267 research outputs found

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

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    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.Comment: Revised versio

    Preference aggregation with multiple criteria of ordinal significance

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    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 framewor

    On a natural fuzzification of Boolean logic

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    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

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

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    International audienceThe main concern of this article is to present the RUBIS method for tackling the choice problem in the context of multiple criteria decision aiding. Its genuine purpose is to help a decision maker to determine a single best decision alternative. Methodologically we focus on pairwise comparisons of these alternatives which lead to the concept of bipolar-valued outranking digraph. The work is centred around a set of five pragmatic principles which are required in the context of a progressive decision aiding methodology. Their thorough study and implementation in the outranking digraph lead us to define a choice recommendation as an extension of the classical digraph kernel concept

    Association between drug intake and incidence of malignancies in patients with Juvenile Idiopathic Arthritis: a nested case-control study

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    Background: Several medications for treatment of Juvenile Idiopathic Arthritis (JIA) are considered to be carcinogenic. Therefore, the aim was to assess whether there is an association between therapeutic interventions and malignancies in JIA patients. Findings: A nested case-control study was carried out within a retrospective cohort study of 3698 JIA patients diagnosed between 1952 and 2010. All 48 JIA patients with a diagnosis of a malignant tumour and up to four matched controls for each received a questionnaire about their use of medication. Subsequently treatment was compared between cases and controls and analyses performed for 37 cases and 125 controls (response 88.5 %). Treatment with DMARD (84 %) was most frequently used, followed by glucocorticoids (66 %) and immunosuppressives (65 %). Twenty percent reported to have ever been taking biologics. Medication use did not differ significantly between cases and controls. Conclusions: Our results did not show an association between medications used and malignancies in JIA patients