Conjoint measurement tools for MCDM. A brief introduction (mai 2003)

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. non- additive models or models tolerating intransitive preferences are then briefly reviewed.

[1]  Ralph L. Keeney,et al.  Assessing and evaluating environmental impacts at proposed nuclear power plant sites , 1977 .

[2]  O. Svenson.  Process descriptions of decision making. , 1979 .

[3]  Michel Grabisch,et al.  Fuzzy aggregation of numerical preferences , 1999 .

[4]  C. B. E. Costa,et al.  Facilitating bid evaluation in public call for tenders: a socio-technical approach , 2002 .

[5]  Nicholas R. Miller,et al.  Graph- Theoretical Approaches to the Theory of Voting* , 1977 .

[6]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[7]  S. French.  Decision Theory: An Introduction to the Mathematics of Rationality , 1986 .

[8]  W. Edwards,et al.  Decision Analysis and Behavioral Research , 1986 .

[9]  David Gale.  The theory of linear economic models , 1960 .

[10]  Philippe De Donder,et al.  Choosing from a weighted tournament , 2000, Math. Soc. Sci..

[11]  Amos Tversky,et al.  A general theory of polynomial conjoint measurement , 1967 .

[12]  Didier Dubois,et al.  The Use of the Discrete Sugeno Integral in Decision-Making: A Survey , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[13]  Jean Siskos,et al.  Evaluating a system of furniture retail outlets using an interactive ordinal regression method , 1986 .

[14]  Peter C. Fishburn,et al.  LEXICOGRAPHIC ORDERS, UTILITIES AND DECISION RULES: A SURVEY , 1974 .

[15]  Ralph L. Keeney,et al.  Constructing a Complex Judgmental Model: An Index of Trauma Severity , 1983 .

[16]  F. Roberts.  Measurement Theory with Applications to Decisionmaking, Utility, and the Social Sciences: Measurement Theory , 1984 .

[17]  J. Leeuw,et al.  Abstract Measurement Theory. , 1986 .

[18]  R. Luce.  Semiorders and a Theory of Utility Discrimination , 1956 .

[19]  Karni,et al.  The Hexagon Condition and Additive Representation for Two Dimensions: An Algebraic Approach. , 1998, Journal of mathematical psychology.

[20]  R. Luce.  Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches , 2000 .

[21]  Peter P. Wakker,et al.  Cardinal coordinate independence for expected utility , 1984 .

[22]  Peter C. Fishburn,et al.  Intransitive Indifference in Preference Theory: A Survey , 1970, Oper. Res..

[23]  K. May.  Intransitivity, Utility, and the Aggregation of Preference Patterns , 1954 .

[24]  Howard Raiffa,et al.  Decision analysis: introductory lectures on choices under uncertainty. 1968. , 1969, M.D.Computing.

[25]  Ralph L. Keeney,et al.  Structuring Objectives for Problems of Public Interest , 1988, Oper. Res..

[26]  Thierry Marchant,et al.  Evaluation and Decision Models: A Critical Perspective , 2000 .

[27]  Heinz J. Skala,et al.  Non-Archimedean Utility Theory , 1975 .

[28]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[29]  Carlos A. Bana e Costa,et al.  Multicriteria approach for strategic town planning: the case of Barcelos , 2001 .

[30]  Constantin Zopounidis,et al.  PREFDIS: a multicriteria decision support system for sorting decision problems , 2000, Comput. Oper. Res..

[31]  Gonzales.  Two Factor Additive Conjoint Measurement with One Solvable Component. , 2000, Journal of mathematical psychology.

[32]  P. Fishburn.  Nontransitive additive conjoint measurement , 1991 .

[33]  Denis Bouyssou,et al.  Noncompensatory and generalized noncompensatory preference structures , 1986 .

[34]  D. Krantz.  Conjoint measurement: The Luce-Tukey axiomatization and some extensions ☆ , 1964 .

[35]  I. Gilboa,et al.  Linear Measures, the Gini Index, and The Income-Equality Trade-off , 1994 .

[36]  Denis Bouyssou,et al.  Some remarks on the notion of compensation in MCDM , 1986 .

[37]  Evangelos Grigoroudis,et al.  Customer satisfaction measurement in the private bank sector , 2001, Eur. J. Oper. Res..

[38]  Peter C. Fishburn,et al.  Utility theory for decision making , 1970 .

[39]  S. Greco,et al.  Conjoint measurement and rough set approach for multicriteria sorting problems in presence of ordinal criteria , 2001 .

[40]  Robert J. Titiev,et al.  Measurement structures in classes that are not universally axiomatizable , 1972 .

[41]  Henry Montgomery,et al.  A Study of Intransitive Preferences using a Think Aloud Procedure , 1977 .

[42]  Philippe Vincke,et al.  Lexicographic aggregation of semiorders , 1992 .

[43]  Christophe Labreuche,et al.  On the extension of pseudo-Boolean functions for the aggregation of interacting criteria , 2003, Eur. J. Oper. Res..

[44]  P. Fishburn.  Condorcet Social Choice Functions , 1977 .

[45]  Jordan J. Louviere,et al.  Analyzing Decision Making: Metric Conjoint Analysis , 1988 .

[46]  D. Scott.  Measurement structures and linear inequalities , 1964 .

[47]  Salvatore Greco,et al.  Rough approximation of a preference relation by dominance relations , 1999, Eur. J. Oper. Res..

[48]  A. Charnes,et al.  Management Models and Industrial Applications of Linear Programming , 1961 .

