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Denis Bouyssou - One of the best experts on this subject based on the ideXlab platform.

  • Conjoint Measurement models for preference relations
    Decision-making Process: Concepts and Methods, 2010
    Co-Authors: Denis Bouyssou, Marc Pirlot
    Abstract:

    Conjoint Measurement [KRA 71, WAK 89] is concerned with the study of binary relations defined on Cartesian products of sets. Such relations are central in many disciplines, for example:– multicriteria or multiattribute decision making, in which the preference of the decision maker is a relation that encodes, for each pair of alternatives, the preferred option taking into account all criteria [BEL 01, KEE 76, WIN 86];– decision under uncertainty, where the preference relation compares alternatives evaluated on several states of nature [FIS 88, GUL 92, SHA 79, WAK 84, WAK89];– consumer theory, dealing with preference relations that compare bundles of goods [DEB 59];– inter-temporal decision making, that uses preference relations for comparing alternatives evaluated at various instants in time [KOO 60, KOO 72, KEE 76]; and– inequality Measurement, that compares distributions of wealth across individuals [ATK 70, BEN 94, BEN 97]

  • Additive Conjoint Measurement with ordered categories
    European Journal of Operational Research, 2010
    Co-Authors: Denis Bouyssou, Thierry Marchant
    Abstract:

    Abstract Conjoint Measurement studies binary relations defined on product sets and investigates the existence and uniqueness of, usually additive, numerical representations of such relations. It has proved to be quite a powerful tool to analyze and compare MCDM techniques designed to build a preference relation between multiattributed alternatives and has been an inspiring guide to many assessment protocols. The aim of this paper is to show that additive representations can be obtained on the basis of much poorer information than a preference relation. We will suppose here that the decision maker only specifies for each object if he/she finds it “attractive” (better than the status quo), “unattractive” (worse than the status quo) or “neutral” (equivalent to the status quo). We show how to build an additive representation, with tight uniqueness properties, using such an ordered partition of the set of objects. On a theoretical level, this paper shows that classical results of additive Conjoint Measurement can be extended to cover the case of ordered partitions and wishes to be a contribution to the growing literature on the foundations of sorting techniques in MCDM. On a more practical level, our results suggest an assessment strategy of an additive model on the basis of an ordered partition.

  • Ordered categories and additive Conjoint Measurement on connected sets
    Journal of Mathematical Psychology, 2009
    Co-Authors: Denis Bouyssou, Thierry Marchant
    Abstract:

    Suppose that a binary relation is given on a n-fold Cartesian product. The study of the conditions guaranteeing the existence of n value functions such that the binary relation can be additively represented is known as additive Conjoint Measurement. In this paper we analyze a related problem: given a partition of a Cartesian product into r ordered categories, what conditions do ensure the representability of the partition in an additive model?

  • Additive and decomposable Conjoint Measurement with ordered categories
    2008
    Co-Authors: Denis Bouyssou, Thierry Marchant
    Abstract:

    Conjoint Measurement studies binary relations defined on product sets and investigates the existence and uniqueness of numerical representations of such relations. It has proved to be quite a powerful tool to analyze and compare MCDM techniques designed to build a preference relation between multiattributed alternatives and has been an inspiring guide to many assessment protocols. These MCDM techniques lead to a relative evaluation model of the alternatives through a preference relation. Such models are not always appropriate to build meaningful recommendations. This has recently lead to the development of MCDM techniques aiming at building evaluation models having a more absolute character. In such techniques, the output of the analysis is, most often, a partition of the set of alternatives into several ordered categories defined with respect to outside norms, e.g., separating “Attractive” and “Unattractive” alternatives. In spite of their interest, the theoretical foundations of such MCDM techniques have not been much investigated. The purpose of this paper is to contribute to this analysis. More precisely, we show how to adapt classic Conjoint Measurement results to make them applicable for the study of such MCDM techniques. We concentrate on additive models. Our results may be seen as an attempt to provide an axiomatic basis to the well-known UTADIS technique that sorts alternatives using an additive value function model. Keywords: Decision with multiple attributes, Sorting, Conjoint Measurement, UTADIS. La théorie du mesurage Conjoint étudie la question de la représentation numérique d'une relation binaire définie sur un produit cartésien. Cette théorie s'est révélée très utile pour comparer et analyser diverses techniques d'aide multicritère à la décision. Elle a également été la source de nombreux protocoles d'élicitation. Les techniques d'aide à la décision utilisant une relation binaire comparant des actions évaluées sur plusieurs attributs conduisent, en général, à des modèles d'évaluation ayant un caractère relatif. Or, de tels modèles ne sont pas toujours adaptés pour bâtir une prescription pertinente. Ceci a conduit au développement de techniques multicritères conduisant à des modèles d'évaluation ayant un caractère plus absolu. Dans ces techniques, le résultat se présente généralement sous la forme d'une aectation des actions à diverses catégories ordonnées, ces catégories étant définies par rapport à des normes indépendantes des actions à évaluer. On pourra, par exemple, séparer les actions satisfaisantes de celles étant insatisfaisantes. En dépit de leur intérêt, les fondements théoriques de telles méthodes ont été peu étudiés. L'objectif de cet article est de contribuer à cette étude. Plus précisément, on montre comment adapter les résultats classiques du mesurage Conjoint pour couvrir le cas de catégories ordonnées. On étudie plus spécifiquement le cas de représentations additives. Ce travail peut alors être vu comme une tentative de donner à la méthode UTADIS une base théorique solide. Mots-clés: Analyse multicritère, Tri, Mesurage Conjoint, UTADIS.

