Daniel Vanderpooten

A generalized definition of rough approximations based on similarity

This paper proposes new definitions of lower and upper approximations, which are basic concepts of the rough set theory. These definitions follow naturally from the concept of ambiguity introduced in this paper. The new definitions are compared to the classical definitions and are shown to be more general, in the sense that they are the only ones which can be used for any type of indiscernibility or similarity relation.

Min–max and min–max regret versions of combinatorial optimization problems: A survey

Min-max and min-max regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the min-max and min-max regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, min cut, min s-t cut, knapsack. Since most of these problems are NP-hard, we also investigate the approximability of these problems. Furthermore, we present algorithms to solve these problems to optimality.

The European school of MCDA: Emergence, basic features and current works

Multiple-criteria decision analysis has evolved considerably since its birth during the 1960s. As part of this evolution, several schools of thought have developed emphasizing different techniques and, more generally, different attitudes as to the way of supporting or aiding decision making. One of these schools is now commonly referred to as the ‘European School’, its members being part of a European Working Group entitled ‘Multicriteria Aid for Decisions’. In the first part of this paper (Section 1) we follow a historical perspective in order to trace the emergence of the European School. Its distinctive features and main ideas are then outlined in Section 2. Finally we provide a general review of the current major research topics developed within this framework (Section 3).

An outranking approach for rank aggregation in information retrieval

Research in Information Retrieval usually shows performanceimprovement when many sources of evidence are combined to produce a ranking of documents (e.g., texts, pictures, sounds, etc.). In this paper, we focus on the rank aggregation problem, also called data fusion problem, where rankings of documents, searched into the same collection and provided by multiple methods, are combined in order to produce a new ranking. In this context, we propose a rank aggregation method within a multiple criteria framework using aggregation mechanisms based on decision rules identifying positive and negative reasons for judging whether a document should get a better rank than another. We show that the proposed method deals well with the Information Retrieval distinctive features. Experimental results are reported showing that the suggested method performs better than the well-known CombSUM and CombMNZ operators.

Description and analysis of some representative interactive multicriteria procedures

Interactive multicriteria procedures have met with a very great success forabout 15 years. We present here some of them which seem to be representative of the literature. Each description is followed by a detailed analysis of the method. This analysis consists of comments about the underlying approach, technical aspects and practical considerations. A final section provides general comments.

Solving efficiently the 0-1 multi-objective knapsack problem

In this paper, we present an approach, based on dynamic programming, for solving the 0-1 multi-objective knapsack problem. The main idea of the approach relies on the use of several complementary dominance relations to discard partial solutions that cannot lead to new non-dominated criterion vectors. This way, we obtain an efficient method that outperforms the existing methods both in terms of CPU time and size of solved instances. Extensive numerical experiments on various types of instances are reported. A comparison with other exact methods is also performed. In addition, for the first time to our knowledge, we present experiments in the three-objective case.

Complexity of the min-max and min-max regret assignment problems

This paper investigates the complexity of the min-max and min-max regret assignment problems both in the discrete scenario and interval data cases. We show that these problems are strongly NP-hard for an unbounded number of scenarios. We also show that the interval data min-max regret assignment problem is strongly NP-hard.

Induction of decision rules in classification and discovery-oriented perspectives

This paper discusses induction of decision rules from data tables representing information about a set of objects described by a set of attributes. If the input data contains inconsistencies, rough sets theory can be used to handle them. The most popular perspectives of rule induction are classification and knowledge discovery. The evaluation of decision rules is quite different depending on the perspective. Criteria for evaluating the quality of a set of rules are presented and discussed. The degree of conflict and the possibility of achieving a satisfying compromise between criteria relevant to classification and criteria relevant to discovery are then analyzed. For this purpose, we performed an extensive experimental study on several well‐known data sets where we compared two different approaches: (1) the popular rough set based rule induction algorithm LEM2 generating classification rules, (2) our own algorithm Explore—specific for discovery perspective. © 2001 John Wiley & Sons, Inc.

Enumeration and interactive selection of efficient paths in a multiple criteria graph for scheduling an Earth observing satellite

We consider a satellite following orbits around the earth in order to take shots corresponding to images requested by various customers. The daily operations of such a satellite consist of defining a feasible and satisfactory shot sequence. This problem involves both combinatorial and multiple criteria difficulties. Indeed, the number of feasible shot sequences grows significantly with the number of images asked for, and the evaluation of a shot sequence is based on several conflicting criteria. We propose to formulate this problem as the selection of a multiple criteria path in a graph without circuit. Our approach for solving this problem involves two stages: generation of efficient paths and selection of a satisfactory path using a multiple criteria interactive procedure. � 2002 Elsevier Science B.V. All rights reserved.

The interactive approach in MCDA: A technical framework and some basic conceptions

The abundance of interactive procedures and the increasing number of real-world applications reflect the wide success met by this approach. Based on different technical concepts, grounded on various conceptions, interactive multicriteria procedures clearly reveal interesting features. However, this diversity make them difficult to encompass in a global view. After briefly introducing the interactive approach in MCDA, a general technical framework which gives new insights for the understanding of existing methods is presented. In the second part of the paper, two conceptions concerning the way of considering the decision making process are introduced. These conceptions give rise to a basic distinction between two main classes of interactive procedures whose respective purposes are quite different.