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Local multigranulation decision-theoretic rough set in ordered information systems. (English) Zbl 1436.68366

Summary: As a generalized extension of Pawlak’s rough set model, the multigranulation decision-theoretic rough set model in ordered information systems utilizes the basic set assignment function to construct probability measure spaces through dominance relations. It is an effective tool to deal with uncertain problems and widely used in practical decision problems. However, when the scale of dataset is large, it takes a lot of time to characterize the approximations of the target concept, as well as complicated calculation processes. In this paper, we develop a novel model called local multigranulation decision-theoretic rough set in an ordered information system to overcome the above-mentioned limitation. Firstly, to reduce the computing time of the information granule independent of the target concept, we only use the characterization of the elements in the target concept to approximate this target concept. Moreover, the corresponding local multigranulation decision-theoretic rough set in an ordered information system is addressed according to the established local model, and the comparisons are made between the proposed local algorithm and the algorithm of original multigranulation decision-theoretic rough set in ordered information systems. Finally, the validity of the local approximation operators is verified through the experimental evaluation using six datasets coming from the University of California-Irvine (UCI) repository.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
Full Text: DOI

References:

[1] Bansal S (2018) Nature-inspired-based multi-objective hybrid algorithms to find near-OGRs for optical WDM systems and their comparison. In: Handbook of research on biomimicry in information retrieval and knowledge management. IGI Global, pp 175-211
[2] Bansal S, Gupta N, Singh AK (2017) NatureCinspired metaheuristic algorithms to find nearCOGR sequences for WDM channel allocation and their performance comparison. Open Math 15(1):520-547 · Zbl 1362.90314 · doi:10.1515/math-2017-0045
[3] Bansal S, Singh AK, Gupta N (2017) Optimal golomb ruler sequences generation for optical WDM systems: a novel parallel hybrid multi-objective bat algorithm. J Inst Eng 98(1):43-64
[4] Bansal S, Sharma K (2018) Nature-inspired-based modified multi-objective BB-BC algorithm to find near-OGRs for optical WDM systems and its performance comparison. In: Handbook of research on biomimicry in information retrieval and knowledge management. IGI Global, pp 1-25
[5] Chen J, Zhang YP, Zhao S (2016) Multi-granular mining for boundary regions in three-way decision theory. Knowl Based Syst 91:287-292 · doi:10.1016/j.knosys.2015.10.020
[6] Du WS, Hu BQ (2016) Dominance-based rough set approach to incomplete ordered information systems. Inf Sci 346-347:106-129 · Zbl 1398.68535 · doi:10.1016/j.ins.2016.01.098
[7] Du WS, Hu BQ (2017) Dominance-based rough fuzzy set approach and its application to rule induction. Eur J Oper Res 261(2):690-703 · Zbl 1403.91109 · doi:10.1016/j.ejor.2016.12.004
[8] Duntsh I, Gediga G (1998) Uncertainty measures of rough set prediction. Artif Intell 106(1):109-137 · Zbl 0909.68040 · doi:10.1016/S0004-3702(98)00091-5
[9] Fang Y, Min F (2019) Cost-sensitive approximate attribute reduction with three-way decisions. Int J Approx Reason 104:148-165 · Zbl 1452.68208 · doi:10.1016/j.ijar.2018.11.003
