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02-12-2021 | Original Paper

Fuzzy time series forecasting based on hesitant fuzzy sets, particle swarm optimization and support vector machine-based hybrid method

Authors: Manish Pant, Sanjay Kumar

Published in: Granular Computing | Issue 4/2022

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Abstract

In this paper, we propose hesitant fuzzy sets-based hybrid time series forecasting method using particle swarm optimization and support vector machine. Length of unequal intervals, weights of intervals and process of defuzzification are major factors that affect the forecasting accuracy of hesitant fuzzy sets-based time series models. The proposed hybrid fuzzy time series forecasting method uses hesitant fuzzy sets which are constructed using fuzzy sets with equal and unequal length intervals. Particle swarm optimization and linear programming are used to optimize length of unequal intervals and weights of equal and unequal intervals. The proposed hybrid method of time series forecasting uses support vector machine for setting input-target pattern for defuzzification. Outperformance of proposed hybrid method of time series forecasting method is revealed by applying it on widely used time series data of enrollments of the University of Alabama, market share price of State Bank of India share at Bombay stock exchange and car sell in Quebec City of Canada. Validity of the proposed hybrid fuzzy time series forecasting method is verified using values of Willmott index and tracking signal.

previous article Multiattribute decision-making by logarithmic operational laws in interval neutrosophic environments

next article Signed distance-based closeness coefficients approach for solving inverse non-linear programming models for multiple criteria group decision-making using interval Type-2 pythagorean fuzzy numbers

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Abhishekh, Gautam SS, Singh SR (2018) A score function-based method of forecasting using intuitionistic fuzzy time series. New Math Nat Comput 14:91–111. https://doi.org/10.1142/S1793005718500072MathSciNetCrossRef

Aladag CH, Basaran MA, Egrioglu E et al (2009) Forecasting in high order fuzzy times series by using neural networks to define fuzzy relations. Expert Syst Appl 36:4228–4231. https://doi.org/10.1016/J.ESWA.2008.04.001CrossRef

Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRef

Atanassov KT (1999) Intuitionistic fuzzy sets: theory and applications

Bas E, Grosan C, Egrioglu E, Yolcu U (2018) High order fuzzy time series method based on pi-sigma neural network. Eng Appl Artif Intell 72:350–356. https://doi.org/10.1016/J.ENGAPPAI.2018.04.017CrossRef

Bisht K, Kumar S (2016) Fuzzy time series forecasting method based on hesitant fuzzy sets. Expert Syst Appl 64:557–568. https://doi.org/10.1016/j.eswa.2016.07.044CrossRef

Bisht K, Kumar S (2018) Intuitionistic fuzzy set-based computational method for financial time series forecasting. Fuzzy Inf Eng 10:307–323. https://doi.org/10.1080/16168658.2019.1631557CrossRef

Bisht K, Kumar S (2019) Hesitant fuzzy set based computational method for financial time series forecasting. Granul Comput 4:655–669. https://doi.org/10.1007/s41066-018-00144-4CrossRef

Cao L (2003) Support vector machines experts for time series forecasting. Neurocomputing 51:321–339. https://doi.org/10.1016/S0925-2312(02)00577-5CrossRef

Chen SM (1996) Forecasting enrollments based on fuzzy time series. Fuzzy Sets Syst 81:311–319. https://doi.org/10.1016/0165-0114(95)00220-0CrossRef

Chen SM (2002) Forecasting enrollments based on high-order fuzzy time series. Cybern Syst 33:1–16. https://doi.org/10.1080/019697202753306479CrossRefMATH

Chen MY (2014) A high-order fuzzy time series forecasting model for internet stock trading. Futur Gener Comput Syst 37:461–467. https://doi.org/10.1016/J.FUTURE.2013.09.025CrossRef

Chen SM, Hsu CC (2008) A new approach for handling forecasting problems using high-order fuzzy time series. Intell Autom Soft Comput 14:29–43. https://doi.org/10.1080/10798587.2008.10642980CrossRef

Chen SM, Jian WS (2017) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups, similarity measures and PSO techniques. Inf Sci 391–392:65–79. https://doi.org/10.1016/J.INS.2016.11.004CrossRef

Chen SM, Kao PY (2013) TAIEX forecasting based on fuzzy time series, particle swarm optimization techniques and support vector machines. Inf Sci 247:62–71. https://doi.org/10.1016/j.ins.2013.06.005MathSciNetCrossRef

