure of utility functions. Review of Economic Studies, XXXV:367-390, 1968.
M. Grabisch. The application of fuzzy integrals to multicriteria decision making. European Journal of Operational Research, 89:445-456, 1996.
M. Grabisch. Fuzzy integral as a flexible and interpretable tool of aggregation. In Aggregation and Fusion of Imperfect Information, pages 51-72. Physica, Heidelberg, 1998.
M. Grabisch, Ch. Labreuche, and J.-C. Vansnick. On the extension of pseudo-boolean functions for the aggregation of interacting criteria. European Journal of Operational Research, 148(1):28-47, 2003.
M. Grabisch, S. A. Orlovski, and R. R. Yager. Fuzzy aggregation of numerical preferences. In editor, Fuzzy Sets in Decision Analysis, Operations Research and Statistics, pages 31-68. Kluwer Academic Publishers, Boston, MA, 1998.
M. Grabisch and P. Perny. Agrégation multicritère. In B. Bouchon-Meunier and C. Marsala, editors, Logique Floue, Principes, Aide à la Décision, pages 82-120. Hermès, 2002.
M. Grabisch and M. Roubens. Application of the Choquet integral in multicriteria decision making. In M. Grabisch, T. Murofushi, and M. Sugeno, editors, Fuzzy Measures and Integrals, pages 348-374. Physica Verlag, Heidelberg, 2000.
N. Grassin. Constructing criteria population for the comparison of different options of high voltage line routes. European Journal of Operational Research, 26:42-47, 1886.
S. Greco, B. Matarazzo, and Rough approximation of a preference relation by dominance relations. European Journal of Operational Research, 117:63-83, 1999.
S. Greco, B. Matarazzo, and The use of rough sets and fuzzy sets in MCDM. In T. Gal, T. Hanne, and T. Stewart, editors, Multicriteria Decision Making, Advances in MCDM Models, Algorithms, Theory and Applications, pages 14.1-14.59. KluwerAcademic Publishers, Dordrecht, 1999.
S. Greco, B. Matarazzo, and Axiomatic basis of noncompensatoty preferences. Communication to Foundations of Utility and Risk Theory, FUR X, 30 May-2 June, Torino, Italy, 2001.
S. Greco, B. Matarazzo, and Conjoint measurement and rough set approach for multicriteria sorting problems in presence of ordinal criteria. In A. Colorni, M. Paruccini, and B. Roy, editors, A-MCD-A, Aide Multicritère à la Décision/Multiple Criteria Decision Aid, pages 117-144. European Commission, Joint Research Centre, 2001.
S. Greco, B. Matarazzo, and Rough sets theory for multicriteria decision analysis. European Journal of Operational Research, 129:1-47, 2001.
S. Greco, B. Matarazzo, and Preference representation by means of conjoint measurement and decision rule model. In D. Bouyssou, É. Jacquet-Lagrèze, P. Perny, D. Vanderpooten, and Ph. Vincke, editors, Aiding Decisions with Multiple Criteria: Essays in Honour of Bernard Roy, pages 263-313. Kluwer Academic Publishers, Dordrecht, 2002.
P. E. Green and V. Srinivasan. Conjoint analysis in consumer research: Issues and outlook. Journal of Consumer Research, 5:103-152, 1978.
P. E. Green, D. S. Tull, and G. Albaum. Research for Marketing Decisions. Englewood Cliffs, 1988.
E. Grigoroudis, Y. Siskos, and O. Saurais. TELOS: A customer satisfaction evaluation software. Computers and Operations Research, 27(7-8):799-817, 2000.
J. Guild. Part III of Quantitative estimation of sensory events. Interim report, British Academy for the Advancement of Science, 1936. pp. 296-328.
F. Gul. Savage’s theorem with a finite number of states. Journal of Economic Theory, 57:99-110, 1992.
G. Iverson and J.-C. Falmagne. Statistical issues in measurement. Mathematical Social Sciences, 10:131-153, 1985.
É. Jacquet-Lagrèze. Interactive assessment of preferences using holistic judgments. The PREFCALC system. In C. A. Bana e Costa, editor, Readings in Multiple Criteria Decision Aid, pages 335-350. Springer Verlag, Berlin, 1990.
É. Jacquet-Lagrèze. An application of the UTA discriminant model for the evaluation of R&D projects. In P. Pardalos, Y. Siskos, and C. Zopounidis, editors, Advances in Multicriteria Analysis, pages 203-211. Kluwer Academic Publishers, Dordrecht, 1995.
