Thierry Marchant

Evaluation and Decision Models

1. Introduction. 2. Choosing on the basis of several opinions. 3. Building and aggregating evaluations. 4. Constructing measures. 5. Assessing competing projects. 6. Comparing on several attributes. 7. Deciding automatically. 8. Dealing with uncertainty. 9. Supporting decisions. Appendix A. Appendix B. 10. Conclusion. Bibliography. Index.

An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories

A number of recent papers have investigated the foundations of methods allowing to sort multi-attributed alternatives between several ordered categories. This paper has a similar objective. Our analysis uses a general conjoint measurement framework, encompassing most sorting models used in MDCM, that was proposed in the literature. Within this framework, we provide an axiomatic analysis of what we call noncompensatory sorting models, with or without veto effects. These noncompensatory sorting models contain the pessimistic version of ELECTRE TRI as a particular case. Our analysis can be seen as an attempt to give a firm axiomatic basis to ELECTRE TRI, while emphasizing its specific feature, i.e., the rather poor information that this model uses on each attribute.

An axiomatic characterization of the ranking based on the h-index and some other bibliometric rankings of authors

In the last few years, many new bibliometric rankings or indices have been proposed for comparing the output of scientific researchers. We propose a formal framework in which rankings can be axiomatically characterized. We then present a characterization of some popular rankings. We argue that such analyses can help the user of a ranking to choose one that is adequate in the context where she/he is working.

Bibliometric rankings of journals based on Impact Factors: An axiomatic approach

This paper proposes an axiomatic analysis of Impact Factors when used as tools for ranking journals. This analysis draws on the similarities between the problem of comparing distribution of citations among papers and that of comparing probability distributions on consequences as commonly done in decision theory. Our analysis singles out a number of characteristic properties of the ranking based on Impact Factors. We also suggest alternative ways of using distributions of citations to rank order journals.

Valued Relations Aggregation with the Borda Method

The Borda method is a well known method used to aggregate a profile of crisp binary relations into one weak order. We present a generalization of the Borda method, allowing it to aggregate a profile of valued relations. We give a characterisation of the Borda method in this context and we show some links with the PROMETHEE method.

Towards a theory of MCDM: stepping away from social choice theory

Abstract Many axiomatic results concerning aggregation procedures in multi-criteria decision aiding have been obtained in the framework of social choice theory. We show that social choice theory, although helpful for a better understanding of some aggregation procedures, is not totally appropriate for multi-criteria decision aiding. We propose a slight modification of this framework making it more relevant for the axiomatization of aggregation procedures in the context of multi-criteria decision aiding. We present some axiomatic results obtained in this framework and showing its interest.

Cognitive maps and fuzzy implications

A cognitive map is a collection of nodes linked by some arcs. Up to this point, there is unanimity in the literature about the previous definition. But if we look closer at the meaning of the nodes and links, we can see that there are crucial differences between the various authors. And these differences are not always explicit. In spite of this, it seems that many authors perform on the maps the same kind of analysis (strongly inspired by the book of Axelrod), even if these analyses are not consistent with their conception of a cognitive map. That is why it is important to clearly and formally define the kind of map used. In this paper, we propose a formal definition of a cognitive map relying on the concept of fuzzy implication. Thus in our framework, a node is a logical proposition and a link is an implication. Starting from our definition, we show some properties of this kind of maps and some analysis techniques.

Consistent bibliometric rankings of authors and of journals

Rankings of journals and rankings of scientists are usually discussed separately. We argue that a consistent approach to both rankings is desirable because both the quality of a journal and the quality of a scientist depend on the papers it/he publishes. We present a pair of consistent rankings (impact factor for the journals and total number of citations for the authors) and we provide an axiomatic characterization thereof.

The measurement of membership by comparisons

Suppose we want to use a particular algebraic operation (for example, the drastic product t-norm) for representing an operation on fuzzy sets (for example, the intersection). This algebraic operation will be used with membership degrees, i.e. most of the time, numbers between 0 and 1. If we want that the results of our calculations make sense, we must be sure that the algebraic operation is compatible with the nature of the membership degrees, which is determined by the technique used to measure them. But this technique must, in turn, be compatible with the structural properties of the knowledge we want to represent. This paper addresses these issues within the framework of measurement theory. We provide sound theoretical foundations for the measurement of membership on ordinal and interval scales. But we also show that the level of measurement (ordinal, interval or even ratio) is not critical for the choice of a particular algebraic operation. Within measurement theory, whatever the scale, only the max and the min can be used for representing the intersection and the union. We also present some results about the complementation.

Does The Borda Rule Provide More Than a Ranking

Abstract. Consider the following problem: a set of candidates {x, y, z} has to be ranked from best to worse by a committee. Each member of the committee provides his own ranking of the three candidates and you decide to use the Borda method to aggregate the rankings. The resulting scores are as follows: 107 for x, 106 for y and 51 for z. Would you conclude that x is better than y? Probably not, because the difference between the scores of x and y is small. The only conclusion you would draw is that z definitely is the worst candidate. But, is it meaningful to consider differences of Borda scores? We characterize the Borda method in this new framework and find conditions that are very close to those characterizing the classical Borda method. Throughout our paper, we consider a generalization of the Borda method designed to aggregate fuzzy relations.