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International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(2): 169-182
Published online June 25, 2022
https://doi.org/10.5391/IJFIS.2022.22.2.169
© The Korean Institute of Intelligent Systems
Using Fuzzy Time Series Models to Estimate the Cost of Benefits of Egyptian Social Insurance System
Reham Raouf and Saad Elsaieed
Department of Insurance & Actuarial Sciences, Faculty of Commerce, Cairo University, Cairo, Egypt
Correspondence to :
Reham Raouf (rehamraouf@foc.cu.edu.eg)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In recent years, many methods have been proposed to forecast data in different fields based on successful fuzzy time series models (FTS). Egyptian social insurance systems (SISs) need support to optimally define and estimate yearly total benefits (pensions), which helps the actuaries who are responsible for the system make optimal decisions. Given that the total benefits have not been forecasted before by prediction methods, this paper proposes FTS models by Chen, Cheng, Yu, and Song to forecast Egyptian social insurance benefits, proposes Huarng for appropriate partition lengths, and constructs the interval length using the difference in the transformation data method, given that the data has not been stationary in recent years and has increased significantly. The proposed approach is based on experiments implemented using four models with interval length partitions of 5, 10, 50, 100, and Huarng partitions of 465. The results show great progress in the performance of yearly benefit forecasting, especially in the Chen model with a Huarng 465 partition, which has high accuracy prediction with low error when training and testing data.
Keywords: Fuzzy time series, Social insurance, Benefits, Pensions
Conflict of Interest
No potential conflict of interest relevant to this article was reported.
Biographies
E-mail: rehamraouf@foc.cu.edu.eg
E-mail: saad.elsaieed@hotmail.com
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Original Article
International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(2): 169-182
Published online June 25, 2022 https://doi.org/10.5391/IJFIS.2022.22.2.169
Copyright © The Korean Institute of Intelligent Systems.
Using Fuzzy Time Series Models to Estimate the Cost of Benefits of Egyptian Social Insurance System
Reham Raouf and Saad Elsaieed
Department of Insurance & Actuarial Sciences, Faculty of Commerce, Cairo University, Cairo, Egypt
Correspondence to:Reham Raouf (rehamraouf@foc.cu.edu.eg)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In recent years, many methods have been proposed to forecast data in different fields based on successful fuzzy time series models (FTS). Egyptian social insurance systems (SISs) need support to optimally define and estimate yearly total benefits (pensions), which helps the actuaries who are responsible for the system make optimal decisions. Given that the total benefits have not been forecasted before by prediction methods, this paper proposes FTS models by Chen, Cheng, Yu, and Song to forecast Egyptian social insurance benefits, proposes Huarng for appropriate partition lengths, and constructs the interval length using the difference in the transformation data method, given that the data has not been stationary in recent years and has increased significantly. The proposed approach is based on experiments implemented using four models with interval length partitions of 5, 10, 50, 100, and Huarng partitions of 465. The results show great progress in the performance of yearly benefit forecasting, especially in the Chen model with a Huarng 465 partition, which has high accuracy prediction with low error when training and testing data.
Keywords: Fuzzy time series, Social insurance, Benefits, Pensions
Fig 1.
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FTS model steps.
Fig 2.
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Plots of total benefits (in millions).
Fig 3.
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Yearly transformation difference.
Fig 4.
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Training and testing prediction.
Fig 5.
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Partitions of interval lengths (training dataset): (a) partition 5, (b) partition 10, (c) partition 50, (d) partition 100, and (e) Huarng 465.
Fig 6.
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Network FLR rules.
Fig 7.
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Training accuracy of the four models: (a) RMSE, (b) MAPE, (c) SMAPE, and (d) Thiel’s coefficient.
Fig 8.
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Testing accuracy of the four models: (a) RMSE, (b) MAPE, (c) SMAPE, and (d) Thiel’s coefficient.
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Table 1 . Range of interval.
Range Base 0.1–1.0 0.1 1.1–10 1 11–100 10 101–1000 100
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Table 2 . Total benefits dataset.
Year Government sector Public & private sector Total benefits in millions Difference Year Government sector Public & private sector Total benefits in millions Difference 1976 121 57 179 0 1977 145 40 185 6 1978 162 51 214 29 1979 195 68 264 50 1980 243 105 348 84 1981 207 121 328 −20 1982 401 351 753 425 1983 436 424 861 108 1984 557 485 1042 181 1985 641 553 1194 152 1986 779 631 1410 216 1987 841 688 1529 119 1988 1013 823 1837 308 1989 1275 969 2244 407 1990 1417 1133 2551 307 1991 1714 1386 3100 549 1992 2037 1705 3743 643 1993 2353 2084 4438 695 1994 3019 2562 5582 1144 1995 3587 3000 6587 1005 1996 4107 3469 7577 990 1997 4810 4090 8901 1324 1998 5252 5003 10255 1354 1999 6034 5845 11880 1625 2000 6689 6797 13487 1607 2001 7742 7563 15305 1818 2002 9590 8314 17904 2599 2003 10791 8996 19787 1818 2004 12240 9756 21996 1818 2005 13988 10590 24578 2599 2006 15441 12865 28306 3728 2007 16867 13398 30265 1959 2008 19311 15170 34481 4216 2009 19488 18139 37627 3146 2010 22660 18456 41116 3489 2011 28724 22124 50848 9732 2012 35568 28164 63732 12884 2013 33640 35777 69417 5685 2014 40558 43175 83733 14316 2015 48554 51816 100370 16637 2016 55495 59169 114664 14294 2017 62300 67600 129900 15236 2018 72800 77600 150400 20500 2019 85700 92800 178500 28100
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Table 3 . Dataset training fuzzyfied and FLR group rules.