É. Jacquet-Lagrèze and J. Siskos. Assessing a set of additive utility functions for multicriteria decision making: The UTA method. European Journal of Operational Research, 10:151-164, 1982.
J.-Y. Jaffray. Existence, propriétés de continuité, additivité de fonctions d’utilité sur un espace partiellement ou totalement ordonné. Thèse de doctorat d’état, Université Paris 6, Paris, France, 1974.
J.-Y. Jaffray. On the extension of additive utilities to infinite sets. Journal of Mathematical Psychology, 11:431-452, 1974.
R. M. Johnson. Trade-off analysis of consumer values. Journal of Marketing Research, 11:121-127, 1974.
E. Karni and Z. Safra. The hexagon condition and additive representation for two dimensions: An algebraic approach. Journal of Mathematical Psychology, 42:393-399, 1998.
R. L. Keeney. Measurement scales for quantifying attributes. Behavioral Science, 26:29-36, 1981.
R. L. Keeney. Building models of values. European Journal of Operational Resesearch, 37(2): 149-157, 1988.
R. L. Keeney. Structuring objectives for problems of public interest. Operations Research, 36:396-405, 1988.
R. L. Keeney. Value-focused Thinking. Harvard University Press, Cambridge, MA, 1992.
R. L. Keeney, J. S. Hammond, and H. Raiffa. Smart Choices: A Guide to Making Better Decisions. Harvard University Press, Boston, 1999.
R. L. Keeney and H. Raiffa. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. John Wiley & Sons, New York, 1976.
R. L. Keeney and G. A. Robillard. Assessing and evaluating environ-mental impacts at proposed nuclear power plant sites. Journal of Environmental Economics and Management, 4:153-166, 1977.
V. Köbberling. Strenth of preference and cardinal utility. Working paper, University of Maastricht, Maastricht, June 2002.
V. Köbberling. Comment on: Edi Karni & Zvi Safra (1998) The hexagon condition and additive representation for two dimensions: An algebraic approach. Journal of Mathematical Psychology, 47(3):370, 2003.
T. C. Koopmans. Stationary ordinal utility and impatience. Econometrica, 28:287-309, 1960.
T. C. Koopmans. Representation of prefernce orderings over time. In C. B. McGuire and R. Radner, editors, Decision and Organization, pages 57-100. Noth-Holland, Amsterdam, 1972.
D. H. Krantz. Conjoint measurement: The Luce-Tukey axiomatization and some extensions. Journal of Mathematical Psychology, 1:248-277, 1964.
D. H. Krantz. Extensive measurement in semiorders. Philosophy of Science, 34:348-362, 1967.
D. H. Krantz, R. D. Luce, P. Suppes, and A. Tversky. Foundations of Measurement, Vol. 1: Additive and Polynomial Representations. Academic Press, New York, 1971.
G. Laffond, J.-F. Laslier, and M. Le Breton. Condorcet choice correspondences: A set-theoretical comparison. Mathematical Social Sciences, 30:23-36, 1995.
J.-F. Laslier. Tournament Solutions and Majority Voting. Springer Verlag, Berlin, 1997.
J. Louvière. Analyzing Decision Making: Metric Conjoint Analysis. Sage, Park, CA, 1988.
R. D. Luce. Semiorders and a theory of utility discrimination. Econometrica, 24:178-191, 1956.
R. D. Luce. Three axiom systems for additive semiordered structures. SIAM Journal of Applied Mathematics, 25:41-53, 1973.
R. D. Luce. Conjoint measurement: A brief survey. In David E. Bell, Ralph L. Keeney, and Howard Raiffa, editors, Conflicting Objectives in Decisions, pages 148-171. John Wiley & Sons, New York, 1977.
R. D. Luce. Lexicographic tradeoff structures. Theory and Decision, 9:187-193, 1978.
R. D. Luce. Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches. Lawrence Erlbaum Publishers, Mahwah, New Jersey, 2000.
R. D. Luce and M. Cohen. Factorizable automorphisms in solvable conjoint structures. I. Journal of Pure and Applied Algebra, 27(3):225-261, 1983.
R. D. Luce, D. H. Krantz, P. Suppes, and A. Tversky. Foundations of Measurement, Vol. 3: Representation, Axiomatisation and Invariance. Academic Press, New York, 1990.