[49]  Peter C. Fishburn,et al.  Nonlinear preference and utility theory , 1988 .

[50]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[51]  Roman Słowiński,et al.  The Use of Rough Sets and Fuzzy Sets in MCDM , 1999 .

[52]  John A. Weymark,et al.  GENERALIZED GIN 1 INEQUALITY INDICES , 2001 .

[53]  Peter C. Fishburn,et al.  On nonstandard nontransitive additive utility , 1992 .

[54]  Peter C. Fishburn,et al.  Additive non-transitive preferences , 1990 .

[55]  C. B. E. Costa,et al.  MACBETH — An Interactive Path Towards the Construction of Cardinal Value Functions , 1994 .

[56]  R. Luce,et al.  Simultaneous conjoint measurement: A new type of fundamental measurement , 1964 .

[57]  Jean-François Laslier,et al.  Tournament Solutions And Majority Voting , 1997 .

[58]  Theodor J. Stewart,et al.  Multiple criteria decision analysis - an integrated approach , 2001 .

[59]  Michel Grabisch,et al.  Application of the Choquet integral in multicriteria decision making , 2000 .

[60]  Donald G. Saari,et al.  Connecting and resolving Sen's and Arrow's theorems , 1998 .

[61]  Constantin Zopounidis,et al.  Stock Evaluation Using a Preference Disaggregation Methodology , 1999 .

[62]  E. W. Adams,et al.  Elements of a Theory of Inexact Measurement , 1965, Philosophy of Science.

[63]  R. Keeney.  Building models of values , 1988 .

[64]  Valerie Belton,et al.  Integrated Support from Problem Structuring through to Alternative Evaluation Using COPE and V·I·S·A , 1997 .

[65]  Vaughan Jones.  The Algebraic Approach , 1991 .

[66]  P. Fishburn.  Axioms for Lexicographic Preferences , 1975 .

[67]  Jean-Luc Marichal,et al.  An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria , 2000, IEEE Trans. Fuzzy Syst..

[68]  B. Roy.  THE OUTRANKING APPROACH AND THE FOUNDATIONS OF ELECTRE METHODS , 1991 .

[69]  P. Fishburn.  Nontransitive measurable utility , 1982 .

[70]  G. Debreu.  Mathematical Economics: Representation of a preference ordering by a numerical function , 1983 .

[71]  R. Luce.  Three Axiom Systems for Additive Semiordered Structures , 1973 .

[72]  Itzhak Gilboa,et al.  On the Measurement of Inequality under Uncertainty , 1997 .

[73]  P. Wakker.  Additive representations on rank-ordered sets: II. The topological approach , 1993 .

[74]  Louis Narens,et al.  The algebra of measurement , 1976 .

[75]  P. Fishburn.  Decision Making: NORMATIVE THEORIES OF DECISION MAKING UNDER RISK AND UNDER UNCERTAINTY , 1988 .

[76]  A. Tversky.  Intransitivity of preferences. , 1969 .

[77]  W. Edwards.  How to Use Multi-Attribute Utility Measurement for Social Decision Making , 1976 .

[78]  S French,et al.  Multicriteria Methodology for Decision Aiding , 1996 .

[79]  D. Krantz.  Extensive Measurement in Semiorders , 1967, Philosophy of Science.

[80]  A. Atkinson.  On the measurement of inequality , 1970 .

[81]  P. Green,et al.  Conjoint Analysis in Consumer Research: Issues and Outlook , 1978 .

[82]  R. Duncan Luce,et al.  Factorizable automorphisms in solvable conjoint structures I , 1983 .

[83]  T. Koopmans.  Stationary Ordinal Utility and Impatience , 1960 .

[84]  Dimitris K. Despotis,et al.  Multiobjective modelling for regional agricultural planning: Case study in Tunisia , 1994 .

[85]  Nikolaos F. Matsatsinis,et al.  Multicriteria analysis in agricultural marketing: The case of French olive oil market , 2001, Eur. J. Oper. Res..

[86]  Begoña Subiza,et al.  Condorcet choice correspondences for weak tournaments , 1999 .

[87]  G. Debreu.  Topological Methods in Cardinal Utility Theory , 1959 .

[88]  Rakesh K. Sarin,et al.  Measurable Multiattribute Value Functions , 1979, Oper. Res..

[89]  Denis Bouyssou,et al.  A characterization of strict concordance relations , 2002 .

[90]  P. Fishburn.  Nontransitive preferences in decision theory , 1991 .

[91]  A. Sen,et al.  Social Choice Theory , 1980 .

[92]  Joel Sobel,et al.  Min, Max, and Sum , 2000, J. Econ. Theory.

[93]  Roman Słowiński,et al.  Preference Representation by Means of Conjoint Measurement and Decision Rule Model , 2002 .

[94]  B. Dosher,et al.  Strategies for multiattribute binary choice. , 1983, Journal of experimental psychology. Learning, memory, and cognition.

[95]  Jean-Claude Falmagne,et al.  Statistical issues in measurement , 1985 .

[96]  P. Wakker.  Additive Representations of Preferences: A New Foundation of Decision Analysis , 1988 .

[97]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..

[98]  Peter C. Fishburn,et al.  Finite linear qualitative probability , 1996 .

[99]  Ralph L. Keeney,et al.  Measurement Scales for Quantifying Attributes , 1981 .

[100]  Bernard Roy,et al.  Main sources of inaccurate determination, uncertainty and imprecision in decision models , 1989 .