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Time series forecasting using fuzzy cognitive maps: a survey

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Abstract

Among various soft computing approaches for time series forecasting, fuzzy cognitive maps (FCMs) have shown remarkable results as a tool to model and analyze the dynamics of complex systems. FCMs have similarities to recurrent neural networks and can be classified as a neuro-fuzzy method. In other words, FCMs are a mixture of fuzzy logic, neural network, and expert system aspects, which act as a powerful tool for simulating and studying the dynamic behavior of complex systems. The most interesting features are knowledge interpretability, dynamic characteristics and learning capability. The goal of this survey paper is mainly to present an overview on the most relevant and recent FCM-based time series forecasting models proposed in the literature. In addition, this article considers an introduction on the fundamentals of FCM model and learning methodologies. Also, this survey provides some ideas for future research to enhance the capabilities of FCM in order to cover some challenges in the real-world experiments such as handling non-stationary data and scalability issues. Moreover, equipping FCMs with fast learning algorithms is one of the major concerns in this area.

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Notes

  1. Notice that in order to compute the effect of the other concepts \(c_{j}\ne c_{i}\) into \(c_{i}\), we need to perform the summation of terms \(w_{ji}a_{j}(t)\), given that \(w_{ji}\) reflects the causal connection between \(c_{j}\) and \(c_{i}\).

References

  • Aguilar J (2003) A dynamic fuzzy-cognitive-map approach based on random neural networks. Int J Comput Cogn 1(4):91–107

    Google Scholar 

  • Aguilar J (2005) A survey about fuzzy cognitive maps papers. Int J Comput Cogn 3(2):27–33

    Google Scholar 

  • Ahmadi S, Forouzideh N, Yeh C-H, Martin R, Papageorgiou E (2014) A first study of fuzzy cognitive maps learning using cultural algorithm. In: 2014 9th IEEE conference on industrial electronics and applications, 2014, pp 2023–2028. https://doi.org/10.1109/ICIEA.2014.6931502

  • Ahmadi S, Forouzideh N, Alizadeh S, Papageorgiou E (2015) Learning fuzzy cognitive maps using imperialist competitive algorithm. Neural Comput Appl 26(6):1333–1354. https://doi.org/10.1007/s00521-014-1797-4

    Article  Google Scholar 

  • Al-Gunaid MA, Shcherbakov MV, Zadiran KS, Melikov AV (2017) A survey of fuzzy cognitive maps forecasting methods. In: 2017 8th International conference on information, intelligence, systems and applications (IISA), 2017. IEEE, pp 1–6

  • Alizadeh S, Ghazanfari M (2009) Learning FCM by chaotic simulated annealing. Chaos Solitons Fractals 41(3):1182–1190

    Google Scholar 

  • Alizadeh S, Ghazanfari M, Jafari M, Hooshmand S (2007) Learning FCM by Tabu search. Int J Comput Sci 2(2):142–149

    Google Scholar 

  • Alves M, Silva P, Severiano C Jr, Vieira G, Guimarães F, Sadaei H (2018) An extension of nonstationary fuzzy sets to heteroskedastic fuzzy time series. In: 26th European symposium on artificial neural networks, computational intelligence and machine learning, 2018

  • Amirkhani A, Papageorgiou EI, Mohseni A, Mosavi MR (2017a) A review of fuzzy cognitive maps in medicine: taxonomy, methods, and applications. Comput Methods Programs Biomed 142:129–145

    Google Scholar 

  • Amirkhani A, Papageorgiou E, Mohseni A, Mosavi M (2017b) A review of fuzzy cognitive maps in medicine: taxonomy, methods, and applications. Comput Methods Programs Biomed 142:129–145. https://doi.org/10.1016/j.cmpb.2017.02.021

    Article  Google Scholar 

  • Andreou A, Mateou N, Zombanakis G (2003) Evolutionary fuzzy cognitive maps: a hybrid system for crisis management and political decision making. In: International conference on computational intelligence for modelling, control and automation, 2003

  • Andreou A, Mateou N, Zombanakis G (2005) Soft computing for crisis management and political decision making: the use of genetically evolved fuzzy cognitive maps. Soft Comput 9:194–210. https://doi.org/10.1007/s00500-004-0344-0

    Article  Google Scholar 

  • Axelrod R (ed) (1976) Structure of decision: the cognitive maps of political elites. Princeton Legacy Library

  • Bağdatli MEC, Şakir Dokuz A (2021) Modeling discretionary lane-changing decisions using an improved fuzzy cognitive map with association rule mining. Transp Lett 13(8):623–633. https://doi.org/10.1080/19427867.2021.1919469

    Article  Google Scholar 

  • Baykasoğlu A, Durmusoglu ZDU, Kaplanoglu V (2011) Training fuzzy cognitive maps via extended great deluge algorithm with applications. Comput Ind 62:187–195

