Abstract
Inheritance is the main theme of schema design for the object-oriented software and object oriented database [10]. It supports class hierarchy design and capture the is-a relationship between a class and its superclass. Obviously, the designer needs tools to assist him to define his conceptual schema. However, very few approaches attempt to provide methods and tools for designing inheritance graph in object databases [29], and object software [1]. In this paper, we propose a semi-automatic method for generating inheritance graph hierarchy. This method is semi-automatic because it takes into account the feedback of the designer based on his expertise. It has a sound mathematical foundation and allows us to obtain a number of classes less than methods which uses Galois Lattice as a support to generate class hierarchy. Steps of our method are : (i) From a binary relation which represents the links between classes and their properties and methods, some heuristics generate a set of Optimal Rectangles (OR: group of classes which share the same properties and methods). (ii) The set of OR is organised by a partial order relation into a Brut Inheritance Graph (BIG). (iii) BIG is simplified and shown to the designer. (iv) The designer can modify, add or remove classes, attributes or methods in the binary relation and activates steps (ii) and (iii) until he obtains a proper class hierarchy or an Optimal Inheritance Graph.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Bibliography
Ann L. Winblad, Samuel d. Edwaards, David R. King — “Object-Oriented Software”: Addison-Wesley Publishing Company, Inc. 1990.
M. Armstrong; Richard J. Mitchell, “Uses and Abuses of Inheritance” Journal Engineering Software, Vol 9 Iss 1 19–26 pp., Jan 1994, Univ. UK
M. Barbut and B. Monjardet, “Ordre et classification”, Algèbre et combinatoire, Tome II, 1970, Hachette.
H. Belaid and Ali Jaoua, “Abstraction of Objects by Conceptual Clustering”, to appear in proceeding of Joint Conference on Information Sciences, 1997.
N. Belkhiter, C. Bourhfir, M.M. Gammoudi, A. Jaoua, N. Le Thanh, M. Reguig, “Architecture rectangulaire optimale d'une base documentaire indexée”, Université Laval, Département d'Informatique (Rapport de Recherche), DIUL-RR-9201, 1992.
N. Belkhiter, C. Bourhfir, M.M. Gammoudi, A. Jaoua, N. Le Thanh, M. Reguig, “Décomposition Rectangulaire Optimale d'une Relation Binaire: Application aux Bases de Données Documentaires” Information Systems and Operational Research Journal, Février 32 (1): 33–54, 1994.
N. Belkhiter, J. Desharnais, G. Ennis, A. Jaoua, H. Ounalli, M.M. Gammoudi, “Formal Properties of Rectangular Relations”, in Proceeding of the Ninth International Symposium on Computer and Information Science, ISCIS IX, Antalya, Turkey, November 7–9, 1994.
Booch Grady, “Object-Oriented Analisys and Design with Applications”, Second Edition-The Benjamin/Cummings Publishing Company, Inc. 1994.
J.P. Bordat, “Sur l'algorithmique combinatoire d'ordre finis”, Thèse de Doctorat d'état mention Sciences de l'Université de Montpellier II, (USTL), 29 avril 1992.
John Daniels, “Objects Design Methods and Tools”, IEEE London, UK, 1994 24 pp.
Ding-An Chiang; Ming-Chi Lee, “Cyclic Inheritance Detection for Object-Oriented Database”, IEEE New York, NY, USA, Vol 2 1047 pp., 1992, Univ. TAIWAM.
Chi-Ming Chung; Lee M. C., “Inheritance-Based Object-Oriented Software Metrics”, IEEE New York, NY, USA, 1992 Vol 2 1047 pp.
Chi-Ming Chung; Chun-Chi Wang, Ming-Chi Lee, “Class Hierarchy Based Metric for Object-Oriented Design”, IEEE New York, NY, USA, 1994 Vol 2 xxvii+1111 pp.
