Abstract
Rough set theory and fuzzy logic are mathematical frameworks for granular computing forming a theoretical basis for the treatment of uncertainty in many real-world problems, including image and video analysis. The focus of rough set theory is on the ambiguity caused by limited discernibility of objects in the domain of discourse; granules are formed as objects and are drawn together by the limited discernibility among them. On the other hand, membership functions of fuzzy sets enables efficient handling of overlapping classes. The hybrid notion of rough fuzzy sets comes from the combination of these two models of uncertainty and helps to exploit, at the same time, properties like coarseness, by invoking rough sets, and vagueness, by considering fuzzy sets. We describe a model of the hybridization of rough and fuzzy sets, that allows for further refinements of rough fuzzy sets. This model offers viable and effective solutions to some problems in image analysis, e.g. image compression.
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References
Sen, D., Pal, S.K.: Generalized Rough Sets, Entropy, and Image Ambiguity Measures. IEEE Trans. on Syst. Man and Cybern. 39, 117–128 (2009)
Caianiello, E.R.: A calculus of hierarchical systems. In: Proc. Internat. Conf. on Pattern Recognition, pp. 1–5 (1973)
Caianiello, E.R., Petrosino, A.: Neural networks, fuzziness and image processing. In: Cantoni, V. (ed.) Machine and Human Perception: Analogies and Divergencies, Plenum Press, NewYork (1994)
Caianiello, E.R., Ventre, A.: A model for C-calculus. International Journal of General Systems 11, 153–161 (1985)
Yao, Y.Y.: Information granulation and rough set approximation. International Journal of Intelligent Systems 16, 87–104 (2001)
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Sys. 17, 191–209 (1990)
Li, Y., Qiao, B.: Hierarchical Reduction Algorithm of Rough Sets. In: Sixth International Conference on Intelligent Systems Design and Applications, vol. 1, pp. 497–502 (2006)
Qian, Y., Liang, J., Yao, Y., Dang, C.: MGRS: A multi-granulation rough set. Information Sciences 180, 949–970 (2010)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Granularity of knowledge, indiscernibility and rough sets. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp. 106–110 (1998)
Petrosino, A., Salvi, G.: Rough fuzzy set based scale space transforms and their use in image analysis. International Journal of Approximate Reasoning 41, 212–228 (2006)
Petrosino, A., Ferone, A.: Rough fuzzy set-based image compression. Fuzzy Sets and Systems 160, 1485–1506 (2009)
Zadeh, L.: Fuzzy sets. Information and Control, pp. 338–353 (1964)
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Petrosino, A., Ferone, A. (2011). Feature Discovery through Hierarchies of Rough Fuzzy Sets. In: Pedrycz, W., Chen, SM. (eds) Granular Computing and Intelligent Systems. Intelligent Systems Reference Library, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19820-5_4
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DOI: https://doi.org/10.1007/978-3-642-19820-5_4
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