Abstract
Reducing the size of the concept lattices is a fundamental problem in formal concept analysis. This paper presents several properties of useful fuzzy-attributes, in the general case of multi-adjoint concept lattices. Moreover, the use of these fuzzy-attributes provides a mechanism to reduce the size of concept lattices considering a subset of the original one and, therefore, without losing and modifying important information.
Partially supported by the Spanish Science Ministry projects TIN2009-14562-C05-03 and TIN2012-39353-C04-04, and by Junta de Andalucía project P09-FQM-5233.
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References
Bělohlávek, R., Vychodil, V.: Reducing the size of fuzzy concept lattices by hedges. In: The 2005 IEEE International Conference on Fuzzy Systems, pp. 663–668 (2005)
Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematical Society, Providence (1967)
Cornejo, M., Medina, J., Ramírez, E.: A comparative study of adjoint triples. Fuzzy Sets and Systems 211, 1–14 (2013)
Cornejo, M., Medina, J., Ramírez, E.: Irreducible elements in multi-adjoint concept lattices. In: Intl Conference on Fuzzy Logic and Technology, EUSFLAT 2013, pp. 125–131 (2013)
Cornejo, M.E., Medina-Moreno, J., Ramírez, E.: On the classification of fuzzy-attributes in multi-adjoint concept lattices. In: Rojas, I., Joya, G., Cabestany, J. (eds.) IWANN 2013, Part II. LNCS, vol. 7903, pp. 266–277. Springer, Heidelberg (2013)
Hájek, P.: Metamathematics of Fuzzy Logic. Trends in Logic. Kluwer Academic (1998)
Kang, X., Li, D., Wang, S., Qu, K.: Formal concept analysis based on fuzzy granularity base for different granulations. Fuzzy Sets and Systems 203, 33–48 (2012)
Konecny, J.: Isotone fuzzy galois connections with hedges. Information Sciences 181(10), 1804–1817 (2011)
Konecny, J., Medina, J., Ojeda-Aciego, M.: Intensifying hedges and the size of multi-adjoint concept lattices with heterogeneous conjunctors. In: The 9th International Conference on Concept Lattices and Their Applications, pp. 245–256 (2012)
Konecny, J., Medina, J., Ojeda-Aciego, M.: Multi-adjoint concept lattices with heterogeneous conjunctors and hedges. In: Annals of Mathematics and Artificial Intelligence, pp. 1–17 (2014)
Li, L., Zhang, J.: Attribute reduction in fuzzy concept lattices based on the t-implication. Knowledge-Based Systems 23(6), 497–503 (2010)
Medina, J., Ojeda-Aciego, M.: Multi-adjoint t-concept lattices. Information Sciences 180(5), 712–725 (2010)
Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Formal concept analysis via multi-adjoint concept lattices. Fuzzy Sets and Systems 160(2), 130–144 (2009)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel (1982)
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Cornejo Piñero, M.E., Medina-Moreno, J., Ramírez-Poussa, E. (2014). Fuzzy-Attributes and a Method to Reduce Concept Lattices. In: Cornelis, C., Kryszkiewicz, M., Ślȩzak, D., Ruiz, E.M., Bello, R., Shang, L. (eds) Rough Sets and Current Trends in Computing. RSCTC 2014. Lecture Notes in Computer Science(), vol 8536. Springer, Cham. https://doi.org/10.1007/978-3-319-08644-6_20
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DOI: https://doi.org/10.1007/978-3-319-08644-6_20
Publisher Name: Springer, Cham
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