M. M. Gammoudi. “Méthode de décomposition rectangulaire d'une relation binaire: une base formelle et uniforme pour le génération automatique des thesaurus et la recherche documentaire, Thèse de doctorat, Université de Nice Sofia Antipolis, Septembre 1993.
M.M. Gammoudi and S. Labidi “An Automatic Generation of Consensual Rules Between Experts Using Rectangular Decomposition of a Binary relation”, in Proceeding of the XI Brazilian Symposium on-Artificial Intelligence, Fortaleza, October 1994.
M.M. Gammoudi “heuristics for Clustering Method and Its use in Information Retieval System”, in Proceeding of the International Conference SCCC'96, Valdivia, Chile, November 1996.
B. Ganter, “Two Basic Algorithms in Concept Analysis”, Preprint 831, Technische Hochschule Darmstad, p. 28, 1984.
M. R. Garay, D. S. Jonhson, “Computer and Interactability: A guide of the theory of NP-Completeness.”, W. H. Freeman, 1979.
R. Godin, Rokia Missaoui, Hassan Alaoui, “leraning Algorithms Using a Galois Lattice Structure”, in Proceedings of the 1991 IEEE Int. Conf. On Tools for AI, San Jose CA-Nov, 1991
R. Godin and H. Mili, “Buildind and Maintaining analysis-level class hierarchies using Galois Lattice”, OOPSLA-93 Washington DC, USA Oct 1993 ACM press pp. 394–410.
R. Godin and H. Mili, “Conceptual Clustering Methods based on Galois lattice ans aplications”, French Revuw on Artificial Intelligence, Vol 9 N 2, 1995 pp. 105–137.
A. Guenoche, “Construction du treillis de Galois d'une relation binaire”, Math. Inf. Sci. hum., 28ème année, (109): 41–53, 1990.
Jean, Mayrand and Guay, François and M. Merlo, Ettore. “Inheritance Graph Assessment Using Metrics”, Proceedings of METRICS '96, 1996 IEEE.
E.M. Norris, “An algorithm for Computing the Maximal Rectangles in a Binary Relation”, Revue Roumaine de Mathématiques Pures et Appliquées, 23(2) p. 243–250, 1978.
R. E. Stepp and R. S. Michalski, “Conceptual clustering: inventing goal-oriented classifications of structured objects”, R. Michalski, J. Carbonnel, and T. Mitchell, (eds)., machine learning: An I.A. Approach. San Mateo, Calif Morgan Kauffmann, 1986.
I. Schmitt and G. Saake, “Integration of inheritance trees as part of view generation for database federations”, In proceeding of the 15th International Conference on Conceptual Modelling — ER'96. Cottbus, Germany, 7th–10th October 1996, B. Thalheim (Ed.), LNCS No 1157, pp. 195–210.
Wei Sun; Sha Guo; Farah Arafi; Shengru Tu, “Supporting Inheritance in Relational Database”, IEEE Computing Soc. Press, Los Alamitos, CA, USA, 1992, xi+641 pp.
R. Wille, “Finite Distributive Lattices as Concept Lattices”, Atti Inc. Logica Matematica, (2) 1985.
R. Wille, “Knowledge Acquisition by Methods of Formal Concept Analysis”, In E. Diday (Eds). Data Analysis, Learning Symbolic and Numeric Knowledge, New York: Nova Science, 1989.
A. Yahia, L. Lakhal, and Jean Paul Bordat, “Designing Class Hierarchies of Object Database Schema”, To appear in the Computer journal, 1997.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gammoud, M.M., Mendes, J.D., Pinto, W.S. (1997). Inheritance graph hierarchy construction using rectangular decomposition of a binary relation and designer feedback. In: Embley, D.W., Goldstein, R.C. (eds) Conceptual Modeling — ER '97. ER 1997. Lecture Notes in Computer Science, vol 1331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63699-4_23
Download citation
DOI: https://doi.org/10.1007/3-540-63699-4_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63699-1
Online ISBN: 978-3-540-69630-8
eBook Packages: Springer Book Archive