Other references: theory

Cardinal value measurement with macbeth

Bana e Costa C.A.; Vansnick J-C.

in Decision Making: Recent Developments and Worldwide Applications, S.H. Zanakis, G. Doukidis, C. Zapounidis (eds.), 2000, Kluwer Academic Publishers, Book Series: Applied Optimization, vol. 45, pp. 317-329.

Abstract:

Decision-making is above all a human activity in which value judgments about the attractiveness of options play a key role. The integration of technology and human decisions by means of the design and use of tools for the representation of value judgments that are simultaneously semantically meaningful, practically operational (user-friendly) and theoretically well founded is therefore an important research challenge. The macbeth approach (Measuring Attractiveness by a Categorical Based Evaluation Technique) overviewed in this paper is a contribution in that direction. macbeth is an approach designed for building a cardinal scale measuring the attractiveness of options, throughout a learning process supported by a visual interactive software. This is interesting for decision-making when one wants to measure by how much an option is better than another one. Moreover, cardinal preference information is required to meaningfully perform operations with numerical scales, such as comparison of average sums, as required by multi-attribute value theory.

Preference relations and MCDM

Bana e Costa C.A.; Vansnick J-C.

in Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory and Applications, T. Gal, T. Stewart, T. Hanne (eds.), 1999, Kluwer Academic Publishers, Book Series: International Series in Operations Research & Management Science, vol. 21, pp. 4-14-23

Abstract:

Multicriteria decision aid is above all a human activity in which value judgements of involved actors play a crucial role. Therefore, ìhow to represent such judgements?î is a key question in MCDM. This chapter is devoted to this subject. Depending on the particular paradigm adopted for preference modelling, different questioning procedures can be conceived which lead to different preference structures. We present a few questioning procedures related to three basic paradigms, together with some preference structures that are useful for MCDM. First, the classical preference-indifference structure is discussed, followed by the introduction of the ideas of ìincomparabilityî and ìhesitationî. Finally, we present some complementary questioning procedures particularly relevant for cardinal modelling of value judgements.

A theoretical framework for Measuring Attractiveness by a Categorical Based Evaluation Technique (macbeth)

Bana e Costa C.A.; Vansnick J-C.

in Multicriteria Analysis, J. ClÌmaco (ed.), 1997, Springer-Verlag, pp. 15-24

Abstract:

This paper presents a theoretical framework for the macbeth approach. Taking as a starting point the measurement rules used for numerically representing the qualitative (categorical) preference information assessed by the questioning procedure of macbeth, we study the existence of a solution for our particular representation problem and we briefly discuss its unicity.

General overview of the MACBETH approach

Bana e Costa C.A.; Vansnick J-C.

in Advances in Multicriteria Analysis, P.M. Pardalos, Y. Siskos, C. Zopounidis (eds.), 1995, Kluwer Academic Publishers, Book Series: Nonconvex Optimization and its Applications, pp. 93-100

Introduction:

macbeth is an interactive approach for cardinal measurement of judgments about the degrees to which the elements of a finite set A possess a property P. The name macbeth, Measuring Attractiveness by a Categorical Based Evaluation Technique, comes from the fact that we conceived our approach with the aim of facilitating the measurement of (degrees of) attractiveness in decision processes. Nevertheless, macbeth can also be applied to measure other properties in domains of knowledge others than Decision Sciences, such as in Psychophysics or in Social Sciences. In this article we offer a general overview of macbeth where we introduce some modifications improving the initial technical formulation of [Bana e Costa and Vansnick, 1993 and 1994a], although the basic conceptual ideas remain the same.

macbeth - An interactive path towards the construction of cardinal value functions

Bana e Costa C.A.; Vansnick J-C.

International Transactions in Operational Research, 1994, vol. 1, no. 4, pp. 489-500

Abstract:

The application of classical models and techniques for cardinal measurement of values usually requires a person (D) to answer very difficult questions. The macbeth approach, presented in this paper, proposes a simple questioning procedure to ëdriveí the interactive quantification of values through pairwise verbal judgements of difference of attractiveness between valuable elements of a set A. Technically, macbeth uses a chain of four linear programs for assigning numbers to the elements of set A based upon the qualitative judgements expressed by D and to reveal possible sources of incoherence. In practice, this information is to be used as a basis for discussion and learning. macbeth stands for Measuring Attractiveness by a Categorical Based Evaluation TecHnique.