R. D. Luce and A. A. J. Marley. Extensive measurement when concatenation is restricted. In S. Morgenbessser, P. Suppes, and M. G. White, editors, Philosophy, Science and Method: Essays in Honor of Ernest Nagel, pages 235-249. St. Martin’s Press, New York, 1969.
R. D. Luce and J. W. Tukey. Simultaneous conjoint measurement: A new type of fundamental measurement. Journal of Mathematical Psychology, 1:1-27, 1964.
A. Maas and P. P. Wakker. Additive conjoint measurement for multiattribute utility. Journal of Mathematical Psychology, 38:86-101, 1994.
J.-L. Marichal. An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. IEEE Transactions on Fuzzy Systems, 8, 2000.
J.-L. Marichal. On Choquet and Sugeno integrals as aggregation functions. In M. Grabisch, T. Murofushi, and M. Sugeno, editors, Fuzzy Measures and Integrals, pages 247-272. Physica Verlag, Heidelberg, 2000.
J.-L. Marichal. On Sugeno integralsas an aggregation function. Fuzzy Sets and Systems, 114, 2000.
J.-L. Marichal and M. Roubens. Determination of weights of interacting criteria from a reference set. European Journal of Operational Research, 124:641-50, 2000.
K. O. May. Intransitivity, utility and the aggregation of preference patterns. Econometrica, 22:1-13, 1954.
G. Mihelis, E. Grigoroudis, Y. Siskos, Y. Politis, and Y. Malandrakis. Customer satisfaction measurement in the private bank sector. European Journal of Operational Research, 130(2):347-360, 2001.
N. R. Miller. Graph theoretical approaches to the theory of voting. American Journal of Political Science, 21:769-803, 1977.
J. Miyamoto and P. P. Wakker. Multiattribure utility theory without expected utility foundations. Operations Research, 44(2):313-326, 1996.
H. Montgomery. A study of intransitive preferences using a think aloud procedure. In H. Jungerman and G. de Zeeuw, editors, Decision-making and Change in Human Affairs, pages 347-362. D. Reidel, Dordrecht, 1977.
H. Montgomery and O. Svenson. On decision rules and information processing strategies for choice among multiattribute alternatives. Scandinavian Journal of Psychology, 17:283-291, 1976.
Y. Nakamura. Lexicographic additivity for multi-attribute preferences on finite sets. Theory and Decision, 42:1-19, 1997.
Y. Nakamura. Additive utility on densely ordered sets. Journal of Mathematical Psychology, 46:515-530, 2002.
L. Narens. Abstract Measurement Theory. MIT press, Cambridge, MA, 1985.
L. Narens and R. D. Luce. The algebra of measurement. Journal of Pure and Applied Algebra, 8(2):191-233, 1976.
A. Ostanello. Action evaluation and action structuring - Different decision aid situations reviewed through two actual cases. In C. A. Bana e Costa, editor, Readings in Multiple Criteria Decision Aid, pages 36-57. Springer Verlag, Berlin, 1990.
J. E. Peris and B. Subiza. Condorcet choice correspondences for weak tournaments. Social Choice and Welfare, 16:217-231, 1999.
J. Pfanzagl. Theory of Measurement. Physica Verlag, Würzburg, 2nd revised edition edition, 1971.
M. Pirlot and Ph. Vincke. Lexicographic aggregation of semiorders. Journal of Multicriteria Decision Analysis, 1:47-58, 1992.
M. Pirlot and Ph. Vincke. Semiorders. Properties, Representations, Applications. Kluwer Academic Publishers, Dordrecht, 1997.
J.-Ch. Pomerol and S. Barba-Romero. Multicriterion Decision in Management, Principles and Practice. Kluwer Academic Publsihers, Dordrecht, 2000.
M. Pöyhönen, H. Vrolijk, and R. P. Hämäläinen. Behavioral and procedural consequences of structural variations in value trees. European Journal of Operational Research, 134(l):216-227, 2001.
H. Raiffa. Decision Analysis - Introductory Lectures on Choices under Uncertainty. Addison-Wesley, Reading, MA, 1968.
H. Raiffa. Preference for multi-attributed alternatives. RAND Memorandum, RM-5868- DOT/RC, December 1968.
M. K. Richter. Rational choice and polynomial measurement theory. Journal of Mathematical Psychology, 12:99-113, 1975.
F. S. Roberts. Measurement Theory with Applications to Decision Making, Utility and the Social Sciences. Addison-Wesley, Reading, 1979.
