Abstract
This paper introduces a framework for flow graphs induced by perceptual systems as well as analysis of such graphs using near set theory. A distinctive feature of such graphs are layers; therefore we shall generally call them flow graphs with layers. In a specific context of perceptual systems, these graphs will referred be to as perceptual flow graphs. A method for determining nearness of flow graphs with layers (perceptual graphs) is given in terms of a practical application to digital image analysis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Pawlak, Z.: Decision algorithms, Bayes’ Theorem, and flow graphs. Working paper, Warsaw (2002)
Pawlak Z.: Decision algorithms and flow graphs: a rough set approach. J. Telecom. Inform. Tech. 3, 98–101 (2003)
Greco S., Pawlak Z., Slowinski R.: Generalized Decision Algorithms, Rough Inference Rules, and Flow Graphs, LNAI, vol. 2475, pp. 93–104. Berlin, Springer (2002)
Pawlak, Z.: Probability, truth and flow graphs. Proc. RS in KD and SC, pp. 1–9 (2003)
Pawlak, Z.: Rough sets and flow graphs. In: Lecture Notes in Computer Science, vol. 3641, pp. 1–11. Berlin, Springer (2005)
Pawlak Z.: Flow graphs and data mining. Trans. Rough Sets III, 1–36 (2005)
Pawlak, Z.: Decision trees and flow graphs. In: Lecture Notes in Computer Science, vol. 4259, pp. 1–11. Berlin, Springer (2006)
Butz, C., Yan, W., Yang, B.: An efficient algorithm for inference in rough set flow graphs. In: Peters, J.F., Skowron A. (eds.) Transactions on Rough Sets, LNAI 4100, pp. 102—122. Berlin, Springer (2006)
Sun, J., Liu, H., Zhang, H.: An extension of Pawlak’s flow graphs. In: Wang, G., Peters, J.F., Skowron, A., Yao, Y. (eds.) Rough Sets and Knowledge Technology, pp. 191–199. Berlin, Springer (2006)
Kostek, B., Czyzewski, A.: A processing of musical metadata employing Pawlak’s flow graphs. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets, LNAI 3100, pp. 279–298, Berlin, Springer (2004)
Chitcharoen, D.: Mathematical aspects of flow graph approaches to data analysis. PhD thesis, Department of Applied Mathematics, King Mongkut Institute of Technology, Ladkrabang (2010)
Peters J.: Near sets, general theory about nearness of objects. Appl. Math. Sci. 1(53), 2609–2629 (2007)
Peters J.F., Naimpally S.: Applications of near sets. Am. Math. Soc. Notices 59(4), 536–542 (2012)
Wolski M.: Perception and classification. A Note on Near sets and Rough sets. Fund. Inform. 101, 143–155 (2010)
Wolski M.: Granular computing: topological and categorical aspects of near and rough set approaches to granulation of knowledge. Trans. Rough Sets 7736, 37–53 (2013)
Henry, C.J., Ramanna, S.: Signature-based perceptual nearness. Application of near sets to image retrieval. Math. Comput. Sci. (2013) (to appear)
Peters J., Wasilewski P.: Foundations of Near Sets. Inf. Sci. 179(18), 3091–3109 (2009)
Naimpally S., Peters J.: Topology with Applications, Topological structures via near and far. World Scientific, Singapore (2013)
Peters, J.F., Chitcharoen, D.: Sufficiently near neighbourhoods of points in flow graphs. A Near Set Approach. Fundamenta Informaticae, to appear (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ramanna, S., Chitcharoen, D. Flow Graphs: Analysis with Near Sets. Math.Comput.Sci. 7, 11–29 (2013). https://doi.org/10.1007/s11786-013-0144-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11786-013-0144-y