Approximate Concepts Analysis Based on {1,0,-1}-valued Formal Contexts

Tiantian Liu; Zhenhao Qi

doi:10.6911/WSRJ.202507_11(7).0006

Authors

Tiantian Liu
Zhenhao Qi

DOI:

https://doi.org/10.6911/WSRJ.202507_11(7).0006

Keywords:

Formal concept analysis, Concept lattice, Approximate concepts.

Abstract

With the rapid growth of data volume and the increasing complexity of data analysis, traditional formal concept analysis (FCA) models have become inadequate for addressing the diverse and intricate requirements of big data environments. In response to these challenges, this paper introduce a novel approximate concept model grounded in three-way concepts and incorporating the notion of {1,0,-1}-valued formal contexts. We formally introduce the foundational definitions of the proposed model, thoroughly examine its essential properties and the partial order relations among concepts, and explore its enhanced capacity for representing and reasoning about uncertain or {1,0,-1}-valued information. Furthermore, a comprehensive comparison with existing concept models is provided to highlight the advantages and distinguishing features of the proposed approach. Finally, we demonstrate the potential applications of this model in data analysis and knowledge representation, illustrating its value for addressing the complexities inherent in modern data-driven tasks.

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References

[1] WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[C]// RIVAL I. Ordered sets. Dordrecht-Boston: Reidel, 1982: 445-470.

[2] Ganter B, Wille R. Formal concept analysis: mathematical foundations[M]. Springer Science & Business Media, 2012.

[3] Outrata J, Vychodil V. Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data[J]. Information Sciences, 2012, 185(1): 114-127.

[4] Outrata J. A lattice-free concept lattice update algorithm[J]. International Journal of General Systems, 2016, 45(2): 211-231.

[5] Muangprathub J. A novel algorithm for building concept lattice[J]. Applied Mathematical Sciences, 2014, 8(11): 507-515.

[6] Zhi H, Zhi D, Liu Z. Principles and Algorithms of Concept Lattice Merging [J]. Journal of Electronics, 2010, 38(2): 455.

[7] Zhi H, Li J. Influence of dynamical changes on concept lattice and implication rules[J]. International Journal of Machine Learning and Cybernetics, 2018, 9(5): 795-805.

[8] Cao L, Wei L, Qi J. Concept approximation of keeps binary relations invariant[J]. Pattern Recognition and Artificial Intelligence, 2018, 31(6): 516-524.

[9] Wei L, Qi J, Zhang W. Concept lattice attributes reduce of decision formal concepts[J]. Science China: 2008, 38(2): 195-208.

[10] Zhi H, Qi Z, Li Y. An efficient conflict analysis method based on splitting and merging of formal contexts[J]. Information Sciences, 2024, 661: 120154.

[11] Burmeister P, Holzer R. On the treatment of {1,0,-1}-valued knowledge in formal concept analysis[C]//International Conference on Concept Structures. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000: 385-398.

[12] Burusco Juandeaburre A, Fuentes-González R. The study of the L-fuzzy concept lattice[J]. Mathware & soft computing. 1994 Vol. 1 Núm. 3 p. 209-218, 1994.

[13] Bêlohlávek R. Fuzzy galois connections[J]. Mathematical Logic Quarterly, 1999, 45(4): 497-504.

[14] Qi J, Wei L, Yao Y. Three-way formal concept analysis[C]//Rough Sets and Knowledge Technology: 9th International Conference, RSKT 2014, Shanghai, China, October 24-26, 2014, Proceedings 9. Springer International Publishing, 2014: 732-741.

[15] Yao Y. Three-way decisions with probabilistic rough sets[J]. Information sciences, 2010, 180(3): 341-353.

[16] Yao Y. An outline of a theory of three-way decision[C]. YAO J T, YANG Y, SLOWINSKIN, et al(eds). Proceedings of 2012 Rough Sets and Current Trends in Computing (Lecture Notes in Computer Science, 7413), Chengdu, China, 2012: 1-17.

[17] Qi J, Wei L, Ren R. 3-way concept analysis based on 3-valued formal contexts[J]. Cognitive Computation, 2021: 1-13.

[18] Zhi H, Qi J, Qian T, et al. Conflict analysis under one-vote veto based on approximate three-way concept lattice[J]. Information Sciences, 2020, 516: 316-330.

[19] Zhi H, Li J, Li Y. Multilevel Conflict Analysis Based on Fuzzy Formal Contexts[J]. IEEE Transactions on Fuzzy Systems, 2022, 30(12): 5128-5142.