[10] Greco S, Matarazzo B, Slowinski R (2002) Rough approximation by dominance relations. Int J Intell Syst 17(2):153-171 · Zbl 0997.68135 · doi:10.1002/int.10014
[11] Greco S, Slwìski R, Yao YY (2007) Bayesian decision theory for dominance-based rough set approach. Rough Sets Knowl Technol 4481:134-141 · doi:10.1007/978-3-540-72458-2_16
[12] Hu XH, Cercone N (1995) Learning in relational databases: a rough set approach. Comput Intell 11(2):323-338 · doi:10.1111/j.1467-8640.1995.tb00035.x
[13] Jeon G, Kim D, Jeong J (2016) Rough sets attributes reduction based expert system in interlaced video sequences. IEEE Trans Consum Electron 52(4):1348-1355 · doi:10.1109/TCE.2006.273155
[14] Li SY, Li TR (2015) Incremental update of approximations in dominance-based rough sets approach under the variation of attribute values. Inf Sci 294:348-361 · Zbl 1360.68840 · doi:10.1016/j.ins.2014.09.056
[15] Li WT, Xu WH (2015) Multigranulation decision-theoretic rough set in ordered information system. Fundam Inform 139(1):67-89 · Zbl 1334.68220 · doi:10.3233/FI-2015-1226
[16] Li HX, Zhang LB, Huang B, Zhou XZ (2016) Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl Based Syst 91:241-251 · doi:10.1016/j.knosys.2015.07.040
[17] Li WT, Pedrycz W, Xue XP, Xu WH, Fan BJ (2018) Distance-based double-quantitative rough fuzzy sets with logic operations. Int J Approx Reason 101:206-233 · Zbl 1448.03043 · doi:10.1016/j.ijar.2018.07.007
[18] Li WT, Pedrycz W, Xue XP et al (2018) Fuzziness and incremental information of disjoint regions in double-quantitative decision-theoretic rough set model. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-018-0893-7 · doi:10.1007/s13042-018-0893-7
[19] Liang DC, Pedrycz W, Liu D, Hu P (2015) Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making. Appl Soft Comput 29:256-269 · doi:10.1016/j.asoc.2015.01.008
[20] Liang DC, Liu D, Kobina A (2016) Three-way group decisions with decision-theoretic rough sets. Inf Sci 345(1):46-64 · doi:10.1016/j.ins.2016.01.065
[21] Li W, Miao DQ, Wang WL et al (2010) Hierarchical rough decision theoretic framework for text classification. In: IEEE international conference on cognitive informatics, pp 484-489
[22] Liu D, Yao YY, Li TR (2011) Three-way investment decisions with decision-theoretic rough sets. Int J Comput Intell Syst 4(1):66-74 · doi:10.1080/18756891.2011.9727764
[23] Liu D, Li TR, Liang DC (2012) Three-way government decision analysis with decision-theoretic rough sets. Int J Uncertain Fuzziness Knowl Based Syst 20(supp01):119-132 · doi:10.1142/S0218488512400090
[24] Ma WM, Sun BZ (2012) Probabilistic rough set over two universes and rough entropy. Int J Approx Reason 539(4):608-619 · Zbl 1246.68234 · doi:10.1016/j.ijar.2011.12.010
[25] Pawlak Z (1982) Rough set. Int J Comput Inf Sci 11(5):341-356 · Zbl 0501.68053 · doi:10.1007/BF01001956
[26] Pawlak Z (1992) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Alphen ann den Rijn · Zbl 0758.68054
[27] Pawlak Z, Wong SKM, Ziarko W (1988) Rough sets: probabilistic versus deterministic approach. Int J Man Mach Stud 29(1):81-95 · Zbl 0663.68094 · doi:10.1016/S0020-7373(88)80032-4
[28] Pedrycz W (2013) Granular computing: analysis and design of intelligent systems. CRC Press, Boca Raton · doi:10.1201/b14862
[29] Qian YH, Liang JY (2006) Rough set method based on multi-Granulations. IEEE Int Conf Cognit Inform 1:297-304
[30] Qian YH, Zhang H, Sang YL et al (2014) Multigranulation decision-theoretic rough sets. Int J Approx Reason 55(1):225-237 · Zbl 1316.68190 · doi:10.1016/j.ijar.2013.03.004