F. S. Roberts and R. D. Luce. Axiomatic thermodynamics and extensive measurement. Synthese, 18:311-326, 1968.
M. Roubens and Ph. Vincke. Preference Modelling. Springer Verlag, Berlin, 1985.
B. Roy. Classement et choix en présence de points de vue multiples (la méthode ELECTRE). R1RO, Revue d’Informatique et de Recherche Operationelle, 2:57-75, 1968.
B. Roy. Main sources of inaccurate determination, uncertainty and imprecision in decision models. Mathematical and Computer Modelling, 12(10-11):1245-1254, 1989.
B. Roy. The outranking approach and the foundations of ELECTRE methods. Theory and Decision, 31:49-73, 1991.
B. Roy. Multicriteria Methodology for Decision Aiding. Kluwer Academic Publishers, Dordrecht, 1996. Original version in French “Methodologie Multicritère d’Aide à la Décision”, Economica, Paris, 1985.
B. Roy and D. Bouyssou. Aide Multicritère à la Décision: Méthodes et Cas. Economica, Paris, 1993.
J. E. Russo and B. A. Dosher. Strategies for multiattribute binary choice. Journal of Experimental Psychology: Learning, Memory and Cognition, 9:676-696, 1983.
D. G. Saari. Connecting and resolving Sen’s and Arrow’s theorems. Social Choice and Welfare, 15:239-261, 1998.
L. J. Savage. The Foundations of Statistics. John Wiley & Sons, New York, 1954.
T. Schwartz. The Logic of Collective Choice. Columbia University Press, 1986.
D. Scott. Measurement structures and linear inequalities. Journal of Mathematical Psychology, 1:233-247, 1964.
D. Scott and P. Suppes. Foundational aspects of theories of measurement. Journal of Symbolic Logic, 23:113-128, 1958.
U. Segal. A sufficient condition for additively separable functions. Journal of Mathematical Economics, 23:295-303, 1994.
U. Segal and J. Sobel. Min, Max and Sum. Journal of Economic Theory, 106:126-150, 2002.
A. K. Sen. Social choice theory. In K. J. Arrow and M. D. Intriligator, editors, Handbook of Mathematical Economics, volume 3, pages 1073-1181. North-Holland, Amsterdam, 1986.
L. Shapiro. Conditions for expected uility maximization. Annals of Statistics, 7:1288-1302, 1979.
Y. Siskos. Evaluating a system of furniture retail outlets using an interactive ordinal regression model. European Journal of Operational Research, 23:179-193, 1986.
Y. Siskos and D. K. Despotis. A DSS oriented method for multiobjective linear programming problems. Decision Support Systems, 5(1):47-56, 1989.
Y. Siskos, D. K. Despotis, and M. Ghediri. Multiobjective modelling for regional agricultural planning: Case study in Tunisia. European Journal of Operational Research, 77(3):375-391, 1993.
Y. Siskos, E. Grigoroudis, C. Zopounidis, and O. Saurais. Measuring customer satisfaction using a collective preference disaggregation model. Journal of Global Optimization, 12(2):175-195, 1998.
Y. Siskos, N. F. Matsatsinis, and G. Baourakis. Multicriteria analysis in agricultural marketing: The case of French olive oil market. European Journal of Operational Research, 130(2):315-331, April 2001.
Y. Siskos, A. Spyridakos, and D. Yannacopoulos. Using artificial intelligence and visual techniques into preference disaggregation analysis: The MIIDAS system. European Journal of Operational Research, 113(2):281-299, 1999.
Y. Siskos and D. Yannacopoulos. UTASTAR, An ordinal regression method for building additive value functions. Investigaçao Operacional, 5(1):39-53, 1985.
Y. Siskos and C. Zopounidis. The evaluation of venture capital investment activity: An interactive assessment. European Journal of Operational Research, 31(3):304-313, 1987.
H. J. Skala. Non-Archimedean Utility Theory. Kluwer Academic Publishers, Dordrecht, 1975.
J. Sounderpandian. Value functions when decision criteria are not totally substitutable. Operations Research, 39:592-600, 1991.
A. Spyridakos, Y. Siskos, D. Yannacopoulos, and A. Skouris. Multicriteria job evaluation for large organizations. European Journal of Operational Research, 130(2):375-387, April 2001.
