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Hierarchy on multigranulation structures: a knowledge distance approach. (English) Zbl 1284.68542
Summary: In this paper, a knowledge distance approach is proposed to study the hierarchy under the frame of multigranulation. In our approach, the finest granulation structure is considered as the frame of reference, and then a knowledge distances algebraic lattice is constructed. Through such algebraic lattice, a partial order is derived, which can be used to characterize the finer or coarser relationships among multigranulation structures. It is also shown that the uncertainty measurements are monotonic in terms of the obtained partial order.

MSC:
68T30 Knowledge representation
68T37 Reasoning under uncertainty in the context of artificial intelligence
06B35 Continuous lattices and posets, applications
06A07 Combinatorics of partially ordered sets
94A17 Measures of information, entropy
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References:
[1] Abu-Donia G. M., Knowledge-Based Systems 26 (1) pp 20– (2012) · doi:10.1016/j.knosys.2011.06.010
[2] Bargiela A., IEEE Transactions on Systems, Man and Cybernetics, Part A 35 (2) pp 288– (2005) · doi:10.1109/TSMCA.2005.843381
[3] Chen Y. H., Information Sciences 178 (1) pp 1– (2008) · Zbl 1126.68593 · doi:10.1016/j.ins.2007.08.011
[4] DOI: 10.1016/S0004-3702(98)00091-5 · Zbl 0909.68040 · doi:10.1016/S0004-3702(98)00091-5
[5] Hu Q. H., IEEE Transactions on Fuzzy Systems 14 (2) pp 191– (2006) · Zbl 05452576 · doi:10.1109/TFUZZ.2005.864086
[6] Khan M. A., International Journal of Approximate Reasoning 49 (2) pp 466– (2008) · Zbl 1191.68684 · doi:10.1016/j.ijar.2008.04.005
[7] DOI: 10.1080/0308107021000013635 · Zbl 1010.94004 · doi:10.1080/0308107021000013635
[8] DOI: 10.1080/03081070600687668 · Zbl 1115.68130 · doi:10.1080/03081070600687668
[9] Lin T. Y., International Journal of Granular Computing, Rough Sets and Intelligent Systems 1 (1) pp 21– (2009) · doi:10.1504/IJGCRSIS.2009.026723
[10] Lin T. Y., IEEE Transactions on Fuzzy Systems 16 (2) pp 282– (2008) · Zbl 05516458 · doi:10.1109/TFUZZ.2008.921400
[11] DOI: 10.1016/j.ijar.2012.05.004 · Zbl 1264.68176 · doi:10.1016/j.ijar.2012.05.004
[12] DOI: 10.1016/j.ijar.2008.11.001 · Zbl 1191.68689 · doi:10.1016/j.ijar.2008.11.001
[13] Min F., Information Sciences 181 (22) pp 4928– (2011) · Zbl 06048197 · doi:10.1016/j.ins.2011.07.010
[14] Pedrycz W., IEEE Transactions on Systems, Man and Cybernetics Part B 32 (2) pp 212– (2002) · doi:10.1109/3477.990878
[15] Qian Y. H., Lecture Notes in Artificial Intelligence 4062 pp 184– (2006)
[16] DOI: 10.1016/j.ijar.2008.08.004 · Zbl 1191.68660 · doi:10.1016/j.ijar.2008.08.004
[17] DOI: 10.1109/TSMCA.2009.2035436 · doi:10.1109/TSMCA.2009.2035436
[18] DOI: 10.1016/j.patcog.2011.02.020 · Zbl 1218.68152 · doi:10.1016/j.patcog.2011.02.020
[19] DOI: 10.1109/TFUZZ.2010.2095461 · doi:10.1109/TFUZZ.2010.2095461
[20] DOI: 10.1016/j.ins.2009.11.023 · Zbl 1185.68695 · doi:10.1016/j.ins.2009.11.023
[21] Wang G. Y., Fundamenta Informaticae 68 (3) pp 289– (2005)
[22] Wei W., International Journal of General Systems 39 (8) pp 813– (2010) · Zbl 1210.94071 · doi:10.1080/03081079.2010.499102
[23] DOI: 10.1016/j.ins.2011.04.047 · Zbl 1242.68258 · doi:10.1016/j.ins.2011.04.047
[24] Wu W. Z., Information Sciences 144 (1) pp 201– (2002) · Zbl 1019.68109 · doi:10.1016/S0020-0255(02)00180-9
[25] DOI: 10.1080/03081079.2012.673598 · Zbl 1277.93043 · doi:10.1080/03081079.2012.673598
[26] Yang X. B., International Journal of Machine Learning and Cybernetics 3 (3) pp 223– (2012) · doi:10.1007/s13042-011-0054-8
[27] Yang X. B., Annals of Fuzzy Mathematics and Informatics 1 (1) pp 55– (2011)
[28] Yang X. B., Knowledge-based Systems 24 (6) pp 858– (2011) · doi:10.1016/j.knosys.2011.03.007
[29] DOI: 10.1002/1098-111X(200101)16:1<87::AID-INT7>3.0.CO;2-S · Zbl 0969.68079 · doi:10.1002/1098-111X(200101)16:1<87::AID-INT7>3.0.CO;2-S
[30] DOI: 10.1109/91.493904 · doi:10.1109/91.493904
[31] DOI: 10.1016/S0165-0114(97)00077-8 · Zbl 0988.03040 · doi:10.1016/S0165-0114(97)00077-8
[32] Zhang L., Fundamenta Informaticae 59 (2) pp 287– (2004)
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