[31] Qian YH, Li SY, Liang JY et al (2014) Pessimistic rough set based decisions: a multigranulation fusion strategy. Inf Sci 264:196-210 · Zbl 1335.68270 · doi:10.1016/j.ins.2013.12.014
[32] Qian YH, Liang XY, Lin GP et al (2017) Local multigranulation decision-theoretic rough sets. Int J Approx Reason 82:119-137 · Zbl 1404.68172 · doi:10.1016/j.ijar.2016.12.008
[33] Qian J, Liu CH, Yue XD (2019) Multigranulation sequential three-way decisions based on multiple thresholds. Int J Approx Reason 105:396-416 · Zbl 1440.68295 · doi:10.1016/j.ijar.2018.12.007
[34] Shao MW, Zhang WX (2005) Dominance relation and rules in an incomplete ordered information system. Int J Intell Syst 20(1):13-27 · Zbl 1089.68128 · doi:10.1002/int.20051
[35] Sun BZ, Ma WM, Li BJ, Li XN (2016) Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set. Int J Approx Reason 93:424-442 · Zbl 1452.68228 · doi:10.1016/j.ijar.2017.11.015
[36] Susmaga R (2014) Reducts and constructs in classic and dominance-based rough sets approach. Inf Sci 271:45-64 · Zbl 1341.68268 · doi:10.1016/j.ins.2014.02.100
[37] Xu WH (2013) Ordered information systems and rough sets theory. Science Press, Beijing
[38] Xu WH, Li WT (2016) Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets. IEEE Trans Cybern 46(2):366-379 · doi:10.1109/TCYB.2014.2361772
[39] Xu WH, Yu JH (2017) A novel approach to information fusion in multi-source datasets: a granular computing viewpoint. Inf Sci 378:410-423 · Zbl 1429.68301 · doi:10.1016/j.ins.2016.04.009
[40] Xu WH, Zhang XY, Zhong JM et al (2010) Attribute reduction in ordered information systems based on evidence theory. Knowl Inf Syst 25(1):169-184 · doi:10.1007/s10115-009-0248-5
[41] Yao YY (1998) Generalized rough set models. Rough Sets Knowl Discov 1:286-318 · Zbl 0946.68137
[42] Yao YY (2007) Decision-theoretic rough set models. Rough Sets Knowl Technol 4481:1-12 · doi:10.1007/978-3-540-72458-2_1
[43] Yao YY (2008) Probabilistic rough set approximation. Int J Approx Reason 49(2):255-271 · Zbl 1191.68702 · doi:10.1016/j.ijar.2007.05.019
[44] Yao YY (2009) Three-way decision: An interpretation of rules in rough set theory. Rough Sets Knowl Technol 5589:642-649 · doi:10.1007/978-3-642-02962-2_81
[45] Yao YY, Wong SKM (1992) A decision theoretic framework for approximating concepts. Int J Man Mach Stud 37(6):793-809 · doi:10.1016/0020-7373(92)90069-W
[46] Yao YY, Zhou B (2010) Naive Bayesian rough sets. Rough Sets Knowl Technol 6401:719-726
[47] Yu JH, Xu WH (2017) Incremental knowledge discovering in interval-valued decision information system with the dynamic data. Int J Mach Learn Cybern 8(1):849-864 · doi:10.1007/s13042-015-0473-z
[48] Yu H, Liu ZG, Wang GY (2014) An automatic method to determine the number of clusters using decision-theoretic rough set. Int J Approx Reason 55(1):101-115 · Zbl 1316.68121 · doi:10.1016/j.ijar.2013.03.018
[49] Yu JH, Zhang B, Chen MH, Xu WH (2018) Double-quantitative decision-theoretic approach to multigranulation approximate space. Int J Approx Reason 98:236-258 · Zbl 1451.91047 · doi:10.1016/j.ijar.2018.05.001
[50] Zhang XY, Miao DQ (2017) Three-way attribute reducts. Int J Approx Reason 88:401-434 · Zbl 1418.68217 · doi:10.1016/j.ijar.2017.06.008
[51] Zhang HY, Leung Y, Zhou L (2013) Variable-precision-dominance-based rough set approach to interval-valued information systems. Inf Sci 244:75-91 · Zbl 1355.68268 · doi:10.1016/j.ins.2013.04.031
[52] Ziarko W (1993) Variable precision rough set model. J Comput Syst Sci 46(1):39-59 · Zbl 0764.68162 · doi:10.1016/0022-0000(93)90048-2
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