Rough Mereology as a Tool for Knowledge Discovery and Reasoning in Intelligent Systems: A Survey

Lech Polkowski

Computer Science Department, Polish-Japanese Institute of Information Technology, Warszawa, Poland.

DOI: 10.4236/ijis.2013.31A007                

Abstract

In this work, we present an account of our recent results on applications of rough mereology to problems of 1) knowledge granulation; 2) granular preprocessing in knowledge discovery by means of decision rules; 3) spatial reasoning in multi-agent systems in exemplary case of intelligent mobile robotics.

Keywords

Knowledge Engineering; Rough Mereology; Granular Computing; Data Mining; Intelligent Robotics

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. Bjoerner, “A Role for Mereology in Domain Science and Engineering,” In: C. Calosi and P. Graziani, Eds., Mereology and the Sciences, Springer Verlag, Berlin, in Press.
[2]	C. Calosi and P. Graziani, “Mereology and the Sciences,” Springer Verlag, Berlin, in Press.
[3]	L. Polkowski, “Mereology in Engineering and Computer Science,” In: C. Calosi and P. Graziani, Eds., Mereology and the Sciences, Springer Verlag, Berlin, in Press.
[4]	L. Polkowski, “Granulation of Knowledge in Decision Systems: The Approach Based on Rough Inclusions. The Method and its Applications,” Proceedings RSEISP 07, Rough Sets and Intelligent Systems Paradigms, Lecture Notes in Artificial Intelligence 4585, Springer Verlag, Berlin, 2007, pp. 271-279.
[5]	L. Polkowski, “A Unified Approach to Granulation of Knowledge and Granular Computing Based on Rough Merology: A Survey,” In: W. Pedrycz, A. Skowron and V. Kreinovich, Eds., Handbook of Granular Computing, John Wiley & Sons, Ltd., Chichester, 2008, pp. 375-400. doi:10.1002/9780470724163.ch16
[6]	L. Polkowski, “Granulation of Knowledge: Similarity Based Approach in Information and Decision Systems,” In: R. A. Meyers, Ed., Encyclopedia of Complexity and System Sciences, Springer Verlag, Berlin, 2009, Article ID: 00788.
[7]	L. Polkowski, “Data Mining and Knowledge Discovery: Case Based Reasoning, Nearest Neighbor and Rough Sets,” In: R. A. Meyers, Ed., Encyclopedia of Complexity and System Sciences, Springer Verlag, Berlin, 2009, Article ID: 00391.
[8]	L. Polkowski, “Approximate Reasoning by Parts. An Introduction to Rough Mereology,” Springer Verlag, Berlin, 2011.
[9]	P. Hajek, “Metamathematics of Fuzzy Logic,” Kluwer Academic Publishers, Dordrecht, 1998. doi:10.1007/978-94-011-5300-3
[10]	Z. Pawlak, “Rough Sets: Theoretical Aspects of Reasoning about Data,” Kluwer, Dordrecht, 1991.
[11]	R. R. Kelly Jr. and C. G. Cegielski, “Introduction to Information Systems: Support and Transforming Business,” 4th Edition, John Wiley & Sons, Ltd., Hoboken, 2012.
[12]	S. Li, T. Li and C. Luo, “A Multi-Granulation Model under Dominance-Based Rough Set Approach,” Lecture Notes in Computer Science, Vol. 7413, Springer Verlag, Berlin, 2012, pp. 18-25.
[13]	B. Liu, Y. Li and Y.-C. Tian, “Discovering Novel Knowledge Using Granule Mining,” Lecture Notes in Computer Science, Vol. 7413, Springer Verlag, Berlin, 2012, pp. 380-387.
[14]	L. Polkowski and P. Osmialowski, “A Framework for Multi-Agent Mobile Robotics: Spatial Reasoning Based on Rough Mereology in Player/Stage System,” Lecture Notes in Artificial Intelligence, Vol. 5306, Springer Verlag, Berlin, 2008, pp. 142-149.
[15]	L. Polkowski and P. Osmialowski, “Navigation for Mobile Autonomous Robots and their Formations: An Application of Spatial Reasoning Induced from Rough Mere- ological Geometry,” In: A Barrera, Ed., Mobile Robots Navigation, InTech, Zagreb, 2010, pp. 329-354. doi:10.5772/8987
[16]	J. Van Benthem, “The Logic of Time,” Reidel, Dordrecht, 1983.
[17]	H. Choset, K. M. Lynch, S. Hutchinson, G. Kantor, W. Burgard, L. E. Kavraki and S. Thrun, “Principles of Robot Motion. Theory, Algorithms and Implementations,” MIT Press, Cambridge, 2005.