Chen SM, Phuong BDH (2017) Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Knowl Based Syst 118:204–216. https://doi.org/10.1016/J.KNOSYS.2016.11.019CrossRef

Chen SM, Wang NY (2010) Fuzzy forecasting based on fuzzy-trend logical relationship groups. IEEE Trans Syst Man Cybern Part B Cybern 40:1343–1358. https://doi.org/10.1109/TSMCB.2009.2038358CrossRef

Chen SM, Manalu GMT, Pan JS, Liu HC (2013) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and particle swarm optimization techniques. IEEE Trans Cybern 43:1102–1117. https://doi.org/10.1109/TSMCB.2012.2223815CrossRef

Chen YH, Hong W-C, Shen W, Huang NN (2016) Electric load forecasting based on a least squares support vector machine with fuzzy time series and global harmony search algorithm. Energies 9:70. https://doi.org/10.3390/EN9020070CrossRef

Chen SM, Zou XY, Gunawan GC (2019) Fuzzy time series forecasting based on proportions of intervals and particle swarm optimization techniques. Inf Sci 500:127–139. https://doi.org/10.1016/J.INS.2019.05.047MathSciNetCrossRef

Cheng CH, Chang JR, Yeh CA (2006) Entropy-based and trapezoid fuzzification-based fuzzy time series approaches for forecasting IT project cost. Technol Forecast Soc Change 73:524–542. https://doi.org/10.1016/J.TECHFORE.2005.07.004CrossRef

Cheng CH, Cheng GW, Wang JW (2008) Multi-attribute fuzzy time series method based on fuzzy clustering. Expert Syst Appl 34:1235–1242. https://doi.org/10.1016/J.ESWA.2006.12.013CrossRef

Egrioglu E (2014) PSO-based high order time invariant fuzzy time series method: application to stock exchange data. Econ Model 38:633–639. https://doi.org/10.1016/J.ECONMOD.2014.02.017CrossRef

Egrioglu E, Yolcu U, Bas E (2019) Intuitionistic high-order fuzzy time series forecasting method based on pi-sigma artificial neural networks trained by artificial bee colony. Granular Computing 4(4) 639–654. https://doi.org/10.1007/s41066-018-00143-5CrossRef

Egrioglu E, Fildes R, Bas E (2021) Recurrent fuzzy time series functions approaches for forecasting. Granul Comput. https://doi.org/10.1007/s41066-021-00257-3CrossRef

Gangwar SS, Kumar S (2012) Partitions based computational method for high-order fuzzy time series forecasting. Expert Syst Appl 39:12158–12164. https://doi.org/10.1016/j.eswa.2012.04.039CrossRef

Gangwar SS, Kumar S (2014) Probabilistic and intuitionistic fuzzy sets-based method for fuzzy time series forecasting. Cybern Syst 45:349–361. https://doi.org/10.1080/01969722.2014.904135CrossRefMATH

Gangwar SS, Kumar S (2015) Computational method for high-order weighted fuzzy time series forecasting based on multiple partitions. Springer Proc Math Stat 125:293–302. https://doi.org/10.1007/978-81-322-2301-6_22CrossRefMATH

Gangwar SS, Kumar S (2016) Cumulative probability distribution based computational method for high order fuzzy time series forecasting. Front Artif Intell Appl 293:3–10. https://doi.org/10.3233/978-1-61499-722-1-3CrossRef

Gautam SS, Abhishekh, Singh SR (2020) A modified weighted method of time series forecasting in intuitionistic fuzzy environment. Opsearch 57:1022–1041. https://doi.org/10.1007/S12597-020-00455-8MathSciNetCrossRefMATH

Gupta KK, Kumar S (2018) Hesitant probabilistic fuzzy set based time series forecasting method. Granul Comput 4:739–758. https://doi.org/10.1007/S41066-018-0126-1CrossRef

Gupta KK, Kumar S (2019) A novel high-order fuzzy time series forecasting method based on probabilistic fuzzy sets. Granul Comput 4:699–713. https://doi.org/10.1007/s41066-019-00168-4CrossRef

Hsu LY, Horng SJ, Kao TW, Chen YH, Run RS, Chen RJ, Lai JL, Kuo IH (2010) Temperature prediction and TAIFEX forecasting based on fuzzy relationships and MTPSO techniques. Expert Syst Appl 37:2756–2770. https://doi.org/10.1016/J.ESWA.2009.09.015CrossRef

