![]() ![]() Bisdorff, Raymond ![]() in European Journal of Operational Research (2008), 187(3), 1293-1295 Detailed reference viewed: 71 (0 UL)![]() Bisdorff, Raymond ![]() in Communications in Computer and Information Science (2008), 14 Detailed reference viewed: 107 (2 UL)![]() Bisdorff, Raymond ![]() in 4OR: a quarterly journal of operations research (2008), 6(2), 143-165 Detailed reference viewed: 122 (7 UL)![]() Bisdorff, Raymond ![]() ![]() in Journal of Integer Sequences (2008), 11(5), 1-16 The number of maximal independent sets of the n-cycle graph C_n is known to be the nth term of the Perrin sequence. The action of the automorphism group of C_n on the family of these maximal independent ... [more ▼] The number of maximal independent sets of the n-cycle graph C_n is known to be the nth 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 unlabeled (i.e., defined up to a rotation) maximal independent sets and the number of unlabeled maximal independent sets having a given number of isomorphic representatives. It turns out that these formulas involve both Perrin and Padovan sequences. [less ▲] Detailed reference viewed: 103 (23 UL)![]() ; Marichal, Jean-Luc ![]() ![]() Scientific Conference (2007, September) Detailed reference viewed: 613 (5 UL)![]() ![]() Bisdorff, Raymond ![]() ![]() in European Journal of Operational Research (2007), 177(3), 1313-2118 Detailed reference viewed: 105 (10 UL)![]() Bisdorff, Raymond ![]() 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 ▲] Detailed reference viewed: 33 (1 UL)![]() Meyer, Patrick ![]() ![]() Scientific Conference (2007, February) We present the problem of the selection of k best alternatives in the context of multiple criteria decision aid. We situate ourselves in the context of pairwise comparisons of alternatives and the ... [more ▼] We present the problem of the selection of k best alternatives in the context of multiple criteria decision aid. We situate ourselves in the context of pairwise comparisons of alternatives and the underlying bipolar-valued outranking digraph. We present three formulations for the best k-choice problem and detail how to solve two of them directly on the outranking digraph. [less ▲] Detailed reference viewed: 42 (0 UL)![]() Bisdorff, Raymond ![]() ![]() 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 ▲] Detailed reference viewed: 65 (9 UL)![]() ![]() Bisdorff, Raymond ![]() in European Journal of Operational Research (2007), 177(3), 1313-1316 Detailed reference viewed: 95 (1 UL)![]() Bisdorff, Raymond ![]() 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 ▲] Detailed reference viewed: 48 (6 UL)![]() Bisdorff, Raymond ![]() in European Journal of Operational Research (2006), 175(1), 155-170 Detailed reference viewed: 101 (2 UL)![]() Bisdorff, Raymond ![]() Presentation (2005, October 11) The presentation discusses the use of the digraph kernels for computing a best choice recommendation from a valued outranking digraph. The classical best decision problem approach is critically reviewed ... [more ▼] The presentation discusses the use of the digraph kernels for computing a best choice recommendation from a valued outranking digraph. The classical best decision problem approach is critically reviewed. New practical principles underlying a best choice recommendation are introduced which promote the outranking kernels as candidates for best choice recommendations. Some illustrative applications were eventually shown in order to convince the audience. [less ▲] Detailed reference viewed: 75 (1 UL)![]() Bisdorff, Raymond ![]() ![]() Book published by SMA - University of Luxembourg (2005) Detailed reference viewed: 60 (6 UL)![]() Bisdorff, Raymond ![]() in Annales du LAMSADE (2004), 3 In this paper we address the problem of aggregating outranking situations in the presence of multiple preference criteria of ordinal significance. The concept of ordinal concordance of the global ... [more ▼] In this paper we address the problem of aggregating outranking situations in the presence of multiple preference criteria of ordinal significance. The concept of ordinal concordance of the global outranking relation is defined and an operational test for its presence is developed. Finally, we propose a new kind of robustness analysis for global outranking relations taking into account classical dominance, ordinal and classical majority oncordance in a same bipolar-valued logical framework [less ▲] Detailed reference viewed: 44 (3 UL)![]() Bisdorff, Raymond ![]() 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 ▲] Detailed reference viewed: 52 (0 UL)![]() Bisdorff, Raymond ![]() in Lecture Notes in Computer Science (2004), 3051 Detailed reference viewed: 89 (3 UL)![]() Bisdorff, Raymond ![]() in 4OR: a quarterly journal of operations research (2004), 2(4), 293-308 Detailed reference viewed: 56 (6 UL)![]() Bisdorff, Raymond ![]() Doctoral thesis (2002) Detailed reference viewed: 58 (6 UL)![]() ![]() ; Bisdorff, Raymond ![]() in European Journal of Operational Research (2002), 136(2), 233-252 Detailed reference viewed: 91 (0 UL) |
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