Abstract
Heterogeneous formal context represents the possible generalization of formal context which allows us to diversify the data structures of objects, attributes and fuzzy relations. Moreover, it can provide the more efficient representation of data in heterogeneous environment. In this paper, we present the extended results on heterogeneous formal context. We provide the equivalent definition of concept-forming operators on heterogeneous formal context and describe their additional properties.
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References
Burusco, A., Fuentes-González, R.: The study of \(L\)-fuzzy concept lattice. Mathw. Soft Comput. 3, 209–218 (1994)
Ganter, G., Wille, R.: Formal Concept Analysis, Mathematical Foundation. Springer, Berlin (1999)
Bělohlávek, R.: Fuzzy concepts and conceptual structures: induced similarities. In: JCIS ’98 proceedings, International Conference on Computer Science and Informatics, pp. 179–182. Association for Intelligent Machinery (1998)
Bělohlávek, R.: Fuzzy Galois connections. Math. Log. Q. 45(4), 497–504 (1999)
Bělohlávek, R.: Concept lattices and order in fuzzy logic. Ann. Pure Appl. Logic 128, 277–298 (2004)
Pollandt, S.: Datenanalyse mit Fuzzy-Begriffen. In: G. Stumme, R. Wille (eds.), Begriffliche Wissensverarbeitung. Methoden und Anwendungen, pp. 72–98. Springer, Heidelberg (2000)
Ben Yahia, S., Jaoua, A.: Discovering knowledge from fuzzy concept lattice. In: Kandel, A., Last, M., Bunke, H. (eds.) Data Mining and Computational Intelligence, pp. 169–190. Physica-Verlag (2001)
Bělohlávek, R., Sklenář, V., Zacpal, J.: Crisply generated fuzzy concepts. Lect. Notes Comput. Sci. 3403, 268–283 (2005)
Krajči, S.: Cluster based efficient generation of fuzzy concepts. Neural Netw. World 13, 521–530 (2003)
Medina, J., Ojeda-Aciego, M., Valverde, A., Vojtáš, P.: Towards biresiduated multi-adjoint logic programming. Lect. Notes Artif. Intell. 3040, 608–617 (2004)
Medina, J., Ojeda-Aciego, M., Vojtáš, P.: Multi-adjoint logic programming with continuous semantics. Lect. Notes Artif. Intell. 2173, 351–364 (2001)
Medina, J., Ojeda-Aciego, M., Vojtáš, P.: Similarity-based unification: a multi-adjoint approach. Fuzzy Sets Syst. 146, 43–62 (2004)
Cornejo, M.E., Medina, J., Ramírez, E.: A comparative study of adjoint triples. Fuzzy Sets Syst. 211, 1–14 (2013)
Cornejo, M.E., Medina, J., Ramírez, E.: Characterizing reducts in multi-adjoint concept lattices. Inf. Sci. 422, 364–376 (2018)
Madrid, N., Ojeda-Aciego, M.: Multi-adjoint lattices from adjoint triples with involutive negation. Fuzzy Sets Syst. 405, 88–105 (2021)
Medina, J., Ojeda-Aciego, M.: Multi-adjoint t-concept lattices. Inf. Sci. 180, 712–725 (2010)
Medina, J., Ojeda-Aciego, M.: On multi-adjoint concept lattices based on heterogeneous conjunctors. Fuzzy Sets Syst. 208, 95–110 (2012)
Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Formal concept analysis via multi-adjoint concept lattices. Fuzzy Sets Syst. 160, 130–144 (2009)
Medina, J., Ojeda-Aciego, M., Pócs, J., Ramírez-Poussa, E.: On the Dedekind-MacNeille completion and formal concept analysis based on multilattices. Fuzzy Sets Syst. 303, 1–20 (2016)
Krajči, S.: A generalized concept lattice. Logic J. IGPL 13, 543–550 (2005)
Krídlo, O., Krajči, S., Antoni, L’.: Formal concept analysis of higher order. Int. J. Gen. Syst. 45(2), 116–134 (2016)
Antoni, L.’, Krajči, S., Krídlo, O., Macek, B., Pisková, L.: On heterogeneous formal contexts. Fuzzy Sets Syst. 234, 22–33 (2014)
Pócs, J.: Note on generating fuzzy concept lattices via Galois connections. Inf. Sci. 185, 128–136 (2012)
Pócs, J.: On possible generalization of fuzzy concept lattices using dually isomorphic retracts. Inf. Sci. 210, 89–98 (2012)
Pócs, J., Pócsová, J.: Basic theorem as representation of heterogeneous concept lattices. Front. Comput. Sci. 9(4), 636–642 (2015)
Butka, P., Pócs, J.: Generalization of one-sided concept lattices. Comput. Inform. 32(2), 355–370 (2013)
Butka, P., Pócs, J., Pócsová, J.: Representation of fuzzy concept lattices in the framework of classical FCA. J. Appl. Math. ID236725 (2013)
Butka, P., Pócs, J., Pócsová, J.: Distributed computation of generalized one-sided concept lattices on sparse data tables. Comput. Inform. 34(1), 77–98 (2015)
Halaš, R., Pócs, J.: Generalized one-sided concept lattices with attribute preferences. Inf. Sci. 303, 50–60 (2015)
Cordero, P., Enciso, M., Mora, Á., Ojeda-Aciego, M., Rossi, C.: A formal concept analysis approach to cooperative conversational recommendation. Int. J. Comput. Intell. Syst. 13(1), 1243–1252 (2020)
Valverde-Albacete, F.J., Peláez-Moreno, C.: A framework for supervised classification performance analysis with information-theoretic methods. IEEE Trans. Knowl. Data. Eng. 32(11), 2075–2087 (2020)
Dubois, D., Medina, J., Prade, H., Ramírez-Poussa, E.: Disjunctive attribute dependencies in formal concept analysis under the epistemic view of formal contexts. Inf. Sci. 561, 31–51 (2021)
Medina, J.: Minimal solutions of generalized fuzzy relational equations: clarifications and corrections towards a more flexible setting. Int. J. Approx. Reason. 84, 33–38 (2017)
Medina, J., Yager, R.R.: OWA operators with functional weights. Fuzzy Sets Syst. 414, 38–56 (2021)
Antoni, L’., Eliaš, P., Krajči, S., Krídlo, O.: Heterogeneous formal context and its decomposition by heterogeneous fuzzy subsets. Fuzzy Sets Syst. Article in Press (2022). https://doi.org/10.1016/j.fss.2022.05.015
Höhle U.: Modules in the category Sup. In: Saminger-Platz, S., Mesiar, R. (eds.) On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory, Vol. 336 of Studies in Fuzziness and Soft Computing. Springer, Berlin (2016)
Acknowledgements
This work was supported by the Slovak Research and Development Agency under contract No. APVV-21-0468 (L’ubomír Antoni, Stanislav Krajči, Ondrej Krídlo) and by the Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic and Slovak Academy of Sciences under contract VEGA 2/0097/20 (Peter Eliaš).
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Eliaš, P., Antoni, L., Krídlo, O., Krajči, S. (2024). Additional Notes on Heterogeneous Concept-Forming Operators. In: Cornejo, M., Kóczy, L.T., Medina, J., Ramírez-Poussa, E. (eds) Computational Intelligence and Mathematics for Tackling Complex Problems 5. Studies in Computational Intelligence, vol 1127. Springer, Cham. https://doi.org/10.1007/978-3-031-46979-4_1
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