Huang W, Nakamori Y, Wang SY (2005) Forecasting stock market movement direction with support vector machine. Comput Oper Res 32:2513–2522. https://doi.org/10.1016/J.COR.2004.03.016CrossRefMATH

Huang YL, Horng SJ, He M, Fan P, Kao TW, Khan MK, Lai JL, Kuo IH (2011) A hybrid forecasting model for enrollments based on aggregated fuzzy time series and particle swarm optimization. Expert Syst Appl 38:8014–8023. https://doi.org/10.1016/J.ESWA.2010.12.127CrossRef

Huarng K (2001) Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets Syst 123:387–394. https://doi.org/10.1016/S0165-0114(00)00057-9MathSciNetCrossRefMATH

Huarng K, Yu THK (2006) Ratio-based lengths of intervals to improve fuzzy time series forecasting. IEEE Trans Syst Man Cybern Part B Cybern 36:328–340. https://doi.org/10.1109/TSMCB.2005.857093CrossRef

Iqbal S, Zhang C (2020) A new hesitant fuzzy-based forecasting method integrated with clustering and modified smoothing approach. Int J Fuzzy Syst 22:1104–1117. https://doi.org/10.1007/s40815-020-00829-6CrossRef

Joshi BP, Kumar S (2012) Intuitionistic fuzzy sets based method for fuzzy time series forecasting. Cybern Syst 43:34–47. https://doi.org/10.1080/01969722.2012.637014CrossRefMATH

Kennedy J, Eberhart R (1995) Particle swarm optimization. Proc ICNN’95 Int Conf Neural Networks 4:1942–1948. https://doi.org/10.1109/ICNN.1995.488968CrossRef

Kocak C, Egrioglu E, Bas E (2020) A new deep intuitionistic fuzzy time series forecasting method based on long short-term memory. J Supercomput 77:6178–6196. https://doi.org/10.1007/S11227-020-03503-8CrossRef

Kocak C, Egrioglu E, Bas E (2021) A new explainable robust high order intuitionistic fuzzy time series method. https://doi.org/10.21203/rs.3.rs-410407/v1

Kumar S, Gangwar SS (2016) Intuitionistic fuzzy time series: an approach for handling nondeterminism in time series forecasting. IEEE Trans Fuzzy Syst 24:1270–1281. https://doi.org/10.1109/TFUZZ.2015.2507582CrossRef

Kuo IH, Horng SJ, Chen YH, Run RS, Kao TW, Chen RJ, Lai JL, Lin TL (2010) Forecasting TAIFEX based on fuzzy time series and particle swarm optimization. Expert Syst Appl 37:1494–1502. https://doi.org/10.1016/J.ESWA.2009.06.102CrossRef

Lee LW, Wang LH, Chen SM (2008) Temperature prediction and TAIFEX forecasting based on high-order fuzzy logical relationships and genetic simulated annealing techniques. Expert Syst Appl 34:328–336. https://doi.org/10.1016/J.ESWA.2006.09.007CrossRef

Pant M, Kumar S (2021) Particle swarm optimization and intuitionistic fuzzy set-based novel method for fuzzy time series forecasting. Granul Comput 2021:1–19. https://doi.org/10.1007/S41066-021-00265-3CrossRef

Pant M, Shukla AK, Kumar S (2021) A novel method to optimize interval length for intuitionistic fuzzy time series. In: Tiwari A, Ahuja K, Yadav A, Bansal JC, Deep K, Nagar AK (eds) Soft computing for problem solving. Advances in intelligent systems and computing, vol 1393. Springer, Singapore. https://doi.org/10.1007/978-981-16-2712-5_5CrossRef

Park JI, Lee DJ, Song CK, Chun MG (2010) TAIFEX and KOSPI 200 forecasting based on two-factors high-order fuzzy time series and particle swarm optimization. Expert Syst Appl 37:959–967. https://doi.org/10.1016/J.ESWA.2009.05.081CrossRef

Pathak HK, Singh P (2011) A new bandwidth interval based forecasting method for enrollments using fuzzy time series. Appl Math 2:504–507. https://doi.org/10.4236/am.2011.24065CrossRef

Pattanayak RM, Panigrahi S, Behera HS (2020) High-order fuzzy time series forecasting by using membership values along with data and support vector machine. Arab J Sci Eng 45:10311–10325. https://doi.org/10.1007/s13369-020-04721-1CrossRef

