Abstract
Formal Concept Analysis (FCA) as inherently relational can be formalized and generalized by using categorical constructions. This provides a categorical view of the relation between “object” and “attributes”, which can be further extended to a more generalized view on relations as morphisms in Kleisli categories of suitable monads. Structure of sets of “objects” and “attributes” can be provided e.g. by term monads over particular signatures, and specific signatures drawn from and developed within social and health care can be used to illuminate the use of the categorical approach.
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References
Díaz, J., Medina, J., Ojeda-Aciego, M.: On basic conditions to generate multi-adjoint concept lattices via Galois connections. Intl Journal of General Systems 43(2), 149–161 (2014)
Eklund, P., Gähler, W.: Fuzzy filter functors and convergence. In: Rodabaugh, S.E., Klement, E.P., Höhle, U. (eds.) Applications of Category Theory to Fuzzy Subsets, pp. 109–136. Kluwer Academic Publishers (1992)
Eklund, P., Galán, M.Á.: Monads can be rough. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 77–84. Springer, Heidelberg (2006)
Eklund, P., Galán, M., Helgesson, R., Kortelainen, J.: Fuzzy terms. Fuzzy Sets and Systems (in press)
Eklund, P., Galán, M.Á., Helgesson, R., Kortelainen, J., Moreno, G., Vázquez, C.: Towards categorical fuzzy logic programming. In: Masulli, F. (ed.) WILF 2013. LNCS, vol. 8256, pp. 109–121. Springer, Heidelberg (2013)
Eklund, P., Höhle, U., Kortelainen, J.: The fundamentals of lative logic. In: LINZ 2014, 35th Linz Seminar on Fuzzy Set Theory (abstract) (2014)
Gähler, W.: General topology – the monadic case, examples, applications. Acta Math. Hungar. 88, 279–290 (2000)
Galán, M.: Categorical Unification. PhD thesis, Umeå University, Department of Computing Science (2004)
Konečný, J., Medina, J., Ojeda-Aciego, M.: Multi-adjoint concept lattices with heterogeneous conjunctors and hedges. Annals of Mathematics and Artificial Intelligence (accepted, 2014)
Krídlo, O., Ojeda-Aciego, M.: Linking L-Chu correspondences and completely lattice L-ordered sets. Annals of Mathematics and Artificial Intelligence (accepted, 2014)
Mac Lane, S.: Categories for the Working Mathematician. Graduate Texts in Mathematics. Springer (September 1998)
Madrid, N., Medina, J., Moreno, J., Ojeda-Aciego, M.: New links between mathematical morphology and fuzzy property-oriented concept lattices. In: IEEE Intl Conf. on Fuzzy Systems, FUZZ-IEEE 2014 (accepted, 2014)
Medina, J.: Multi-adjoint property-oriented and object-oriented concept lattices. Information Sciences 190, 95–106 (2012)
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. NATO Advanced Study Institutes Series, vol. 83, pp. 445–470. Springer, Heidelberg (1982)
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Eklund, P., Galán García, M.Á., Kortelainen, J., Ojeda-Aciego, M. (2014). Monadic Formal Concept Analysis. 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_21
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DOI: https://doi.org/10.1007/978-3-319-08644-6_21
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