By Ivan Rival (auth.), Ivan Rival (eds.)

ISBN-10: 9400926391

ISBN-13: 9789400926394

ISBN-10: 940107691X

ISBN-13: 9789401076913

This quantity comprises the texts of the relevant survey papers awarded at ALGORITHMS -and ORDER, held· at Ottawa, Canada from June 1 to June 12, 1987. The convention was once supported by way of offers from the N.A.T.O. complicated examine Institute programme, the collage of Ottawa, and the average Sciences and Engineering study Council of Canada. we're thankful for this massive aid. Over fifty years in the past, the Symposium on Lattice thought, in Charlottesville, u.s., proclaimed the energy of ordered units. in simple terms two decades later the Symposium on in part Ordered units and Lattice thought, held at Monterey, united states, had solved a number of the difficulties that were initially posed. In 1981, the Symposium on Ordered units held at Banff, Canada, persisted this custom. It used to be marked through a landmark quantity containing twenty-three articles on just about all present subject matters within the concept of ordered units and its purposes. 3 years after, Graphs and Orders, additionally held at Banff, Canada, aimed to rfile the position of graphs within the conception of ordered units and its functions. due to its specific position within the panorama of the mathematical sciences order is principally delicate to new developments and advancements. this present day, an important present within the conception and alertness of order springs from theoretical laptop seience. topics of computing device technology cleared the path. the 1st is info constitution. Order is usual to info structures.

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This can be avoided by changing the generating vectors of the grid. In drawing with a computer it has been proven to be useful that one let the computer determine the minimal distance of a lattice point to a line segment which should not be incident with this point (cf. [18J). (n-2, " n-2) (0,0,0) (n-2. 0,0) fig. 3: Embeddings of the concept lattice of the context in fig. 2 into a 3-dimensional grid The idea of conceptual measurement has been elaborated more explicitly in [23J and [9J. If we follow this idea, we have to consider V-embeddings of concept lattices into direct products of chains.

2. (1983),275-287. [25J R. Wille: Complete tolerance relations of concept lattices. In: G. K. B. Muller, W. ): Contributions to general algebra 3. H5Ider-Pichler-Tempsky, Wien 1985, 397-415. [26J R. Wille: Tensorial decomposition of concept lattices. Order 2 (1985), 81-95 [27J R. Wille: Liniendiagramme hierarchischer Begriffssysteme. H. ): Anwendungen der Klassifikation: Datenanalyse und numerische Klassifikation. INDEKS Verlag, Frankfurt 1984, 77 -86; Line diagrams of hierarchical concep~sys tems (engl.

X. Viennot (1985) Problemes combinatoires poses par la physique statistique, Semina ire Bourbaki, No. 626. in Asterisque, No. 121-122,225-246. K. Wagner (1936) Bemerkungen Zum Vierfarbenproblem, Jber. Deutsch. -Verein. 46, 26-32. LATTICES IN DATA ANALYSIS: HOW TO DRAW THEM WITH A COMPUTER Rudolf Wille Fachbereich Mathematik Technische Hochschule D-6100 Darmstadt FRG ABSTRACT. There is a growing demand for lattice diagrams in concept analysis and for this computer programs are needed. The diagrams should not only reflect the structure of the concept lattices but also unfold views for interpreting the data.

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Algorithms and Order by Ivan Rival (auth.), Ivan Rival (eds.)

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