Y. De Smet

About the applicability of MCDA to some robustness problems

Coping with uncertainties or ignorance in decision problems may lead to the idea that several scenarios can occur or that several sets of data can constitute a good representation of the reality. In consequence, numerous authors have focused on the robust aspect of these problems. In such a context, one can consider that a scenario (or a particular instance of the data) permits to partially qualify the solutions, just as a criterion does. In other words, the evaluation of a specific solution for a given scenario could be perceived as the evaluation of this solution according to one particular criterion. With this in mind, the applicability of classic multicriteria concepts to the robustness framework, in the context of optimization problems, is explored. We achieve this by studying their similarities and differences. The distinguishing characteristics bring us to introduce a new problematic: the multicriteria evaluation of robustness.

Rank reversal in the PROMETHEE II method: Some new results

The aim of this paper is to study properties of multicriteria decision-aid ranking methods based on pairwise comparisons in regards to rank reversals. At first we introduce the notion of pairwise rank reversal and we show that this notion is equivalent to rank reversal. Then we analyze more particularly the PROMETHEE II method and we clarify conditions under which the PROMETHEE II ranking might suffer from rank reversal problems. Finally, we prove that the PROMETHEE multicriteria net flow is the centered score that minimizes the sum of the squared deviations from the pairwise comparisons of the alternatives.

Visual PROMETHEE: Developments of the PROMETHEE & GAIA multicriteria decision aid methods

PROMETHEE and GAIA are multicriteria decision aid methods belonging to the family of outranking methods. PROMETHEE is prescriptive: it provides the decision-maker with rankings of a set of alternative decisions evaluated on several often conflicting criteria. GAIA is descriptive: it uncovers important features of the decision problem and assists the decision-maker in eliciting preferences and finalizing the decision. After a brief summary of the basis of PROMETHEE and GAIA, we focus on the new development of Visual PROMETHEE. We propose several visual representations to enhance the efficiency of the methods. In particular the PROMETHEE Diamond is used to visualize the PROMETHEE I partial ranking and the GAIA Brain representation can be used to facilitate the assessment of the criteria weights. These developments are illustrated on a numerical example.

Extending the PROMETHEE II method to continuous and combinatorial multi-objective optimization problems: a first model

PROMETHE II is a multicriteria decision aid method based on pairwise comparisons. As a consequence, it cannot reasonably be applied to problems involving a large number of alternatives (such as for instance in combinatorial or continuous multi-objective optimization). The aim of this paper is to present an approach inspired by genetic algorithms that allows to overcome these difficulties. An illustrative example based on financial portfolio management is presented.

An empirical analysis of elicited weights in AHP

The Analytic Hierarchy Process (AHP) requires the decision maker to provide pair wise comparisons to obtain a complete ranking of the alternatives. One of the main concerns of this method is related to the level of consistency needed to produce reliable results. When the decision maker is not consistent enough, resulting scores and weights values are questionable. The aim of this paper is to study the robustness of AHP regarding the use of the eigenvector method (to derive weights and scores) and the consequences of imposing a 9 level scale for the pair wise comparisons. These two points were considered when tackling the problem of weights elicitation for the criteria. To that aim, we use a simulation approach.

On the use of reference profiles to compute alternative PROMETHEE II rankings: A preliminary study

Engineering decision problems often involve the simultaneous optimization of several conflicting criteria. Among multicriteria decision aid methods, PROMETHEE has gained a lot of attention during the last three decades. Despite its successful application in different fields, some researchers have emphasized that PROMETHEE does not respect the independence to third alternatives assumption. This leads to the so-called “rank reversal” phenomenon (potential manipulation threat); the relative position of two alternatives may depend on a third one. In this paper, inspired by the ideas of reference profiles to establish rankings, we propose a new way to compute an alternative PROMETHEE II ranking that does not suffer from rank reversal (common basis for the pairwise comparisons for all the alternatives). We show on an illustrative example the results given by this new method and observe that the obtained ranking is compatible with the one established with the classical PROMETHEE II method.

An extension of PROMETHEE to divisive hierarchical multicriteria clustering

We consider an extension of PROMETHEE II for multicriteria ordered clustering. The method is based on a divisive hierarchical clustering algorithm. A new property of the net flow score is proved and then used to divide existing clusters. The method is illustrated on two applications: the ranking of management masters by the financial times and the human development index.

P2CLUST: An extension of PROMETHEE II for multicriteria ordered clustering

We address the problem of multicriteria ordered clustering i.e. The detection of ordered categories in a multicriteria context. Therefore, we propose an extension of PROMETHEE II called P2CLUST. The algorithm is both inspired by the k-means procedure and the underlying idea of the FLOWSORT method. The algorithm is tested on two real examples.

A preliminary study about the application of multicriteria decision aid to the evaluation of the road projects' performance on sustainable safety

Since 2002, improving road safety has been a main issue in policies for transport and mobility in Europe. In Belgium, the Federal Commission for the Road Safety had defined an objective of reducing the number of deaths on Belgian roads to 500 by 2015. Then, this research aims to improve road safety on Belgian roads by developing a multicriteria decision aid model for the evaluation of sustainable road safety on secondary rural roads. In this preliminary study, we describe the approach which led us to the development of the first elements of our methodology. At first, we define the set of criteria that structures the problem, and then, we apply them to a specific case study - the redevelopment of the N243a. Finally, we analyze the results to prove the complexity of this type of problems and to point out the usefulness of a multicriteria decision aid methodology to resolve them.

About the computation of robust PROMETHEE II rankings: Empirical evidence

Engineering decision problems often involve the simultaneous optimization of several conflicting criteria. Among multicriteria decision aid methods, PROMETHEE has gained a lot of attention during the last three decades. Despite its successful application in different fields, some researchers have pointed out the fact that PROMETHEE does not respect the independence to third alternatives assumption. This leads to the so-called “rank reversal” phenomenon; the relative position of two alternatives may depend on a third one (and so a manipulation threat might exist). In this paper, we propose an alternative method to compute a complete ranking. Inspired by the ideas of robust statistics, we assess the probability of having a given alternative being ranked before another one based on different samplings of the set of alternatives. This allows us to assess a new pairwise comparison matrix that is then exploited by means of net flow scores. We show on an illustrative example that the new method does not suffer from rank reversal (while the PROMETHEE II ranking does).