  • Additive and decomposable Conjoint Measurement with ordered categories
    2008
    Co-Authors: Denis Bouyssou, Thierry Marchant
    Abstract:

    Conjoint Measurement studies binary relations defined on product sets and investigates the existence and uniqueness of numerical representations of such relations. It has proved to be quite a powerful tool to analyze and compare MCDM techniques designed to build a preference relation between multiattributed alternatives and has been an inspiring guide to many assessment protocols. These MCDM techniques lead to a relative evaluation model of the alternatives through a preference relation. Such models are not always appropriate to build meaningful recommendations. This has recently lead to the development of MCDM techniques aiming at building evaluation models having a more absolute character. In such techniques, the output of the analysis is, most often, a partition of the set of alternatives into several ordered categories defined with respect to outside norms, e.g., separating "Attractive" and "Unattractive" alternatives. In spite of their interest, the theoretical foundations of such MCDM techniques have not been much investigated. The purpose of this paper is to contribute to this analysis. More precisely, we show how to adapt classic Conjoint Measurement results to make them applicable for the study of such MCDM techniques. We concentrate on additive models. Our results may be seen as an attempt to provide an axiomatic basis to the well-known UTADIS technique that sorts alternatives using an additive value function model.

Marc Pirlot - One of the best experts on this subject based on the ideXlab platform.

  • Conjoint Measurement models for preference relations
    Decision-making Process: Concepts and Methods, 2010
    Co-Authors: Denis Bouyssou, Marc Pirlot
    Abstract:

    Conjoint Measurement [KRA 71, WAK 89] is concerned with the study of binary relations defined on Cartesian products of sets. Such relations are central in many disciplines, for example:– multicriteria or multiattribute decision making, in which the preference of the decision maker is a relation that encodes, for each pair of alternatives, the preferred option taking into account all criteria [BEL 01, KEE 76, WIN 86];– decision under uncertainty, where the preference relation compares alternatives evaluated on several states of nature [FIS 88, GUL 92, SHA 79, WAK 84, WAK89];– consumer theory, dealing with preference relations that compare bundles of goods [DEB 59];– inter-temporal decision making, that uses preference relations for comparing alternatives evaluated at various instants in time [KOO 60, KOO 72, KEE 76]; and– inequality Measurement, that compares distributions of wealth across individuals [ATK 70, BEN 94, BEN 97]

  • Conjoint Measurement Tools for MCDM
    2005
    Co-Authors: Denis Bouyssou, Marc Pirlot
    Abstract:

    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.

  • Following the traces: An introduction to Conjoint Measurement without transitivity and additivity
    European Journal of Operational Research, 2005
    Co-Authors: Denis Bouyssou, Marc Pirlot
    Abstract:

    This paper presents a self-contained introduction to a general Conjoint Measurement framework for the analysis of nontransitive and/or incomplete binary relations on product sets. It is based on the use of several kinds of marginal traces on coordinates induced by the binary relation. This framework leads to defining three general families of models depending on the kind of trace that they use. Contrary to most Conjoint Measurement models, these models do not involve an addition operation. This allows for a simple axiomatic analysis at the cost of very weak uniqueness results.

