Patrice Perny

The use of fuzzy outranking relations in preference modelling

This paper deals with preference modelling in the context of Decision Aid. In this framework, conflicting systems of logic, uncertain knowledge, ambiguous positions are always present. In order to tackle this problem, a multiple criteria methodology is proposed, mainly based on fuzzy outranking relations introduced both at one-dimensional and multi-dimensional levels. Some properties of outranking relations are investigated. Such relations are then combined using fuzzy logical connectives to generate relational systems of fuzzy preferences that are shown to be very useful to reflect the vagueness of information in the various preference situations that may be considered in the modelling process.

Multicriteria filtering methods based onconcordance and non-discordance principles

This paper introduces multicriteria decision-aid methods for assigning alternatives topre-defined categories and develops a unified framework for preference aggregation methodsthat are based on concordance and non-discordance principles. Within this framework,we propose new multicriteria classification procedures based on non-totally compensatorymeasures of preference and similarity. We assume that the categories are given a priori andare characterised by fictitious alternatives serving as reference points, each representing atypical element of a category, or each representing a boundary between two categories.Several assignment methods are presented, all based on a filtering process exploiting binaryrelations constructed following the concordance and non-discordance principles. We firstconsider the case of ordered categories and a filtering procedure exploiting valued preferencerelations is proposed for assessing the membership of alternatives in categories. Then weconsider the case of non-ordered categories and filtering methods exploiting valued in-difference relations are introduced. Finally, a small example is given.

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.

Qualitative decision theory with preference relations and comparative uncertainty: an axiomatic approach

This paper investigates a purely qualitative approach to decision making under uncertainty. Since the pioneering work of Savage, most models of decision under uncertainty rely on a numerical representation where utility and uncertainty are commensurate. Giving up this tradition, we relax this assumption and introduce an axiom of ordinal invariance requiring that the Decision Makers preference between two acts only depends on the relative position of their consequences for each state. Within this qualitative framework, we determine the only possible form of the corresponding decision rule. Then assuming the transitivity of the strict preference, the underlying partial confidence relations are those at work in non-monotonic inference and thus satisfy one of the main properties of possibility theory. The satisfaction of additional postulates of unanimity and anonymity enforces the use of a necessity measure, unique up to a monotonic transformation, for encoding the relative likelihood of events.

Aggregation of measures to produce an overall assessment of animal welfare. Part 1: a review of existing methods.

Several systems have been proposed for the overall assessment of animal welfare at the farm level for the purpose of advising farmers or assisting public decision-making. They are generally based on several measures compounded into a single evaluation, using different rules to assemble the information. Here we discuss the different methods used to aggregate welfare measures and their applicability to certification schemes involving welfare. Data obtained on a farm can be (i) analysed by an expert who draws an overall conclusion; (ii) compared with minimal requirements set for each measure; (iii) converted into ranks, which are then summed; or (iv) converted into values or scores compounded in a weighted sum (e.g. TGI35L) or using ad hoc rules. Existing methods used at present (at least when used exclusively) may be insufficiently sensitive or not routinely applicable, or may not reflect the multidimensional nature of welfare and the relative importance of various welfare measures. It is concluded that different methods may be used at different stages of the construction of an overall assessment of animal welfare, depending on the constraints imposed on the aggregation process.

Qualitative decision theory: from savage's axioms to nonmonotonic reasoning

This paper investigates to what extent a purely symbolic approach to decision making under uncertainty is possible, in the scope of artificial intelligence. Contrary to classical approaches to decision theory, we try to rank acts without resorting to any numerical representation of utility or uncertainty, and without using any scale on which both uncertainty and preference could be mapped. Our approach is a variant of Savages where the setting is finite, and the strict preference on acts is a partial order. It is shown that although many axioms of Savage theory are preserved and despite the intuitive appeal of the ordinal method for constructing a preference over acts, the approach is inconsistent with a probabilistic representation of uncertainty. The latter leads to the kind of paradoxes encountered in the theory of voting. It is shown that the assumption of ordinal invariance enforces a qualitative decision procedure that presupposes a comparative possibility representation of uncertainty, originally due to Lewis, and usual in nonmonotonic reasoning. Our axiomatic investigation thus provides decision-theoretic foundations to the preferential inference of Lehmann and colleagues. However, the obtained decision rules are sometimes either not very decisive or may lead to overconfident decisions, although their basic principles look sound. This paper points out some limitations of purely ordinal approaches to Savage-like decision making under uncertainty, in perfect analogy with similar difficulties in voting theory.

Ranking methods for valued preference relations : A characterization of a method based on leaving and entering flows

Abstract In this paper we study a particular method that builds a partial ranking on the basis of a valued preference relation. This method, which is used in the MCDM method PROMETHEE I, is based on ‘leaving’ and ‘entering’ flows. We show that this method is characterized by system of three independent axioms.

Subjective Evaluation of Discomfort in Sitting Positions

We study the modelling of the subjective sensation of discomfort for subjects seated during a long time, in terms of local discomforts. The methodology uses fuzzy measures and integrals in a multicriteria decision making process, which enables the modelling of complex interaction between variables. Results of the experiment are detailed, giving models with respect to different kinds of discomfort, and to different macro-zones of the body.

A decision-theoretic approach to robust optimization in multivalued graphs

This paper is devoted to the search of robust solutions in finite graphs when costs depend on scenarios. We first point out similarities between robust optimization and multiobjective optimization. Then, we present axiomatic requirements for preference compatibility with the intuitive idea of robustness in a multiple scenarios decision context. This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of Lorenz optima, we show how the search can be embedded in algorithms designed to enumerate k best solutions. Then, we apply it in order to enumerate Lorenz optimal spanning trees and paths. We investigate possible refinements of Lorenz dominance and we propose an axiomatic justification of OWA operators in this context. Finally, the results of numerical experiments on randomly generated graphs are provided. They show the numerical efficiency of the suggested approach.

A Characterization of Generalized Concordance Rules in Multicriteria Decision Making

This article proposes a principled approach to multicriteria decision making (MCDM) where the worth of decisions along attributes is not supposed to be quantified, as in multiattribute utility theory, or even measured on a unique scale. This approach actually generalizes additive concordance rules a la Electre and is rigorously justified in an axiomatic way by representation theorems. We indeed show that the use of a generalized concordance (GC) rule is the only possible approach when in a purely ordinal framework and that the satisfaction of very simple principles forces the use of possibility theory as the unique way of expressing the importance of coalitions of criteria.