R UBIS: A bipolar-valued outranking method for the choice problem

in 4OR: a quarterly journal of operations research (2008), 6(2), 143-165

Disaggregation of bipolar-valued outranking relations and application to the inference of model parameters

Scientific Conference (2007, September)

On maximal independent sets in circulant digraphs

E-print/Working paper (2007)

In this research note we introduce St-Nicolas graphs, i.e. circulant digraphs showing exactly n maximal independent sets, isomorph under the digraph’s automorphisms group. This class of digraphs represent ... [more ▼]

In this research note we introduce St-Nicolas graphs, i.e. circulant digraphs showing exactly n maximal independent sets, isomorph under the digraph’s automorphisms group. This class of digraphs represent a generalisation of Andrásfai graphs with interesting links to finite group theory. [less ▲]

Counting non-isomorphic maximal independent sets of the n-cycle graph

Scientific Conference (2007, January)

It is known that the number of maximal independent sets of the $n$-cycle graph $C_n$ is given by the $n$th term of the Perrin sequence. The action of the automorphism group of $C_n$ on the family of these ... [more ▼]

It is known that the number of maximal independent sets of the $n$-cycle graph $C_n$ is given by the $n$th term of the Perrin sequence. The action of the automorphism group of $C_n$ on the family of these maximal independent sets partitions this family into disjoint orbits, which represent the non-isomorphic (i.e., defined up to a rotation and a reflection) maximal independent sets. We provide exact formulas for the total number of orbits and the number of orbits having a given number of isomorphic representatives. We also provide exact formulas for the total number of unlabelled (i.e., defined up to a rotation) maximal independent sets and the number of unlabelled maximal independent sets having a given number of isomorphic representatives. It turns out that these formulas involve both Perrin and Padovan sequences. [less ▲]

On enumerating the kernels in a bipolar-valued digraph

in Annales du Lamsade (2006), 6

In this paper we would like to thoroughly cover the problem of computing all kernels, i.e. minimal outranking and/or outranked independent choices in a bipolar- valued outranking digraph. First we ... [more ▼]

In this paper we would like to thoroughly cover the problem of computing all kernels, i.e. minimal outranking and/or outranked independent choices in a bipolar- valued outranking digraph. First we introduce in detail the concept of bipolar-valued characterisation of outranking digraphs, choices and kernels. In a second section we present and discuss several algorithms for enumerating the kernels in a crisp digraph. A third section will be concerned with extending these algorithms to bipolar-valued outranking digraphs. [less ▲]

Proc. of the 61st Meeting of the Eur. Working Group "Multiple Criteria Decision Aiding" (Luxembourg, March 10-12, 2005) - Theme: Preference Modelling

Book published by SMA - University of Luxembourg (2005)

On a natural fuzzification of Boolean logic

in Klement, Erich Peter, Pap, Endre (Ed.) Proceedings of the 25th Linz Seminar on Fuzzy Set Theory, Mathematics of Fuzzy Systems (2004, February)

In this communication we propose two logically sound fuzzification and defuzzifi- cation techniques for implementing a credibility calculus on a set of propositional expressions. Both rely on a ... [more ▼]

In this communication we propose two logically sound fuzzification and defuzzifi- cation techniques for implementing a credibility calculus on a set of propositional expressions. Both rely on a credibility evaluation domain using the rational in- terval [−1, 1] where the sign carries a split truth/falseness denotation. The first technique implements the classic min and max operators where as the second technique implements Bochvar-like operators. Main interest in the communica- tion is given to the concept of natural fuzzification of a propositional calculus. A formal definition is proposed and the demonstration that both fuzzification techniques indeed verify this definition is provided. [less ▲]

Concordant outranking with multiple criteria of ordinal significance: A contribution to robust multicriteria aid for decision

in 4OR: a quarterly journal of operations research (2004), 2(4), 293-308

Logical foundation of multi-criteria decision-aiding

in Perny, Patrice; Slowinski, Roman; VanderPooten, Daniel (Eds.) et al Aiding decisions with multiple criteria: Essays in Honor of Bernard Roy (2002)

In this chapter, we would like to show Bernard Roy’s contribution to modern computational logic. Therefore we first present his logical approach for multi-criteria preference modelling. Here, decision aid ... [more ▼]

In this chapter, we would like to show Bernard Roy’s contribution to modern computational logic. Therefore we first present his logical approach for multi-criteria preference modelling. Here, decision aid is based upon a refined methodological construction, that provides the family of criteria with important logical properties giving access to the concordance principle used for aggregating preferential assertions from multiple semiotical points of view. In a second section, we introduce the semiotical foundation of the concordance principle and present a new formulation of the concordance principle with its associated necessary coherence axioms imposed on the family of criteria. This new methodological framework allows us, in a third part, to extend the classical concordance principle and its associated coherence axioms imposed on the family of criteria – first to potentially redundant criteria, – but also to missing individual evaluations and even partial performance tableaux. [less ▲]

Human centered processes and decision support systems

in European Journal of Operational Research (2002), 136(2), 233-252