  • Following the traces. An introduction to Conjoint Measurement without transitivity and additivity (sept. 2002, révisé avril 2003)
    European Journal of Operational Research, 2005
    Co-Authors: Denis Bouyssou, Marc Pirlot
    Abstract:

    This paper presents a self-contained introduction to a general Conjoint Measurement framework for the analysis of nontransitive and/or incomplete binary relations on product sets. It is based on the use of several kinds of marginal traces on coordinates induced by the binary relation. This framework leads to defining three general families of models depending on the kind of trace that they use. Contrary to most Conjoint Measurement models, these models do not involve an addition operation. This allows for a simple axiomatic analysis at the cost of very weak uniqueness results.

  • Conjoint Measurement tools for MCDM. A brief introduction (mai 2003)
    2004
    Co-Authors: Denis Bouyssou, Marc Pirlot
    Abstract:

    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.

Joel Michell - One of the best experts on this subject based on the ideXlab platform.

  • Conjoint Measurement underdone comment on gunter trendler 2019
    Theory & Psychology, 2019
    Co-Authors: Joel Michell
    Abstract:

    Trendler’s (2019) critique of Conjoint Measurement fails because he neglects to distinguish standard sequences (human constructions) from series of equal magnitudes (features of quantitative struct...

  • COMMENT Conjoint Measurement and the Rasch Paradox A Response to
    2016
    Co-Authors: Joel Michell
    Abstract:

    ABSTRACT. Unlike Andrew Kyngdon, I think the issue he has addressed is most informatively considered outside the confines of the representational theory of Measurement. Then it becomes clear that while the theory of con-joint Measurement is about situations like that treated by the Rasch model, the former isolates a different feature of those situations to the latter. But, if the relevant attributes are already presumed to be quantitative, the perceived differences are minimized and the Rasch model might seem to be a version of Conjoint Measurement. It is on this basis that Rasch modellers pursue their paradoxical quest for Measurement. However, because the relevant attributes are not actually known to be quantitative, use of the Rasch model to measure psychological attributes remains logically dependent upon the outcome of research involving the theory of Conjoint Measurement or some-thing very similar. KEY WORDS: Conjoint Measurement, psychometrics, Rasch model, represen-tational theory The socio-economic conditions sustaining modern psychometrics discourage critical attitudes and it now stands suspended in a post-critical bubble. As a science, it desperately needs deflating. So it would be churlish to let my dis-agreement with the detail of Andrew Kyngdon’s (2008) argument prevent me applauding his critical spirit by offering further critical thoughts supplement-ing his on the relationship between the Rasch model and Conjoint measure-ment. The former is, as he says, sometimes promoted as the latter. He favours a narrow focus, concentrating upon formal matters within the framework of representational theory. But a wider lens may be helpful, for the Rasch model does not easily fit the representational schema, as Kyngdon found, and the theory of Conjoint Measurement transcends its narrow frame

  • The Rasch paradox, Conjoint Measurement, and psychometrics: Response to Humphry and Sijtsma
    Theory & Psychology, 2014
    Co-Authors: Joel Michell
    Abstract:

    This response to Humphry (2013) and Sijtsma (2012) is confined to three issues: the nature of the Rasch paradox, the relevance of the theory of Conjoint Measurement to psychometrics, and the relationship between test items on the one hand and the character of the attributes they assess on the other. First, contrary to Sijtsma’s view, it is argued that the Rasch model does involve a genuine paradox. Second, typical of psychometricians generally, both Humphry and Sijtsma misunderstand the role the theory of Conjoint Measurement is able to play in psychometrics. It is argued that in conjunction with item response theory models, it has a significant role. Finally, complementary to Humphry’s and Sijtsma’s insistence upon the importance of theories of the attribute, I argue that features of attribute structure can be inferred from the character of test items and briefly sketch an argument that in the first instance at least, the attributes tests assess contain a feature logically incompatible with quantitative ...

  • Conjoint Measurement and the Rasch Paradox: A Response to Kyngdon
    Theory & Psychology, 2008
    Co-Authors: Joel Michell
    Abstract:

    Unlike Andrew Kyngdon, I think the issue he has addressed is most informatively considered outside the confines of the representational theory of Measurement. Then it becomes clear that while the theory of Conjoint Measurement is about situations like that treated by the Rasch model, the former isolates a different feature of those situations to the latter. But, if the relevant attributes are already presumed to be quantitative, the perceived differences are minimized and the Rasch model might seem to be a version of Conjoint Measurement. It is on this basis that Rasch modellers pursue their paradoxical quest for Measurement. However, because the relevant attributes are not actually known to be quantitative, use of the Rasch model to measure psychological attributes remains logically dependent upon the outcome of research involving the theory of Conjoint Measurement or something very similar.

