Abstract
The paper compares the concepts of reduction of binary attributes in rough set theory (RST) and the reduction of unary attributes or dychotomic attributes in formal concept analysis (FCA). We present some basics of both theories together with a brief presentation of elements of the theory of set spaces used in the paper as a platform for mentioned comparison. Then we deliver some results on binary attribute reduction in RST and attribute reduction in FCA. We characterize independence of sets of binary attributes in RST by complete algebras of sets completely generated by completely irredundant families of sets. Then by means of complete algebras of sets and indiscernibility relations with respect to families of sets we investigate some families of FCA-attributes. And finally we present some formal context for which we prove that RST-binary attribute reduction and FCA-unary attribute reduction give the same results.
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References
Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Amsterdam (2003)
Fedrizzi, M., Kacprzyk, J., Nurmi, H.: How different are social choice functions: a rough sets approach. Qual. Quant. Int. J. Methodol. 30(1), 87–99 (1996)
Fishburn, P.C.: The Theory of Social Choice functions. Princeton University Press, Princeton (1973)
Fishburn, P.C.: Social choice functions. Soc. Ind. Appl. Math. Rev. 16(1), 63–90 (1974)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundation. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-59830-2
Kacprzyk, J.: Group decision making with a fuzzy majority. Fuzzy Sets Syst. 18, 105–118 (1986)
Kacprzyk, J., Fedrizzi, M., Nurmi, H.: Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets Syst. 49, 21–31 (1992)
Kacprzyk, J., Merigó, J.M., Nurmi, H., Zadrożny, S.: Multi-agent systems and voting: how similar are voting procedures. In: Lesot, M.-J., et al. (eds.) IPMU 2020. CCIS, vol. 1237, pp. 172–184. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-50146-4_14
Kacprzyk, J., Nurmi, H., Zadrożny, S.: Reason vs. rationality: from rankings to tournaments in individual choice. In: Mercik, J. (ed.) Transactions on Computational Collective Intelligence XXVII. LNCS, vol. 10480, pp. 28–39. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70647-4_2
Kacprzyk, J., Nurmi, H., Zadrozny, S.: Towards a comprehensive similarity analysis of voting procedures using rough sets and similarity measures. In: Skowron, A., Suraj, Z. (eds.) Rough Sets and Intelligent Systems - Professor Zdzislaw Pawlak in Memoriam. Intelligent Systems Reference Library, vol. 42, pp. 359–380. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-30344-9_13
Kacprzyk, J., Zadrozny, S.: Towards a general and unified characterization of individual and collective choice functions under fuzzy and nonfuzzy preferences and majority via the ordered weighted average operators. Int. J. Intell. Syst. 24, 4–26 (2009)
Kacprzyk, J., Zadrozny, S.: Towards human consistent data driven decision support systems using verbalization of data mining results via linguistic data summaries. Bull. Polish Acad. Sci. Techn. Sci. 58(3), 359–370 (2010)
Kelly, J.S.: Social Choice Theory. Springer, Heidelberg (1988). https://doi.org/10.1007/978-3-662-09925-4
Lin, T.Y., Liau, C.J., Kacprzyk, J. (eds.): Granular, Fuzzy, and Soft Computing: A Volume in the Encyclopedia of Complexity and Systems Science Series. 1st edn. Springer, Cham (2023)
Lipski, W.: Informational systems with incomplete information. In: 3rd International Symposium on Automata, Languages and Programming, Edinburgh, Scotland, pp. 120–130 (1976)
Nurmi, H.: Comparing Voting Systems. D. Reidel, Dordrecht (1987)
Nurmi, H.: Voting Paradoxes and How to Deal With Them. Springer, Heidelberg (1999)
Nurmi, H.: The choice of voting rules based on preferences over criteria. In: Kamiński, B., Kersten, G.E., Szapiro, T. (eds.) GDN 2015. LNBIP, vol. 218, pp. 241–252. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19515-5_19
Nurmi, H., Kacprzyk, J.: On fuzzy tournaments and their solution concepts in group decision making. Eur. J. Oper. Res. 51(2), 223–232 (1991)
Nurmi, H., Kacprzyk, J., Zadrożny, S.: Voting systems in theory and practice. In: Szapiro, T., Kacprzyk, J. (eds.) Collective Decisions: Theory, Algorithms And Decision Support Systems. SSDC, vol. 392, pp. 3–16. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-84997-9_1
Orłowska, E., Pawlak, Z.: Representation of nondeterministic information. Theoret. Comput. Sci. 29, 27–39 (1984)
Pawlak, Z.: Information systems - theoretical foundations. Inf. Syst. 6, 205–218 (1981)
Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 18, 341–356 (1982)
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)
Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook on Granular Computing. Wiley, New York (2009)
Rauszer, C., Skowron, A.: The discernibility matrices and functions in information systems. In: R. Słowiński, (Ed.) Intelligent Decision Support. Handbook of Applications and Advances in the Rough Set Theory, pp. 331–362. Kluwer (1991)
Stumme, G.: Conceptual knowledge discovery and data mining with formal concept analysis. Tutorial slides at the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases ECML/PKDD’2002
Wasilewski, P.: Dependency and supervenience. In: L. Czaja (ed.) Proceedings of the Concurrence, Specifiation and Programming (CS &P’2003), vol. 2, pp. 550–560. University of Warsaw Press (2003)
Wasilewski, P.: On selected similarity relations and their applications into cognitive science (in Polish). Unpublished doctoral dissertation, Jagiellonian University: Department of Logic, Krakow, Poland (2004)
Wasilewski, P.: Concept lattices vs. approximation spaces. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 114–123. Springer, Heidelberg (2005). https://doi.org/10.1007/11548669_12
Wasilewski, P.: Algebras of definable sets vs. concept lattices. Fundamenta Informaticae 167(3), 235–256 (2019)
Wasilewski, P. Kacprzyk, J., Zadrozny, S.: On some concept lattice of social choice functions. In: M. Paprzycki (ed.) Proceedings of 18th Conference on Computer Sciences and Intelligent Systems FedCSIS 2023 (2023)
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. Reidel, Dordrecht (1982)
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Wasilewski, P., Kacprzyk, J., Zadrożny, S. (2023). Reduction of Binary Attributes: Rough Set Theory Versus Formal Concept Analysis. In: Campagner, A., Urs Lenz, O., Xia, S., Ślęzak, D., Wąs, J., Yao, J. (eds) Rough Sets. IJCRS 2023. Lecture Notes in Computer Science(), vol 14481. Springer, Cham. https://doi.org/10.1007/978-3-031-50959-9_4
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