Algebraic visualization of relations using REL VIEW
Pages 58 - 72
Abstract
For graphs there exist highly elaborated drawing algorithms. We concentrate here in an analogous way on visualizing relations represented as Boolean matrices as, e.g., in RelView. This means rearranging the matrix appropriately, permuting rows and columns simultaneously or independently as required. In this way, many complex situations may successfully be handled in various application fields. We show how relation algebra and RelView can be combined to solve such tasks.
References
[1]
Behnke, R., et al.: RelView - A system for calculation with relations and relational programming. In: Astesiano, E. (ed.) ETAPS 1998 and FASE 1998. LNCS, vol. 1382, pp. 318-321. Springer, Heidelberg (1998).
[2]
Berghammer, R., Hoffmann, T.: Modelling sequences within the RelView system. J. Universal Comput. Sci. 7, 107-123 (2001).
[3]
Berghammer, R., Leoniuk, B., Milanese, U.: Implementation of relation algebra using binary decision diagrams. In: de Swart, H. (ed.) RelMiCS 2001. LNCS, vol. 2561, pp. 241-257. Springer, Heidelberg (2002).
[4]
Berghammer, R., Neumann, F.: RelView - An OBDD-based Computer Algebra system for relations. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2005. LNCS, vol. 3718, pp. 40-51. Springer, Heidelberg (2005).
[5]
Bona, M.: A walk through combinatorics: An introduction to combinatorics and graph theory. World Scientific Publishing, Singapore (2002).
[6]
Colorni, A., Paruccini, M., Roy, B.: A-MCD-A - Multiple criteria decision aiding. Joint Research Centre of the European Commission (2001).
[7]
de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds.): Theory and Applications of Relational Structures as Knowledge Instruments. LNCS, vol. 2929. Springer, Heidelberg (2003).
[8]
de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds.): Theory and Applications of Relational Structures as Knowledge Instruments II. LNCS (LNAI), vol. 4342. Springer, Heidelberg (2006).
[9]
di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph drawing - Algorithms for the visualization of graphs. Prentice-Hall, Englewood Cliffs (1999).
[10]
Fishburn, P.: On the construction of weak orders from fragmentary information. Psychometrika 38, 459-472 (1973).
[11]
Fishburn, P.: Interval orders and interval graphs. Wiley, Chichester (1985).
[12]
Guttmann, L.: A basis for scaling qualitative data. American Sociological Review 9, 139-150 (1944).
[13]
Gansner, E.R., North, S.C., Vo, K.P.: DAG - A program that draws directed graphs. Software - Practice and Experience 17, 1047-1062 (1988).
[14]
Ganter, B., Wille, R.: Formal concept analysis. Springer, Heidelberg (1999).
[15]
Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Inf. Proc. Letters 31, 7-15 (1989).
[16]
Kaufmann, M., Wagner, D. (eds.): Drawing Graphs. LNCS, vol. 2025. Springer, Heidelberg (2001).
[17]
Öztürk, M., Tsoukias, A., Vincke, P.: Preference modelling. In: Ehrgott, M., Greco, S., Figueira, J. (eds.) Multiple criteria decision analysis: State of the art surveys. Int. Series in Operat. Res. and Manag. Sci, vol. 78, pp. 27-71. Springer, Heidelberg (2005).
[18]
Schmidt, G., Ströhlein, T.: Relationen und Graphem. Springer. Available also in English: Relations and graphs. In: EATCS Monographs on Theoret. Comput. Sci., Springer, Heidelberg (1993).
[19]
Scott, D., Suppes, P.: Foundational aspects of the theories of measurement. J. Symbolic Logic 23, 113-128 (1958).
[20]
Szpilrajn, E.: Sur l'extension de l'ordre partiel. Fund. Math. 16, 386-389 (1930).
[21]
Tarski, A.: On the calculus of relations. J. Symbolic Logic 6, 73-89 (1941).
- Algebraic visualization of relations using REL VIEW
Recommendations
A frequentist view on cycle-transitivity of reciprocal relations
We establish a connection between two transitivity frameworks: the transitivity of fuzzy relations based on a commutative quasi-copula and the cycle-transitivity of reciprocal relations w.r.t. the dual quasi-copula as an upper bound function. Loosely ...
On the algebraic structure of binary lattice-valued fuzzy relations
From a general algebraic point of view, this paper aims at providing an algebraic analysis for binary lattice-valued relations based on lattice implication algebras--a kind of lattice-valued propositional logical algebra. By abstracting away from the ...
T-similarity of fuzzy relations and related algebraic structures
In this paper, we show that fuzzy Alexandrov topologies can be induced by fuzzy relations. The concept of T-similarity of fuzzy relations is introduced. Variations of the same fuzzy relation are investigated. The fact that every fuzzy relation is solely ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 16 September 2007
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 23 Feb 2025