Peter P. Wakker - One of the best experts on this subject based on the ideXlab platform.

  • Utility Independence of Multiattribute Utility Theory is Equivalent to Standard Sequence Invariance of Conjoint Measurement
    Journal of Mathematical Psychology, 2011
    Co-Authors: Han Bleichrodt, Jason N. Doctor, Martin Filko, Peter P. Wakker
    Abstract:

    Utility independence is a central condition in multiattribute utility theory, where attributes of outcomes are aggregated in the context of risk. The aggregation of attributes in the absence of risk is studied in Conjoint Measurement. In Conjoint Measurement, standard sequences have been widely used to empirically measure and test utility functions, and to theoretically analyze them. This paper shows that utility independence and standard sequences are closely related: utility independence is equivalent to a standard sequence invariance condition when applied to risk. This simple relation between two widely used conditions in adjacent fields of research is surprising and useful. It facilitates the testing of utility independence because standard sequences are flexible and can avoid cancelation biases that affect direct tests of utility independence. Extensions of our results to nonexpected utility models can now be provided easily. We discuss applications to the Measurement of quality-adjusted life-years (QALY) in the health domain.

  • Additive Conjoint Measurement for multiattribute utility
    Journal of Mathematical Psychology, 1994
    Co-Authors: Arne Maas, Peter P. Wakker
    Abstract:

    This paper shows that the role of risky alternatives can be greatly reduced in the clicitation procedures of multiattribute utility. This reduction can be achieved by invoking methods from additive Conjoint Measurement; it is desirable because risky choices involve more cognitive problems, thus more biases and unreliability, than riskless ones. Existing results of multiattribute utility are generalized to obtain a complete axiomatization of the new clicitation procedure. The approach has been developed in a medical decision analysis project to advise on the choice between surgery and radiotherapy for laryngeal cancer.

Laurence T. Maloney - One of the best experts on this subject based on the ideXlab platform.

  • Research Article Conjoint Measurement of Gloss and Surface
    2016
    Co-Authors: Michael S. L, Laurence T. Maloney
    Abstract:

    ABSTRACT—The image of a material’s surface varies not only with viewing and illumination conditions, but also with the material’s surface properties, including its 3-D texture and specularity. Previous studies on the visual perception of surface material have typically focused on single material properties, ignoring possible interactions. In this study, we used a Conjoint-Measurement design to determine how observers represent perceived 3-D texture (‘‘bumpiness’’) and specularity (‘‘glossiness’’) andmodeled how each of these two surface-material properties affects perception of the other. Observers made judgments of bumpiness and glossiness of surfaces that varied in both surface texture and specularity.We quantified howchanges in each surface-material property affected judgments of the other and found that a simple additive model capture

  • Maximum Likelihood Conjoint Measurement
    Modeling Psychophysical Data in R, 2012
    Co-Authors: Kenneth Knoblauch, Laurence T. Maloney
    Abstract:

    Conjoint Measurement allows the experimenter to estimate psychophysical scales that capture how two or more physical dimensions contribute to a perceptual judgment. It is most easily explained by an example. Figure 8.1 shows a range of stimuli taken from a study by Ho et al. [80]. Each stimulus was the image of an irregular surface (the original stimuli were rendered for binocular viewing at a higher resolution than those shown in the figure). The experimenters were interested in how the perceived roughness (which they refer to as “bumpiness) and glossiness of a surface were affected by variations in two physical parameters that plausibly affect perceived roughness and glossiness. They reported two experiments that differed only in the judgments observers made. In the first, observers judged perceived roughness, in the second, perceived glossiness.

  • Conjoint Measurement of Gloss and Surface Texture
    Psychological science, 2008
    Co-Authors: Michael S. Landy, Laurence T. Maloney
    Abstract:

    The image of a material's surface varies not only with viewing and illumination conditions, but also with the material's surface properties, including its 3-D texture and specularity. Previous studies on the visual perception of surface material have typically focused on single material properties, ignoring possible interactions. In this study, we used a Conjoint-Measurement design to determine how observers represent perceived 3-D texture (“bumpiness”) and specularity (“glossiness”) and modeled how each of these two surface-material properties affects perception of the other. Observers made judgments of bumpiness and glossiness of surfaces that varied in both surface texture and specularity. We quantified how changes in each surface-material property affected judgments of the other and found that a simple additive model captured visual perception of texture and specularity and their interaction. Conjoint Measurement is potentially a powerful tool for analyzing perception of surface material in realistic ...