T. Stewart. An interactive multiple objective linear programming method based on piecewise linear additive value functions. IEEE Transactions on Systems, Man, and Cybernetics, SMC-17(5):799-805, 1987.
W. G. Stillwell, D. von Winterfeldt, and R. S. John. Comparing hierarchical and nonhierarchical weighting methods for eliciting multiattribute value models. Management Science, 33:442-50, 1987.
P. Suppes, D. H. Krantz, R. D. Luce, and A. Tversky. Foundations of Measurement, Vol. 2: Geometrical, Threshold, and Probabilistic Representations. Academic Press, New York, 1989.
P. Suppes and M. Winet. An axiomatization of utility based on the notion of utility difference. Management Science, 1:259-270, 1955.
O. Svenson. Process description of decision making. Organizational Behavior and Human Performance, 23:86-112, 1979.
R. J. Titiev. Measurement structures in classes that are not universally axiomatizable. Journal of Mathematical Psychology, 9:200-205, 1972.
A. Tversky. A general theory of polynomial conjoint measurement. Journal of Mathematical Psychology, 4:1-20, 1967.
A. Tversky. Intransitivity of preferences. Psychological Review, 76:31-48, 1969.
Ph. Vincke. Multi-criteria Decision Aid. John Wiley & Sons, New York, 1992. Original version in French “L’Aide Multicritère à la Décision”, Éditions de l’Université de Bruxelles-Éditions Ellipses, Brussels, 1989.
Ph. Vincke. Outranking approach. In T. Gal, T. Stewart, and T. Hanne, editors, Multicriteria Decision Making, Advances in MCDM Models, Algorithms, Theory and Applications, pages 11.1-11.29. Kluwer Academic Publishers, Dordrcht, 1999.
K. Vind. Independent preferences. Journal of Mathematical Economics, 20:119-135, 1991.
J. von Neumann and O. Morgenstern. Theory of Games and Economic Behavior. John Wiley & Sons, New York, 2nd edition, 1947.
R. von Nitzsch and M. Weber. The effect of attribute ranges on weights in multiattribute utility measurements. Management Science, 39(8):937-943, August 1993.
D. von Winterfeldt and W. Edwards. Decision Analysis and Behavioral Research. Cambridge University Press, Cambridge, 1986.
P. P. Wakker. Cardinal coordinate independence for expected utility. Journal of Mathematical Psychology, 28(1): 110-117, 1984.
P. P. Wakker. Additive Representations of Preferences: A New Foundation of Decision Analysis. Kluwer Academic Publishers, Dordrecht, 1989.
P. P. Wakker. Additive representation for equally spaced structures. Journal of Mathematical Psychology, 35:260-266, 1991.
P. P. Wakker. Additive representations of preferences, A new foundation of decision analysis; The algebraic approach. In J.-P. Doignon and J.-C. Falmagne, editors, Mathematical Psychology: Current Developments, pages 71-87. Springer Verlag, Berlin, 1991.
P. P. Wakker. Additive representations on rank-ordered sets. I. The algebraic approach. Journal of Mathematical Psychology, 35(4):501-531, 1991.
P. P. Wakker. Additive representations on rank-ordered sets. II. The topological approach. Journal of Mathematical Economics, 22(1):1-26, 1993.
M. Weber, F. Eisenfuhr, and D. von Winterfeld. The effects of splitting attributes on weights in multiattribute utility measurement. Management Science, 34(4):431-445, 1988.
J. A. Weymark. Generalized Gini inequality indices. Mathematical Social Sciences, 1:409-30, 1981.
U. Wille. Linear measurement models: Axiomatizations and axiomatizability. Journal of Mathematical Psychology, 44:617-650, 2000.
C. Zopounidis and M. Doumpos. Stock evaluation using a preference disaggregation methodology. Decision Science, 30:313-336, 1999.
C. Zopounidis and M. Doumpos. Building additive utilities for multi-group hierarchical discrimination: The MHDIS method. Optimization Methods & Software, 14(3):219-240, 2000.
C. Zopounidis and M. Doumpos. PREFDIS: A multicriteria decision support system for sorting decision problems. Computers & Operations Research, 27(7-8):779-797, June 2000.
C. Zopounidis and M. Doumpos. Multicriteria preference disaggregation for classification problems with an application to global investing risk. Decision Sciences, 32(2):333-385, 2001.
C. Zopounidis and M. Doumpos. A preference disaggregation decision support system for financial classification problems. European Journal of Operational Research, 130(2):402-413, April 2001.