Abstract
Fuzzy property-oriented concept lattices are a formal tool for modeling and processing incomplete information in information systems. This paper relates this theory to fuzzy mathematical morphology, which scope, for instance, is to process and analyze images and signals. Consequently, the theory developed in the concept lattice framework can be used in these particular settings.
Partially supported by Spanish Ministry of Science and FEDER funds through project TIN09-14562-C05-03 and Junta de Andalucía project P09-FQM-5233.
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References
Alcalde, C., Burusco, A., Fuentes-González, R.: An interpretation of the L-Fuzzy Concept Analysis as a tool for the Morphological Image and Signal Processing. In: Proc. of CLA 2012, Fuengirola, Málaga, pp. 81–92 (2012)
De Baets, B.: Fuzzy morphology: a logical approach. In: Ayyub, B., Gupta, M. (eds.) Uncertainty Analysis, Engineering and Science: Fuzzy Logic, Statistics and neural network Approach, pp. 53–67. Kluwer Academic Publishers (1997)
Bartl, E., Bělohlávek, R., Konecny, J., Vychodil, V.: Isotone galois connections and concept lattices with hedges. 4th International IEEE Conference “Intelligent Systems”, 15.24–15.28 (2008)
Bělohlávek, R.: Concept lattices and order in fuzzy logic. Annals of Pure and Applied Logic 128, 277–298 (2004)
Bloch, I., Maître, H.: Fuzzy Mathematical Morphologies: a comparative study. Télécom Paris 94D001 (1994)
Bloch, I.: Duality vs. adjunction for fuzzy mathematical morphology and general form of fuzzy erosions and dilations. Fuzzy Sets and Systems 160, 1858–1867 (2009)
Burillo, P., Fuentes-González, R., Frago, N.: Inclusion grade and fuzzy implication operators. Fuzzy Sets and Systems 114, 417–429 (2000)
Burillo, P., Frago, N., Fuentes-González, R.: Generation of Fuzzy Mathematical Morphologies. Mathware & Soft Computing VIII (1), 31–46 (2001)
Georgescu, G., Popescu, A.: Non-dual fuzzy connections. Arch. Math. Log. 43(8), 1009–1039 (2004)
Goutsias, J., Heijmans, H.J.A.M.: Fundamenta Morphologicae Mathematicae. Fundamenta Informaticae 41, 1–31 (2000)
Heijmans, H.J.A.M.: Morphological Image Operators. Academic Press Inc. (1994)
Lai, H., Zhang, D.: Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory. International Journal of Approximate Reasoning 50(5), 695–707 (2009)
Maragos, P.: Lattice Image Precessing: A Unification of Morphological and Fuzzy Algebric Systems. Journal of Mathematical Imaging and Vision 22, 333–353 (2005)
Mas, M., Monserrat, M., Torrens, J.: S-implications and R-implications on a finite chain. Kybernetika 40(1), 3–20 (2004)
Matheron, G.: Random Sets and Integral Geometry. Wiley, New York (1975)
Serra, J.: Image Analysis and Mathematical Morphology. Academic Press I (fourth printing 1990) and II (second printing 1992)
Soille, P.: Morphological Image Analysis, 2nd edn. Springer (2004)
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Alcalde, C., Burusco, A., Díaz, J.C., Fuentes-González, R., Medina-Moreno, J. (2013). Fuzzy Property-Oriented Concept Lattices in Morphological Image and Signal Processing. In: Rojas, I., Joya, G., Cabestany, J. (eds) Advances in Computational Intelligence. IWANN 2013. Lecture Notes in Computer Science, vol 7903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38682-4_28
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DOI: https://doi.org/10.1007/978-3-642-38682-4_28
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