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This paper considers the nearness of sets in local descriptive admissible covers of nonempty sets and the problem of quantifying the nearness of such sets. A brief review of descriptive Efremovič spaces as well descriptive intersection and union provides a foundation for the study of descriptive admissible covers. Descriptively near sets in admissible covers contain sequences of points with members having similar descriptions. The motivation for this approach stems from the need to consider fine-grained neighbourhoods of points in admissible covers that facilitate highly accurate measures of nearness of tiny parts of sets of objects of interest. A practical application of local admissible covers is given in terms of micropalaeontology and the detection of minute similarities and differences in microfossils, useful in the study of climate change, mineral and fossil fuel exploration.
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Czasopismo
Rocznik
Tom
Strony
433--444
Opis fizyczny
Bibliogr. 31 poz., fot.
Twórcy
autor
- Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, Univ. of Manitoba, E1-526, 75A Chancellor's Circle, Winnipeg, MB R3T 5V6, Canada
Bibliografia
- [1] Armstrong, H., Brasier, M.: Microfossils, 2nd Ed., Blackwell Publishing, Malden, MA, U.S.A., 2005.
- [2] Collins, P., Roscoe, A.: Criteria for metrisability, Proc. Amer. Math. Soc., 90(4), 1984, 631-640.
- [3] Di Concilio, A.: Proximity: A powerful tool in extension theory, functions spaces, hyperspaces, boolean algebras and point-free geometry, in: Beyond Topology, AMS Contemporary Mathematics 486 (F. Mynard, E. Pearl, Eds.), Amer. Math. Soc., 2009, 89-114.
- [4] Efremovic, V: The geometry of proximity I, Mat. Sb., 31, 1951, 189-200 (in Russian), MR 14, 1106.
- [5] Ellison, S.: Microfossils as environment indicators in marine shales, J Sedimentary Petrology, 21(4), 1951, 214-225.
- [6] Fashandi, H.: Topological Framework for Digital Image Analysis with Extended Interior and Closure Operators, Ph.D. Thesis, Winnipeg, Manitoba, 2012, Supervisor: J.F. Peters.
- [7] Fashandi, H.: Nearness of covering uniformities: Theory and application in image analysis, Math. in Comp. Sci., 7(1), 2013,43-50.
- [8] Fashandi, H., Peters, J.: A fuzzy topological framework for classifying image databases, Int. J. of Intelligent Systems, 26(7), 2011, 621-635, DOI: 10.1002/int.20479.
- [9] Hassanien, A., Abraham, A., Peters, J., Schaefer, G., Henry, C.: Rough sets and near sets in medical imaging: A review, IEEE Trans. Info. Tech. in Biomedicine, 13(6), 2009, 955-968, Digital object identifier: 10.1109/TITB.2009.2017017.
- [10] Henry, C.: Near Sets: Theory and Application, Ph.D. Thesis, Manitoba, Canada, 2010, Supervisor: J.F. Peters.
- [11] Henry, C., Peters, J.: Image Pattern Recognition Using Approximation Spaces and Near Sets, Proc. 11thInt. Conf. on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2007), Joint Rough Set Symposium (JRS 2007), Lecture Notes in Artificial Intelligence 4482, Heidelberg, Germany, 2007, 475-482.
- [12] Henry, C., Peters, J.: Near set image in an objective image segmentation evaluation framework, GEOBIA 2008 Pixels, Objects, Intelligence. GEOgraphic Object Based Image Analysis for the 21st Century, University of Calgary, Alberta, 2008, 1-6.
- [13] Henry, C., Peters, J. F.: Near Set Evaluation and Recognition (NEAR) System, Technical report, Computational Intelligence Laboratory, University of Manitoba, 2009, UM CI Laboratory Technical Report No. TR-2009-015.
- [14] Jones, D.: Displacement of microfossils, J Sedimentary Petrology, 28(4), 1958, 453-467.
- [15] Katetov, M.: On continuity structures and spaces of mappings, Comment. Math. Univ. Carolinae, 6, 1965, 257-278.
- [16] Meghdadi, A.: Fuzzy Tolerance Neighbourhood Approach to Image Similarity in Content-Based Image Retrieval, Ph.D. Thesis, Winnipeg, Manitoba, 2012, Supervisor: J.F. Peters.
- [17] Naimpally, S.: Proximity Spaces, Cambridge University Press, Cambridge, UK, 1970, X+128 pp., ISBN 978-0-521-09183-1.
- [18] Naimpally, S.: Proximity approach to problems in topology and analysis, Oldenbourg Verlag, Munich, Germany, 2009, 73 pp., ISBN 978-3-486-58917-7.
- [19] Naimpally, S., Peters, J.: Topology with Applications. Topological Spaces Via Near and Far, World Scientific, Singapore, 2013, xv + 277pp, ISBN: 978-981-4407-65-6.
- [20] Niemytzki, V: On the third axiom of metric spaces, Trans. Amer. Math. Soc., 29(3), 1927, 507-513.
- [21] Peters, J.: Sufficiently near sets of neighbourhoods, Lecture Notes in Artificial Intelligence, 6954, 2011, 17-24.
- [22] Peters, J.: e-near collections, Lecture Notes in Artificial Intelligence, 6954, 2011,533-544.
- [23] Peters, J.: How near are Zdzisław Pawlak’s paintings? Study of merotopic distances between digital picture regions-of-interest, in: Rough Sets and Intelligent Systems (A. Skowron, Z. Suraj, Eds.), Springer, 2012, 89-114.
- [24] Peters, J.: Local near sets. Pattern discovery in proximity spaces, Math. Comp. Sci., 7(1), 2013, 87-106, doi 10.1007/s11786-013-0143-z.
- [25] Peters, J., Naimpally, S.: Applications of near sets, Notices of the Amer. Math. Soc., 59(4), 2012, 536-542.
- [26] Peters, J., Ramanna, S.: Pattern discovery with local near sets, Proc. Jornadas Chilenas de Computacion 2012 workshop on pattern recognition (R. Alarcon, P. Barcelo, Eds.), The Chilean Computing Society, Valparaiso, 2012, 1-4.
- [27] Peters, J., Tiwari, S.: Approach merotopies and near filters. Theory and application, Gen. Math. Notes, 2(2), 2011,1-15.
- [28] Peters, J., Tiwari, S.: Completing extended metric spaces: An alternative approach, Applied Math. Letters, 25(10), 2012, 1544-1547, Doi:10.1016/j.aml.2012.01.012.
- [29] Thron, W.: Topological Spaces, Holt, Rinehart and Winston, NY, 1966, Xi + 240pp.
- [30] Tiwari, S.: Some Aspects of General Topology and Applications. Approach Merotopic Structures and Applications, Ph.D. Thesis, Allahabad, U.P., India, 2010, Supervisor: M. Khare.
- [31] Wilson, W.: On semi-metric spaces, Amer. J. Math., 53, 1933, 361-373.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d3d55d8f-a8a5-45dc-9b7d-631fa16653ca