Semiconcept, a new data processing model, enriches the development of formal concept analysis. However, the classical semiconcept is supported by two-way decisions. In the study of classical semiconcept theory, how to express the information of jointly not possessed is also essential in making decisions. Therefore, this paper tries to combine the classical semiconcept theory with three-way decisions to present three-way semiconcepts, and carry on the further study. Firstly, we define new operators and give some properties of them. Two kinds of three-way semiconcepts —OE-semiconcept and AE-semiconcept, are presented. And the corresponding structures are searched out from the perspective of lattice theory. Furthermore, we analyze the relationship among three-way concepts, three-way semiconcepts and classical semiconcepts. On this basis, the algorithms to build OE-semiconcept and AE-semiconcept are presented. At the meanwhile, we take some examples to examine and explain the obtained results.
ChenJ., ZhangY. and ZhaoS., Multi-granular mining for boundary regions in three-way decision theory, Knowledge-Based Systems91 (2016), 287–292. DOI: 10.1016/j.knosys.2015.10.020
2.
DaveyB. and PriestleyH., Introduction to Lattices and Order, Cambridge University John Wilely and Sons (2002).
3.
DengX. and YaoY., Decision-theoretic three-way approximations of fuzzy sets, Information Sciences379 (2014), 702–715. DOI: 10.1016/j.ins.2014.04.022
4.
FujitaH., LiT. and YaoY., Advances in three-way decisions and granular computing, Knowledge-Based Systems91 (2016), 1–3. DOI: 10.1016/j.knosys.2015.10.026
JianY. and YangM., Semantic search exploiting formal concept analysis, rough sets, and Wikipedia, International Journal on Semantic Web and Information Systems14(3) (2018), 99–119. DOI: 10.4018/IJSWIS.2018070105
7.
CarpinetoC., RomanoG. and EbraryI., Concept Data analysis: theory and applications, John Wiley and Sons (2004).
8.
YaoY., Interval sets and three-way concept analysis in incomplete contexts, International Journal of Machine Learning and Cybernetics8(1) (2017), 3–20. DOI: 10.1007/s13042-016-0568-1
9.
LiJ., HuangC., QiJ., QianY. and LiuW., Three-way cognitive concept learning via multi-granularity, Information Sciences378 (2017), 244–263. DOI: 10.1016/j.ins.2016.04.051
10.
LiM. and WangG., Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts, Knowledge-Based Systems91 (2016), 165–178. DOI: 10.1016/j.knosys.2015.10.010
11.
LukschP. and WilleR., A mathematical model for conceptual knowledge systems, in: H.H. Bock and P. Ihm (Eds.), Classification, Data Analysis, and Knowledge Organisation, Springer-Verlag Berlin, Heidelberg, (1991), 156–162. DOI:10.1007/978-3-642-76307-6-21
12.
LiX., Three-way fuzzy matroids and granular computing, International Journal of Approximate Reasoning114 (2019), 44–50. DOI: 10.1016/j.ijar.2019.08.003
13.
MalikG., An extension of the theory of information flow to semiconcept and protoconcept graphs, in: K.E. Wolff, et al. (Eds.), ICCS 2004, LNAI 3127, Springer-Verlag Berlin, Heidelberg, (2004), 213–226. DOI:10.1007/978-3-540-27769-9-14
14.
MaoH., Approximation operators for semiconcept, Journal of Intelligence and Fuzzy Systems36 (2019), 333–343. DOI: 10.3233/JIFS-18104
15.
MaoH. and KangR., Variable precision rough set approximations in concept lattice, Journal of Progressive Research in Mathematics2(1) (2015), 47–56. DOI: 10.3969/j.issn.1007-130X.2017.12.026
16.
BurmeisterP. and HolzerR., On the treatment of incomplete knowledge in formal concept analysis, in: Proceedings of ICCS 2000, LNCS (LNAI), (1867), 385–398. DOI:10.1007/10722280-27
PeiZ., RuanD., MengD. and LiuZ., Formal concept analysis based on the topology for attributes of a formal context, Information Sciences236 (2013), 66–82. DOI: 10.1016/J.INS.2013.02.027
19.
QiJ., QianT. and WeiL., The Connections between Three-way and Classical Concept Lattices, Knowledge-Based Systems91 (2016), 143–151. DOI: 10.1016/j.knosys.2015.08.006
20.
QiJ., WeiL. and YaoY., Three-way formal concept analysis, in: Rough Sets and Knowledge Technology, Springer8818 (2014), 732–741. DOI: 10.1007/978-3-319-11740-9-67
21.
RenR. and WeiL., The attribute reductions of three-way concept lattices, Knowledge-Based Systems99 (2016), 92–102. DOI: 10.1016/j.knosys.2016.01.045
22.
VormbrockB., Complete subalgebras of semiconcept algebras and protoconcept algebras, in: B. Ganter and R. Godin (Eds.), ICFCA 2005, LNAI 3403, Springer-Verlag Berlin, Heidelberg, (2005), 329–343. DOI:10.1007/978-3-540-32262-7-23
23.
VormbrockB. and WilleR., Semiconcept and protoconcept algebras:The basic theorems, in:B.Ganter, et al.(Eds.), Formal Concept Analysis, LNAI 3626, Springer-Verlag Berlin, Heidelberg, (2005), 34–48. DOI:10.1007/11528784-2
24.
WilleR., Restructuring lattice theory: an approach based on hierarchies of concepts, in: I. Rival (Eds.), Ordered Sets, Reidel Publishing Company, Dordrecht Boston, (1982), 445–470. DOI:10.1007/978-3-642-01815-2-23
25.
YaoY., An outline of a theory of three-way decisions, in: Proceedings of RSCTC 2012, LNCS (LNAI)7413 (2012), 1–17. DOI: 10.1007/978-3-642-32115-3-1
26.
YaoY., Three-way granular computing, rough sets, and formal concept analysis, International Journal of Approximate Reasoning116 (2020), 106–125. DOI: 10.1016/j.ijar.2019.11.002
27.
YaoY., Three-way decision: an interpretation of rules in rough set theory, in:P. Wen, Y. Li, L. Polkowski, Y. Yao, S. Tsumoto, G. Wang (Eds.), Rough Sets and Knowledge Technology, Lecture Notes Computer Science 5589, Springer-Verlag, Berlin, Heidelberg, (2009), 642–649. DOI:10.1007/978-3-642-02962-2-81
JihoonK. and YunK., Galois Lattices-based Formal Design Concept Analysis for Crowdsourcing Design, Journal of Integrated Design and Process Science23(4) (2021), 61–89. DOI: 10.3233/JID190016
