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On the use of thresholds in multi-adjoint concept lattices. (English) Zbl 1327.06008

Summary: The size of the concept lattices increases exponentially from the number of objects and attributes. This situation is more complicated in the fuzzy case, in which the considered carriers to evaluate the objects and attributes, and for the relation, are also taken into account. Hence, it is very important to study mechanisms to reduce the size of fuzzy concept lattices maintaining the main information. One of the most important mechanisms to reduce the size of concept lattices is the use of thresholds in the concept-forming operators. This paper studies this mechanism in the general fuzzy framework of multi-adjoint concept lattices, obtaining interesting properties and consequences.

MSC:

06B23 Complete lattices, completions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
08A72 Fuzzy algebraic structures
03E72 Theory of fuzzy sets, etc.
68T30 Knowledge representation
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References:

[1] DOI: 10.1016/j.apal.2003.01.001 · Zbl 1060.03040
[2] DOI: 10.1016/j.ins.2007.02.024 · Zbl 1119.06004
[3] DOI: 10.1109/TFUZZ.2010.2041006
[4] DOI: 10.1016/S0165-0114(96)00318-1 · Zbl 0927.06006
[5] DOI: 10.1016/j.fss.2012.05.004 · Zbl 1272.03111
[6] DOI: 10.1017/CBO9780511809088
[7] DOI: 10.1016/j.ins.2003.06.013 · Zbl 1076.68085
[8] DOI: 10.1142/S0218488510006465 · Zbl 05712317
[9] DOI: 10.1016/j.ins.2010.08.027 · Zbl 05911288
[10] Georgescu G., Soft Comput 7 (7) pp 458– (2003)
[11] DOI: 10.1007/978-94-011-5300-3
[12] DOI: 10.1016/j.fss.2005.03.013 · Zbl 1099.68017
[13] DOI: 10.1016/j.fss.2012.03.003 · Zbl 1254.68249
[14] DOI: 10.1093/jigpal/jzi045 · Zbl 1088.06005
[15] DOI: 10.1142/S0218339010003512
[16] DOI: 10.1016/j.eswa.2009.09.026
[17] DOI: 10.1016/j.knosys.2010.03.006
[18] DOI: 10.1016/j.advengsoft.2012.07.001
[19] DOI: 10.1016/j.ins.2011.11.016 · Zbl 1248.68479
[20] DOI: 10.1016/j.camwa.2012.03.087 · Zbl 1268.06007
[21] DOI: 10.1016/j.ins.2009.11.018 · Zbl 1187.68587
[22] DOI: 10.1016/j.fss.2003.11.005 · Zbl 1073.68026
[23] DOI: 10.1016/j.fss.2008.05.004 · Zbl 1187.68589
[24] DOI: 10.1016/j.knosys.2008.03.001
[25] DOI: 10.1016/j.knosys.2010.07.001
[26] DOI: 10.1007/978-94-009-7798-3_15
[27] DOI: 10.1016/j.ins.2007.05.031 · Zbl 1130.06004
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