L. ?-opérateur-de-similarité-sur and . Nombres, En effet, s'il existe une formule qui permet de calculer la similarité de deux valeurs de (D a , ? a ), la construction de la taxonomie à partir d'un ensemble de valeurs de départ peut se faire de manière automatique. C'est le cas par exemple avec l'opéra-teur de similarité ? inter sur les intervalles de nombres entiers, tel que présenté dans la Section 5.3. Les attributs représentant des entiers ou des réels sont de bons candidats pour la construction automatique de taxonomies. Il est possible de définir un opérateur de similarité (associé à une formule) par défaut, ou d'en proposer plusieurs à l'expert du domaine. Par exemple, la formule a 1 ? ? a 2 = max(a 1 , a 2 ) est une autre façon de définir automatiquement une taxonomie sur des nombres. La Figure 5.12 présente les taxonomies construites automatiquement sur les valeurs de l'attribut FirstRelease de la Table 5.2 avec (à gauche) l'opérateur de similarité construisant des intervalles ? inter et (à droite) l'opérateur de similarité ? ? . Il est aussi possible de laisser l'expert définir manuellement la taxonomie, Selon le type des valeurs de l'attribut et l'opérateur de similarité défini, cette complétion peut se faire de manière automatique, ou manuelle, 1986.

L. ?-opérateur-de-similarité-sur and . Littéraux, Tout d'abord, une taxonomie extérieure peut exister, provenant d'une ontologie métier telles que DBPedia 4 ou BioPortal 5 . Si on n'en dispose pas, on peut proposer une taxonomie construite automatiquement. Pour ce type d'attribut, plusieurs cas sont possibles. Nous avons vu précédem-ment qu'un attribut d'une MCP peut donner plusieurs valeurs pour un produit (i.e., attribut multivalué à valeurs multiples). C'est le cas par exemple de l'attribut ProgrammingLanguage. Si certaines valeurs sont partagées par plusieurs produits (i.e., la valeur C ou shell scripts dans notre exemple), on peut utiliser l'AFC pour construire automatiquement une taxonomie basée sur l'intersection ensembliste des ensembles de littéraux. Dans ce cas-là, un pattern de la taxonomie ne représente pas une des valeurs de l'attribut (i.e., un littéral), mais un ensemble de littéraux, Lorsque les valeurs d'un attribut sont des littéraux, il est plus difficile de compléter automatiquement la taxonomie

, Le treillis de concepts correspondant et la taxonomie qui en est extraite sont présentés dans la

, l'AFC ne groupe pas de littéraux et on obtient une taxonomie spécifiant que toutes les valeurs de a sont incomparables, en utilisant la valeur de dissimilarité "*". Cependant, même si cette solution permet à l'attribut d'être traité par le cadre 4, Dans le cas où les valeurs de l'attribut a sont uniques pour chaque produit (i.e., attribut multivalué à valeurs uniques)

, Si la matrice est au bon format, le programme sépare automatiquement les caractéristiques booléennes (features) et les multivaluées (attributs)

. Rq4, employabilité de la méthode) Enfin, nous évaluons l'employabilité de la mé-thode, c'est-à-dire si le nombre de relations extraites après les deux types de réduction est facilement manipulable par un expert. Pour cela, nous commentons les chiffres obtenus lors de la réponse aux questions RQ2

, Analyse des résultats RQ1. (applicabilité de la méthode) : La distribution des tailles des treillis de concepts et des AOC-posets associés aux 27 MPCs étudiées est présentée à la Figure 5.22. La construction des structures a été réalisée avec RCAExplore, sur un ordinateur Intel(R) Core(TM) i7-6700HQ CPU@2.60GHz, 16GiB RAM

, nous présentons d'abord une synthèse des travaux réalisés dans cette thèse qui montrent que l'analyse formelle de concepts est un cadre structurel de représenta-tion de la variabilité (Chapitre 3) qui est réutilisable

, La première concerne l'étude de la variabilité complexe dans le contexte de l'ingénierie des lignes de produits logiciels complexes grâce aux extensions de l'analyse formelle de concepts. La deuxième aborde la né-cessité d'établir un parallèle avec l'ingénierie dirigée par les modèles et la modélisation des familles de produits logiciels sur plusieurs niveaux d'abstraction. La troisième s'intéresse à la représentation des connaissances et à l'association entre l'analyse formelle de concepts et les ontologies pour compléter les travaux actuels. Enfin, la quatrième concerne l'approfondissement des expérimentations réalisées

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