Pattanayak RM, Behera HS, Panigrahi S (2021) A novel probabilistic intuitionistic fuzzy set based model for high order fuzzy time series forecasting. Eng Appl Artif Intell 99:104136. https://doi.org/10.1016/j.engappai.2020.104136CrossRef

Qiu W, Liu X, Li H (2011) A generalized method for forecasting based on fuzzy time series. Expert Syst Appl 38:10446–10453. https://doi.org/10.1016/J.ESWA.2011.02.096CrossRef

Shuai Y, Song T, Wang J (2017) Integrated parallel forecasting model based on modified fuzzy time series and SVM. J Syst Eng Electron 28:766–775. https://doi.org/10.21629/JSEE.2017.04.16CrossRef

Singh P (2020) A novel hybrid time series forecasting model based on neutrosophic-PSO approach. Int J Mach Learn Cybern 118(11):1643–1658. https://doi.org/10.1007/S13042-020-01064-ZCrossRef

Singh P, Borah B (2014) Forecasting stock index price based on M-factors fuzzy time series and particle swarm optimization. Int J Approx Reason 55:812–833. https://doi.org/10.1016/J.IJAR.2013.09.014MathSciNetCrossRefMATH

Song Q, Chissom BS (1993a) Fuzzy time series and its models. Fuzzy Sets Syst 54:269–277. https://doi.org/10.1016/0165-0114(93)90372-OMathSciNetCrossRefMATH

Song Q, Chissom BS (1993b) Forecasting enrollments with fuzzy time series—Part I. Fuzzy Sets Syst 54:1–9. https://doi.org/10.1016/0165-0114(93)90355-LCrossRef

Tay FEH, Cao LJ (2001a) Application of support vector machines in financial time series forecasting. Omega 29:309–317. https://doi.org/10.1016/S0305-0483(01)00026-3CrossRef

Tay FEH, Cao LJ (2001b) Improved financial time series forecasting by combining Support Vector Machines with self-organizing feature map. Intell Data Anal 5:339–354. https://doi.org/10.3233/IDA-2001-5405CrossRefMATH

Tay FEH, Cao LJ (2002) Modified support vector machines in financial time series forecasting. Neurocomputing 48:847–861. https://doi.org/10.1016/S0925-2312(01)00676-2CrossRefMATH

Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539. https://doi.org/10.1002/INT.20418CrossRefMATH

Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. IEEE Int Conf Fuzzy Syst. https://doi.org/10.1109/FUZZY.2009.5276884CrossRefMATH

Vapnik V (1995) The nature of statistical learning theory. Springer, BerlinCrossRef

Wang Y, Lei Y, Fan X, Wang Y (2016) Intuitionistic fuzzy time series forecasting model based on intuitionistic fuzzy reasoning. Math Probl Eng. https://doi.org/10.1155/2016/5035160MathSciNetCrossRefMATH

Willmort CJ (1981) On the validation of models. Physical geography 184–194. https://doi.org/10.1080/02723646.1981.10642213

Yolcu U, Egrioglu E, Uslu VR, Basaran MA, Aladag C (2009) A new approach for determining the length of intervals for fuzzy time series. Appl Soft Comput 9:647–651. https://doi.org/10.1016/J.ASOC.2008.09.002CrossRefMATH

Yolcu O, Yolcu U, Egrioglu E, Aladag CH (2016) High order fuzzy time series forecasting method based on an intersection operation. Appl Math Model 40:8750–8765. https://doi.org/10.1016/J.APM.2016.05.012MathSciNetCrossRefMATH

Zadeh LA (1965) Fuzzy set. Inf Control 8:338–353. https://doi.org/10.1109/TFUZZ.2012.2188897CrossRefMATH

Zeng S, Chen SM, Teng MO (2019) Fuzzy forecasting based on linear combinations of independent variables, subtractive clustering algorithm and artificial bee colony algorithm. Inf Sci 484:350–366. https://doi.org/10.1016/J.INS.2019.01.071CrossRef

Zhiqiang G, Huaiqing W, Quan L (2012) Financial time series forecasting using LPP and SVM optimized by PSO. Soft Comput 17:805–818. https://doi.org/10.1007/S00500-012-0953-YCrossRef

Title: Fuzzy time series forecasting based on hesitant fuzzy sets, particle swarm optimization and support vector machine-based hybrid method
Authors: Manish Pant
Sanjay Kumar
Publication date: 02-12-2021
Publisher: Springer International Publishing
Published in: Granular Computing / Issue 4/2022
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI: https://doi.org/10.1007/s41066-021-00300-3

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