Year Benefits Difference Fuzzyfied FLR Group Defuzzification Forecasting value 1976 179 0 A 0→ A 0,A 1—— 0 1977 185 6 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 179 622.96 1978 214 29 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 185 628.96 1979 264 50 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 214 657.96 1980 348 84 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 264 707.96 1981 328 −20 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 348 791.96 1982 753 425 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 328 771.96 1983 861 108 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 753 1196.96 1984 1042 181 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 861 1304.96 1985 1194 152 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 1042 1485.96 1986 1410 216 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 1194 1637.96 1987 1529 119 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 1410 1853.96 1988 1837 308 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 1529 1972.96 1989 2244 407 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 1837 2280.96 1990 2551 307 A 0→ A 0,A 1[(−22.0) + (909.9)]/2 + 2244 2687.96 1991 3100 549 A 1→ A 1,A 2[(−22.0) + (909.9)]/2 + 2551 2994.96 1992 3743 643 A 1→ A 1,A 2[(909.9) + (1841.8)]/2 + 3100 4475.88 1993 4438 695 A 1→ A 1,A 2[(909.9) + (1841.8)]/2 + 3743 5118.88 1994 5582 1144 A 1→ A 1,A 2[(909.9) + (1841.8)]/2 + 4438 5813.88 1995 6587 1005 A 1→ A 1,A 2[(909.9) + (1841.8)]/2 + 5582 6957.88 1996 7577 990 A 1→ A 1,A 2[(909.9) + (1841.8)]/2 + 6587 7962.88 1997 8901 1324 A 1→ A 1,A 2[(909.9) + (1841.8)]/2 + 7577 8952.88 1998 10255 1354 A 1→ A 1,A 2[(909.9) + (1841.8)]/2 + 8901 10276.88 1999 11880 1625 A 2→ A 2,A 3,A 4[(909.9) + (1841.8)]/2 + 10255 11630.88 2000 13487 1607 A 2→ A 2,A 3,A 4[(1841.8) + (2773.7) + (3705.6)]/3 + 11880 14653.76 2001 15305 1818 A 2→ A 2,A 3,A 4[(1841.8) + (2773.7) + (3705.6)]/3 + 13487 16260.76 2002 17904 2599 A 3→ A 2,A 4[(1841.8) + (2773.7) + (3705.6)]/3 + 15305 18078.76 2001 15305 1818 A 2→ A 2,A 3,A 4[(1841.8) + (3705.6)]/2 + 17904 20677.76 2001 15305 1818 A 2→ A 2,A 3,A 4[(1841.8) + (2773.7) + (3705.6)]/3 + 15305 22560.76 2002 17904 2599 A 3→ A 2,A 4[(1841.8) + (2773.7) + (3705.6)]/3 + 15305 24769.76 2006 28306 3728 A 4→ A 2[(1841.8) + (3705.6)]/2 + 17904 27351.76 2007 30265 1959 A 2→ A 2,A 3,A 41841.8 + 28306 30147.84 2008 34481 4216 A 4→ A 2[(1841.8) + (2773.7) + (3705.6)]/3 + 30265 33038.76 2009 37627 3146 A 4→ A 21841.8 + 34481 36322.84 2010 41116 3489 A 4→ A 21841.8 + 37627 40400.76 2011 50848 9732 A 4→ A 21841.8 + 41116 42957.84 2012 63732 12884 A 4→ A 21841.8 + 50848 52689.84 2013 69417 5685 A 4→ A 21841.8 + 63732 65573.84 2014 83733 14316 A 4→ A 21841.8 + 69417 71258.84 2015 100370 16637 A 4→ A 21841.8 + 83733 85574.84 2016 114664 14294 A 4→ A 21841.8 + 100370 102211.84 2017 129900 15236 A 4→ A 21841.8 + 114664 116505.84 2018 150400 20500 A 4→ A 21841.8 + 129900 131741.84 2019 178500 28100 A 4→ A 21841.8 + 150400 152241.84 1841.8 + 178500 180341.84
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Table 4 . Training accuracy.
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Table 5 . Testing accuracy.
