Betweenness, Łukasiewicz Rough Inclusions, Euclidean Representations in Information Systems, Hyper-granules and Conflict Resolution

• Autorzy: Polkowski L. T. , Nowak B.

Identyfikatory

DOI

10.3233/FI-2016-1411

• Konferencja: International Workshop on CONCURRENCY, SPECIFICATION, and PROGRAMMING (CS&P 2015), (24; 28-30.09.2015, Rzeszów, Poland).
• Języki publikacji: EN

Abstrakty

EN

In this work, we approach the problem of data analysis from a new angle: we investigate a relational method of separation of data into disjoint sub–data employing a modified betweenness relation, successfully applied by us in the area of behavioral robotics, and, we set a scheme for applications to be studied. The effect of the action by that relation on data is selection of a sub–data, say, ‘kernel’ with the property that each thing in it is a convex combination, in a sense explained below, of some other things in the kernel. One can say that kernel thus exhibited is ‘self–closed’. Algorithmically, this is achieved by means of a new construct, called by us a ‘dual indiscernibility matrix’. On the other hand, the complement to kernel consists of things in the data, which have some attribute values not met in any other thing. It is proper to call this complement to kernel the residuum. We examine both the kernel and the residuum from the point of view of quality of classification into decision classes for a few standard data sets from the UC Irvine Repository finding the results very satisfactory. Conceptually, our work is set in the framework of rough set theory and rough mereology and the main tool in inducing of the betweenness relation is the Łukasiewicz rough inclusion. Apart from the classification problem, we propose some strategies for conflict resolution based on concepts introduced in this work, and in this way we continue conflict analysis in rough set framework initiated by Zdzisław Pawlak.

Słowa kluczowe

EN

rough inclusions; betweenness; Euclidean representation of a granule; hyper–granules; coalition; conflict resolution; classifiers synthesis

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2016
• Tom: Vol. 147, nr 2/3
• Strony: 337--352
• Opis fizyczny: Bibliogr. 22 poz., tab.

Twórcy

autor

Polkowski L. T.

• Polish–Japanese Institute of IT, Warsaw, Poland

autor

Nowak B.

• Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

Bibliografia

• [1] van Benthem J. The Logic of Time. Springer Netherlands, Synthese Library 1983;156. doi: 10.107/978-94-010-9868-7.
• [2] Devroye L, Györfi L, Lugosi G. A Probabilistic Theory of Pattern Recognition. Springer Verlag, New York 1996;31. doi: 10.1007/978-1-4612-0711-5. ISBN: 978-1-4612-6877-2, 978-1-4612-0711-5.
• [3] Grzymała–Busse JW. LERS–a system for learning from examples based on rough sets. In: Słowiński, R. (ed.). Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory. Springer Netherlands, 1992 pp. 3–18. doi:10.1007/978-94-015-7579-5.
• [4] Harsanyi J, Selten R. A General Theory of Equilibrium Selection in Games. MIT Press, Cambridge, MA 1988. doi: 10.1002/bs.3930340206. ISBN: 10.0262582384, 13.978-0262582384.
• [5] Knaster B. Sur le problème du partage pragmatique de H. Steinhaus. Annales de la Société Polonaise de Mathématique 1946;19:228-230.
• [6] Nash JF. Equilibrium points in N-person games. Proceedings of the National Academy of Sciences 1950;36(1):48–49. doi:10.1073/pnas.36.1.48.
• [7] von Neumann J, Morgenstern O. Theory of Games and Economic Behavior. Princeton University Press 1947. OCLC: 1629708.
• [8] Pawlak Z. Rough sets. Int. J. Computer and Information Sciences 1982;11:341–356.
• [9] Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning about Data. Springer Netherlands 1991;9. doi:10.1007/978-94-011-3534-4. ISBN: 978-0-7923-1472-1, 978-94-010-5564-2.
• [10] Pawlak Z. An inquiry into anatomy of conflicts. Journal of Information Sciences 1998;109(1-4):65–78. doi:10.1016/S0020-0255(97)10072-X.
• [11] Pawlak Z, Skowron A. A rough set approach for decision rules generation. Proceedings of IJCAI 1993 Workshop W12. 1993;50:264–275. Available from: http://dblp.uni-trier.de/rec/bib/journals/eatcs/SkowronS93.
• [12] Polkowski L. Approximate Reasoning by Parts. An Introduction to Rough Mereology. Springer Verlag, Berlin, ISRL vol. 20, 2011. Available from: http://dx.doi.org/10.1007/978-3-642-22279-5, doi:10.1007/978-3-642-22279-5.
• [13] Polkowski L. Mereology in engineering and computer science. In: Calosi, C., Graziani, P.(eds.): Mereology and the Sciences. Springer Intl. Publ. Switzerland, Cham Heidelberg. Synthese Library 371, 2014 pp. 217–292. doi:10.1007/978-3-319-05356-1.
• [14] Polkowski L. Betweenness, Lukasiewicz Rough Inclusions, Euclidean Representations in Information Systems, Hyper-granules, Conflict Resolution. Proceedings of the 24th International Workshop on Concurrency, Specification and Programming, Volume II. 2015 pp. 97–110. Available from: http://ceur-ws.org/Vol-1492/.
• [15] Polkowski L, Artiemjew P. Granular Computing in Decision Approximation. An Application of Rough Mereology. Intelligent Systems Reference Library 77, Springer 2015. Available from: http://dx.doi.org/10.1007/978-3-319-12880-1, doi:10.1007/978-3-319-12880-1.
• [16] Polkowski L, Skowron A. Rough mereology: a new paradigm for approximate reasoning. Int. J. Approximate Reasoning 1997;15(4):333–365. Available from: http://dx.doi.org/10.1016/S0888-613X(96)00072-2, doi:10.1016/S0888-613X(96)00072-2.
• [17] Quinlan JR. C4. 5: Programs for Machine Learning. Morgan Kaufmann Publ., San Francisco CA 1993. ISBN: 1-55860-238-0.
• [18] Skowron A. Boolean reasoning for decision rules generation. In: Proceedings of the 7th International Symposium on Methodologies for Intelligent Systems, ISMIS ’93, LNCS 689, 1993 pp. 295–305. Available from: http://dl.acm.org/citation.cfm?id=646354.688944.
• [19] Skowron A, Rauszer C. The discernibility matrices and functions in decision systems. In: Słowiński, R. (ed.): Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory. Springer Netherlands 11, 1992 pp. 311–362. doi: 10.1007/978-94-015-7579-5.
• [20] Steinhaus H. Remarques sur le partage pragmatique. Annales de la Société Polonaise de Mathématique 1946;19:230-231.
• [21] Tarski A, Givant S. Tarski’s system of geometry. Bull. Symbolic Logic 1999;5(2):175–214. doi:10.2307/421089.
• [22] UCI Repository. Available from: http//www.ics.uci.edu/~mlearn/databases.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).