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Counting non-isomorphic maximal independent sets of the n-cycle graph Bisdorff, Raymond ; Marichal, Jean-Luc 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: 82 (22 UL)R UBIS: A bipolar-valued outranking method for the choice problem Bisdorff, Raymond ; ; in 4OR: a quarterly journal of operations research (2008), 6(2), 143-165 Detailed reference viewed: 94 (6 UL)OR and the management of electronic services - EURO'2004 Bisdorff, Raymond ; ; in European Journal of Operational Research (2008), 187(3), 1293-1295 Detailed reference viewed: 54 (0 UL)Disaggregation of bipolar-valued outranking relations and application to the inference of model parameters ; Marichal, Jean-Luc ; Bisdorff, Raymond Scientific Conference (2007, September) Detailed reference viewed: 600 (5 UL)Human centered processes: Toward a naturalistic decision making paradigm Bisdorff, Raymond ; ; Marichal, Jean-Luc in European Journal of Operational Research (2007), 177(3), 1313-2118 Detailed reference viewed: 80 (10 UL)On maximal independent sets in circulant digraphs 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: 21 (1 UL)Exploitation of a bipolar-valued outranking relation for the choice of k best alternatives Meyer, Patrick ; Bisdorff, Raymond 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: 17 (0 UL)Counting non-isomorphic maximal independent sets of the n-cycle graph Bisdorff, Raymond ; Marichal, Jean-Luc 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: 47 (9 UL)Human centered processes: Toward a naturalistic decision making paradigm Bisdorff, Raymond ; in European Journal of Operational Research (2007), 177(3), 1313-1316 Detailed reference viewed: 78 (1 UL)On enumerating the kernels in a bipolar-valued digraph 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: 24 (4 UL)Choices and kernels in bipolar valued digraphs Bisdorff, Raymond ; ; in European Journal of Operational Research (2006), 175(1), 155-170 Detailed reference viewed: 72 (1 UL)Proc. of the 61st Meeting of the Eur. Working Group "Multiple Criteria Decision Aiding" (Luxembourg, March 10-12, 2005) - Theme: Preference Modelling Bisdorff, Raymond ; Marichal, Jean-Luc ; Book published by SMA - University of Luxembourg (2005) Detailed reference viewed: 48 (6 UL)Preference aggregation with multiple criteria of ordinal significance 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: 21 (1 UL)On a natural fuzzification of Boolean logic 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: 39 (0 UL)Choice procedures in pairwise comparison multiple-attribute decision making methods Bisdorff, Raymond ; in Lecture Notes in Computer Science (2004), 3051 Detailed reference viewed: 72 (3 UL)Concordant outranking with multiple criteria of ordinal significance: A contribution to robust multicriteria aid for decision Bisdorff, Raymond in 4OR: a quarterly journal of operations research (2004), 2(4), 293-308 Detailed reference viewed: 28 (4 UL)Design and Implementation of Decision Making Checkers for Industrial Production Scheduling, Control, and Maintenance Bisdorff, Raymond Doctoral thesis (2002) Detailed reference viewed: 41 (2 UL)Logical foundation of multi-criteria decision-aiding Bisdorff, Raymond 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 ▲] Detailed reference viewed: 17 (0 UL)Electre-like clustering from a pairwise fuzzy proximity index Bisdorff, Raymond in European Journal of Operational Research (2002), 138(2), 320-331 Detailed reference viewed: 61 (0 UL)Human centered processes and decision support systems ; Bisdorff, Raymond ; in European Journal of Operational Research (2002), 136(2), 233-252 Detailed reference viewed: 76 (0 UL) |
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