[18]	P. Osmialowski, “On Path Planning for Mobile Robots: Introducing the Mereological Potential Field Method in the Framework of Mereological Spatial Reasoning,” Journal of Automation, Mobile Robotics and Intelligent Systems (JAMRIS), Vol. 3, No. 2, 2009, pp. 24-33.
[19]	P. Osmialowski, “Planning and Navigation for Mobile Autonomous Robots,” PJIIT Publishers, Warszawa, 2011.
[20]	P. Osmialowski and L. Polkowski, “Spatial Reasoning Based on Rough Mereology: Path Planning Problem for Autonomous Mobile Robots,” Transactions on Rough Sets, Vol. 12, Lecture Notes in Computer Science, Vol. 6190, Springer Verlag, Berlin, 2009, pp. 143-169.
[21]	R. Michalski, “Pattern Recognition as Rule-Guided Inductive Inference,” IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI, Vol. 2, No. 4, 1990, pp. 349-361. doi:10.1109/TPAMI.1980.4767034
[22]	L. Polkowski, “Formal Granular Calculi Based on Rough Inclusions (a Feature Talk),” Proceedings of IEEE 2005 Conference on Granular Computing GrC05, Beijing, 2005, pp. 57-62.
[23]	L. Polkowski, “A Model of Granular Computing with Applications (a Feature Talk),” Proceedings of IEEE 2006 Conference on Granular Computing GrC06, Atlanta, 2006, pp. 9-16.
[24]	J. W. Grzymala-Busse, “Mining Numerical Data—A Rough Set Approach,” Transactions on Rough Sets, Vol. 11, Lecture Notes in Computer Science, Vol. 5946, Springer Verlag, Berlin, 2010, pp. 1-14.
[25]	J. G. Bazan, “A Comparison of Dynamic and Non-Dynamic Rough Set Methods for Extracting Laws from Decision Tables,” In: L. Polkowski and A. Skowron, Eds., Rough Sets in Knowledge Discovery, Vol. 1, Physica Ver- lag, Heidelberg, 1998, pp. 321-365.
[26]	N. S. Hoa, “Regularity Analysis and Its Applications in Data Mining,” In: L. Polkowski, S. Tsumoto and T. Y. Lin, Eds., Rough Set Methods and Applications. New Developments in Knowledge Discovery in Information Systems, Physica Verlag, Heidelberg, 2000, pp. 289-378.
[27]	J. Wroblewski, “Adaptive Aspects of Combining Approximation Spaces,” In: S. K. Pal, L. Polkowski and A. Skowron, Eds., Rough Neural Computing. Techniques for Computing with Words, Springer Verlag, Berlin, 2004, pp. 139-156. doi:10.1007/978-3-642-18859-6_6
[28]	“Rough Set Exploration System (RSES),” http://logic.mimuw.edu.pl/~rses/
[29]	P. Artiemjew, “A Review of the Knowledge Granulation Methods: Discrete vs. Continuous Algorithms,” In: A. Skowron and Z. Suraj, Eds., Rough Sets and Intelligent Systems— Professor Zdzislaw Pawlak in Memoriam, Springer Verlag, Berlin, 2012, pp. 41-59.
[30]	L. Polkowski and P. Artiemjew, “A Study in Granular Computing: On Classifiers Induced from Granular Reflections of Data,” Transactions on Rough Sets, Vol. 9, Lecture Notes in Computer Science, Vol. 5390, Springer Verlag, Berlin, 2009, pp. 230-263. doi:10.1007/978-3-540-89876-4_14
[31]	L. Polkowski and P. Artiemjew, “On Classifying Mappings Induced by Granular Structures,” Transactions on Rough Sets, Vol. 9, Lecture Notes in Computer Science, Vol. 5390, Springer Verlag, Berlin, 2009, pp. 264-286.
[32]	L. Polkowski and P. Artiemjew, “On Knowledge Granulation and Applications to Classifier Induction in the Framework of Rough Mereology,” International Journal of Computational intelligence Systems (IJCIS), Vol. 2-4, 2009, pp. 315-331. doi:10.2991/ijcis.2009.2.4.1
[33]	J. W. Grzymala-Busse and Ming Hu, “A Comparison of Several Approaches to Missing Attribute Values in Data Mining,” Lecture Notes in Artificial Intelligence, Vol. 2005, Springer Verlag, Berlin, 2000, pp. 378-385.
[34]	L. Polkowski and P. Artiemjew, “On Granular Rough Computing with Missing Values,” Lecture Notes in Artificial Intelligence, Vol. 4585, Springer Verlag, Berlin, 2007, pp. 271-279.
[35]	P. Artiemjew, “Classifiers from Granulated Data Sets: Concept Dependent and Layered Granulation,” Proceedings RSKD’07 Rough Sets and Knowledge Discovery. Workshop at ECML/PKDD’07, Warsaw University Press, 2007, pp. 1-9.