Summary
This chapter considers how one might utilize fuzzy sets, near sets, and rough sets, taken separately or taken together in hybridizations as part of a computational intelligence toolbox. These technologies offer set theoretic approaches to solving many types of problems where the discovery of similar perceptual granules and clusters of perceptual objects is important. Perceptual information systems (or, more concisely, perceptual systems) provide stepping stones leading to nearness relations and properties of near sets. This work has been motivated by an interest in finding a solution to the problem of discovering perceptual granules that are, in some sense, near each other. Fuzzy sets result from the introduction of a membership function that generalizes the traditional characteristic function. Near set theory provides a formal basis for observation, comparison and classification of perceptual granules. Near sets result from the introduction of a description-based approach to perceptual objects and a generalization of the traditional rough set approach to granulation that is independent of the notion of the boundary of a set approximation. Near set theory has strength by virtue of the strength it gains from rough set theory, starting with extensions of the traditional indiscernibility relation. This chapter has been written to establish a context for three forms of sets that are now part of the computational intelligence umbrella. By way of introduction to near sets, this chapter considers various nearness relations that define partitions of sets of perceptual objects that are near each other. Every perceptual granule is represented by a set of perceptual objects that have their origin in the physical world. Objects that have the same appearance are considered perceptually near each other, i.e., objects with matching descriptions. Pixels, pixel windows, and segmentations of digital images are given by way of illustration of sample near sets. This chapter also briefly considers fuzzy near sets and near fuzzy sets as well as rough sets that are near sets.The main contribution of this chapter is the introduction of a formal foundation for near sets considered in the context of fuzzy sets and rough sets.
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References
Grimaldi, D., Engel, M.: Evolution of the Insects. Cambridge University Press, Cambridge (2005)
Gupta, S., Patnaik, K.: Enhancing performance of face recognition system by using near set approach for selecting facial features. Journal of Theoretical and Applied Information Technology 4(5), 433–441 (2008), http://www.jatit.org/volumes/fourth_volume_5_2008.php
Hassanien, A., Abraham, A., Peters, J., Schaefer, G.: Rough sets and near sets in medical imaging: A review. IEEE Trans. on Information Technology in Biomedicine (submitted) (2008)
Henry, C., Peters, J.: Image pattern recognition using approximation spaces and near sets. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 475–482. Springer, Heidelberg (2007)
Henry, C., Peters, J.: Near set image segmentation quality index. In: GEOBIA 2008 Pixels, Objects, Intelligence. GEOgraphic Object Based Image Analysis for the 21st Century, pp. 284–289. University of Calgary, Alberta (2008), http://www.ucalgary.ca/geobia/Publishing
Henry, C., Peters, J.: Perception based image classification. IEEE Transactions on Systems, Man, and Cybernetics–Part C: Applications and Reviews (submitted) (2008)
Iturralde-Vinent, M., MacPhee, R.: Age and paleogeographical origin of dominican amber. Science 273, 1850–1852 (1996)
Jähne, B.: Digital Image Processing, 6th edn. Springer, Heidelberg (2005)
Murray, J., Bradley, H., Craigie, W., Onions, C.: The Oxford English Dictionary. Oxford University Press, Oxford (1933)
Orłowska, E. (ed.): Incomplete Information: Rough Set Analysis. Studies in Fuzziness and Soft Computing, vol. 13. Physica-Verlag, Heidelberg (1998)
Orłowska, E., Pawlak, Z.: Representation of nondeterministic information. Theoretical Computer Science 29, 27–39 (1984)
Pavel, M.: Fundamentals of Pattern Recognition, 2nd edn. Marcel Dekker, Inc., N.Y. (1993)
Pawlak, Z.: Classification of objects by means of attributes. Polish Academy of Sciences 429 (1981)
Pawlak, Z., Peters, J.: Jak blisko. Systemy Wspomagania Decyzji I, 57 (2007)
Pawlak, Z., Skowron, A.: Rough sets and boolean reasoning. Information Sciences 177, 41–73 (2007)
Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177, 28–40 (2007)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177, 3–27 (2007)
Pedrycz, W., Gomide, F.: An Introduction to Fuzzy Sets. Analysis and Design. MIT Press, Cambridge (1998)
Peters, J.: Classification of objects by means of features. In: Proc. IEEE Symposium Series on Foundations of Computational Intelligence (IEEE SCCI 2007), Honolulu, Hawaii, pp. 1–8 (2007)
Peters, J.: Near sets. General theory about nearness of objects. Applied Mathematical Sciences 1(53), 2029–2609 (2007)
Peters, J.: Near sets, special theory about nearness of objects. Fundamenta Informaticae 75(1-4), 407–433 (2007)
Peters, J.: Near sets. toward approximation space-based object recognition. In: Yao, J., Lingras, P., Wu, W.-Z., Szczuka, M.S., Cercone, N.J., Ślȩzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 22–33. Springer, Heidelberg (2007)
Peters, J.: Classification of perceptual objects by means of features. Int. J. of Info. Technology & Intelligent Computing 3(2), 1–35 (2008)
Peters, J.: Discovery of perceputally near information granules. In: Yao, J. (ed.) Novel Developments in Granular Computing: Applications of Advanced Human Reasoning and Soft Computation. Information Science Reference, Hersey, N.Y., U.S.A. (to appear) (2008)
Peters, J., Ramanna, S.S.: Feature selection: A near set approach. In: ECML & PKDD Workshop on Mining Complex Data, Warsaw (2007)
Peters, J., Shahfar, S., Ramanna, S., Szturm, T.: Biologically-inspired adaptive learning: A near set approach. In: Frontiers in the Convergence of Bioscience and Information Technologies, Korea (2007)
Peters, J., Skowron, A.: Zdzisław pawlak: Life and work. Transactions on Rough Sets V, 1–24 (2006)
Peters, J., Skowron, A., Stepaniuk, J.: Nearness in approximation spaces. In: Proc. Concurrency, Specification and Programming (CS&P 2006), Humboldt Universität, pp. 435–445 (2006)
Peters, J., Skowron, A., Stepaniuk, J.: Nearness of objects: Extension of approximation space model. Fundamenta Informaticae 79(3-4), 497–512 (2007)
Peters, J., Wasilewski, P.: Foundations of near sets. Information Sciences (submitted) (2008)
Polkowski, L.: Rough Sets. Mathematical Foundations. Springer, Heidelberg (2002)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)
Zadeh, L.: Fuzzy sets. Information and Control 8, 338–353 (1965)
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Peters, J.F. (2009). Fuzzy Sets, Near Sets, and Rough Sets for Your Computational Intelligence Toolbox. In: Hassanien, AE., Abraham, A., Herrera, F. (eds) Foundations of Computational Intelligence Volume 2. Studies in Computational Intelligence, vol 202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01533-5_1
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