Sufficiently Near Neighbourhoods of Points in Flow Graphs. A Near Set Approach

• Autorzy: Peters J.F. , Chitcharoen D.
• Języki publikacji: EN

Abstrakty

EN

This paper introduces sufficiently near visual neighbourhoods of points and neighbourhoods of sets in digital image flow graphs (NDIFGs). An NDIFG is an extension of a Pawlak flow graph. The study of sufficiently near neighbourhoods in NDIFGs stems from recent work on near sets and topological spaces via near and far, especially in terms of visual neighbourhoods of points that are sufficiently near each other. From a topological perspective, non-spatially near sets represent an extension of proximity space theory and the original insight concerning spatially near sets by F. Riesz at the International Congress of Mathematicians (ICM) in 1908. In the context of Herrlich nearness, sufficiently near neighbourhoods of sets in NDIFGs provide a new perspective on topological structures in NDIFGs. The practical implications of this work are significant. With the advent of a study of the nearness of open as well as closed neighbourhods of points and of sets in NDIFGs, it is now possible to do information mining on a more global level and achieve new insights concerning the visual information embodied in the images that provide input to an NDIFG.

Słowa kluczowe

EN

digital image; near sets; Pawlak flow graphs; sufficiently near; topological structure; visual neighbourhood

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2013
• Tom: Vol. 124, nr 1/2
• Strony: 175--196
• Opis fizyczny: Bibliogr. 15 poz., wykr.

Twórcy

autor

Peters J.F.

• Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 51-V6, Canada and School of Mathematics, University of Hyderabad, Hyderabad-500046, India

autor

Chitcharoen D.

• Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 51-V6, Canada

Bibliografia

• [1] Chitcharoen, D.: Mathematical Aspects Of Flow Graph Approaches to Data Analysis, Ph.D. Thesis, Department of Applied Mathematics, King Mongkut Institute of Technology, Ladkrabang, 2010.
• [2] Greco, S., Pawlak, Z., Slowinski, R.: Generalized decision algorithms, rough inference rules, and flow graphs, LNAI, vol 2475, Springer, Berlin, 2002, 93-104.
• [3] Naimpally, S., Peters, J.: Topology with Applications. Topological structures via near and far, World Scientific, Singapore, 2012,to appear.
• [4] Pawlak, Z.: Rough sets, decision algorithms and Bayes’ theorem, Eur. J. Oper. Res., 136, 2002, 181-189.
• [5] Pawlak, Z.: Decision algorithms and flow graphs: A rough set approach, J. Telecom. and Inform. Tech, 3, 2003,98-101.
• [6] Pawlak, Z.: Probability, truth and flow graphs, Proc. RS in KD and SC, 2003, 1-9.
• [7] Pawlak, Z.: Flow graphs and data mining, Trans. on Rough Sets, III, 2005, 1-36.
• [8] Pawlak, Z.: Rough sets and flow graphs, Lect. Notes Artif. Intell. 3641, Springer, Berlin, 2005,1-11.
• [9] Pawlak, Z.: Decision trees and flow graphs, Lect. Notes Artif. Intell. 4259, Springer, Berlin, 2006,1-11.
• [10] Peters, J.: Near sets. General theory about nearness of objects, Applied Math. Sci., 1(53), 2007, 2609-2629.
• [11] Peters, J.: Near Sets. Special Theory about Nearness of Objects, Fundam. Inf., 75(1-4), 2007, 407-433, ISSN 0169-2968.
• [12] Peters, J.: Sufficiently Near Sets of Neighbourhoods, Lect. Notes Com. Scince. 6954, Springer, Berlin, 2011, 17-24.
• [13] Peters, J., Naimpally, S.: Applications of near sets, Amer. Math. Soc. Notices, 2012, , to appear.
• [14] Peters, J., Wasilewski, P.: Foundations of near sets, Inf. Sci., 179(18), 2009, 3091-3109.
• [15] Peters, J. F., Tiwari, S.: Completing extended metric spaces: An alternative approach, Applied Math. Let., 2011, in press.