Abstract
Given a mapping f : A → B from a partially ordered set A into an unstructured set B, we study the problem of defining a suitable partial ordering relation on B such that there exists a mapping g : B → A such that the pair of mappings (f,g) forms an isotone Galois connection between partially ordered sets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Antoni, L., Krajči, S., Krídlo, O., Macek, B., Pisková, L.: On heterogeneous formal contexts. Fuzzy Sets and Systems 234, 22–33 (2014)
Bělohlávek, R.: Fuzzy Galois connections. Math. Logic Q. 45(4), 497–504 (1999)
Bělohlávek, R., Konečný, J.: Concept lattices of isotone vs. antitone Galois connections in graded setting: Mutual reducibility revisited. Information Sciences 199, 133–137 (2012)
Bělohlávek, R., Osička, P.: Triadic fuzzy Galois connections as ordinary connections. In: IEEE Intl Conf. on Fuzzy Systems (2012)
Blyth, T.S.: Lattices and Ordered Algebraic Structures. Springer (2005)
Butka, P., Pócs, J., Pócsová, J.: On equivalence of conceptual scaling and generalized one-sided concept lattices. Information Sciences 259, 57–70 (2014)
Castellini, G., Koslowski, J., Strecker, G.: Closure operators and polarities. Annals of the New York Academy of Sciences 704, 38–52 (1993)
Cohen, D.A., Creed, P., Jeavons, P.G., Živný, S.: An Algebraic theory of complexity for valued constraints: Establishing a Galois Connection. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 231–242. Springer, Heidelberg (2011)
Denecke, K., Erné, M., Wismath, S.L.: Galois connections and applications, vol. 565. Springer (2004)
Díaz, J.C., Medina, J.: Multi-adjoint relation equations: Definition, properties and solutions using concept lattices. Information Sciences 253, 100–109 (2013)
Dubois, D., Prade, H.: Possibility theory and formal concept analysis: Characterizing independent sub-contexts. Fuzzy Sets and Systems 196, 4–16 (2012)
Dzik, W., Järvinen, J., Kondo, M.: Intuitionistic propositional logic with Galois connections. Logic Journal of the IGPL 18(6), 837–858 (2010)
Dzik, W., Järvinen, J., Kondo, M.: Representing expansions of bounded distributive lattices with Galois connections in terms of rough sets. International Journal of Approximate Reasoning 55(1), 427–435 (2014)
Erné, M., Koslowski, J., Melton, A., Strecker, G.E.: A primer on Galois connections. Annals of the New York Academy of Sciences 704, 103–125 (1993)
Frascella, A.: Fuzzy Galois connections under weak conditions. Fuzzy Sets and Systems 172(1), 33–50 (2011)
García-Pardo, F., Cabrera, I.P., Cordero, P., Ojeda-Aciego, M.: On Galois Connections and Soft Computing. In: Rojas, I., Joya, G., Cabestany, J. (eds.) IWANN 2013, Part II. LNCS, vol. 7903, pp. 224–235. Springer, Heidelberg (2013)
Järvinen, J.: Pawlak’s information systems in terms of Galois connections and functional dependencies. Fundamenta Informaticae 75, 315–330 (2007)
Järvinen, J., Kondo, M., Kortelainen, J.: Logics from Galois connections. Int. J. Approx. Reasoning 49(3), 595–606 (2008)
Kan, D.M.: Adjoint functors. Transactions of the American Mathematical Society 87(2), 294–329 (1958)
Kerkhoff, S.: A general Galois theory for operations and relations in arbitrary categories. Algebra Universalis 68(3), 325–352 (2012)
Konecny, J.: Isotone fuzzy Galois connections with hedges. Information Sciences 181(10), 1804–1817 (2011)
Medina, J.: Multi-adjoint property-oriented and object-oriented concept lattices. Information Sciences 190, 95–106 (2012)
Melton, A., Schmidt, D.A., Strecker, G.E.: Galois connections and computer science applications. In: Poigné, A., Pitt, D., Rydeheard, D., Abramsky, S. (eds.) Category Theory and Computer Programming. LNCS, vol. 240, pp. 299–312. Springer, Heidelberg (1986)
Mu, S.-C., Oliveira, J.N.: Programming from Galois connections. The Journal of Logic and Algebraic Programming 81(6), 680–704 (2012)
Ore, Ø.: Galois connections. Trans. Amer. Math. Soc. 55, 493–513 (1944)
Restrepo, M., Cornelis, C., Gómez, J.: Duality, conjugacy and adjointness of approximation operators in covering-based rough sets. International Journal of Approximate Reasoning 55(1), 469–485 (2014)
Wolski, M.: Galois connections and data analysis. Fundamenta Informaticae 60, 401–415 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
García-Pardo, F., Cabrera, I.P., Cordero, P., Ojeda-Aciego, M., Rodríguez, F.J. (2014). Generating Isotone Galois Connections on an Unstructured Codomain. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-08852-5_10
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08851-8
Online ISBN: 978-3-319-08852-5
eBook Packages: Computer ScienceComputer Science (R0)