    Google Scholar 

  • Beena P, Ganguli R (2011a) Structural damage detection using fuzzy cognitive maps and Hebbian learning. Appl Soft Comput 11:1014–1020

    Google Scholar 

  • Beena P, Ganguli R (2011b) Structural damage detection using fuzzy cognitive maps and Hebbian learning. Appl Soft Comput 11(1):1014–1020

    Google Scholar 

  • Bose M, Mali K (2019) Designing fuzzy time series forecasting models: a survey. Int J Approx Reason 111:78–99

    MathSciNet  MATH  Google Scholar 

  • Boutalis Y, Kottas TL, Christodoulou M (2009) Adaptive estimation of fuzzy cognitive maps with proven stability and parameter convergence. IEEE Trans Fuzzy Syst 17(4):874–889

    Google Scholar 

  • Bueno S, Salmeron JL (2009) Benchmarking main activation functions in fuzzy cognitive maps. Expert Syst Appl 36(3):5221–5229

    Google Scholar 

  • Cai Y, Miao C, Tan A-H, Shen Z, Li B (2009) Creating an immersive game world with evolutionary fuzzy cognitive maps. IEEE Comput Graph Appl 30(2):58–70

    Google Scholar 

  • Carvalho J, Tomé J (2001) Rule based fuzzy cognitive maps—expressing time in qualitative system dynamics. In: 10th IEEE international conference on fuzzy systems, 2001, vol 1, pp 280–283. https://doi.org/10.1109/FUZZ.2001.1007303

  • Carvalho J, Tomé J (2007) Qualitative optimization of fuzzy causal rule bases using fuzzy boolean nets. Fuzzy Sets Syst 158:1931–1946. https://doi.org/10.1016/j.fss.2007.04.018

    Article  MathSciNet  MATH  Google Scholar 

  • Chen Y, Mazlack L, Lu L (2012) Inferring fuzzy cognitive map models for gene regulatory networks from gene expression data. In: 2012 IEEE international conference on bioinformatics and biomedicine, 2012, pp 1–4. https://doi.org/10.1109/BIBM.2012.6392627

  • Chen Y, Mazlack LJ, Minai AA, Lu LJ (2015) Inferring causal networks using fuzzy cognitive maps and evolutionary algorithms with application to gene regulatory network reconstruction. Appl Soft Comput 37:667–679

    Google Scholar 

  • Chi Y, Liu J (2014) Learning large-scale fuzzy cognitive maps using a hybrid of memetic algorithm and neural network. In: 2014 IEEE international conference on fuzzy systems (FUZZ-IEEE), 2014, pp 1036–1040. https://doi.org/10.1109/FUZZ-IEEE.2014.6891604

  • Chi Y, Liu J (2015) Learning of fuzzy cognitive maps with varying densities using a multiobjective evolutionary algorithm. IEEE Trans Fuzzy Syst 24:1–1. https://doi.org/10.1109/TFUZZ.2015.2426314

    Article  Google Scholar 

  • Chunmei L, Yue H (2012) Cellular automata learning of fuzzy cognitive map. In: 2012 International conference on system science and engineering (ICSSE), 2012, pp 334–338. https://doi.org/10.1109/ICSSE.2012.6257202

  • Chunying Z, Lu L, Dong O, Ruitao L (2011) Research of rough cognitive map model. Commun Comput Inf Sci. https://doi.org/10.1007/978-3-642-20370-1_37

    Article  Google Scholar 

  • de Lima Silva PC, Sadaei HJ, Ballini R, Guimarães FG (2019) Probabilistic forecasting with fuzzy time series. IEEE Trans Fuzzy Syst 28(8):1771–1784

    Google Scholar 

  • de Lima e Silva PC, Severiano CA, Alves MA, Silva R, Cohen MW, Guimarães FG (2020) Forecasting in non-stationary environments with fuzzy time series. Appl Soft Comput 97:106825. https://doi.org/10.1016/j.asoc.2020.106825

    Article  Google Scholar 

  • de Silva PCL, Alves MA, Alberto C, Junior S, Vieira GL, Guimaraes FG, Sadaei HJ (2017) Probabilistic forecasting with seasonal ensemble fuzzy time-series. In: XIII Brazilian congress on computational intelligence, 2017, Rio de Janeiro

  • Dickerson JA, Kosko B (1993) Virtual worlds as fuzzy cognitive maps. In: Proceedings of the 1993 IEEE virtual reality annual international symposium, VRAIS ’93, 1993. IEEE Computer Society, pp 471–477. https://doi.org/10.1109/VRAIS.1993.380742

  • Dickerson J, Kosko B (1994) Virtual worlds as fuzzy cognitive maps. Presence 3:173–189. https://doi.org/10.1162/pres.1994.3.2.173

    Article  Google Scholar 

  • Ding F, Luo C (2022) Interpretable cognitive learning with spatial attention for high-volatility time series prediction. Appl Soft Comput 117:108447

    Google Scholar 

  • Ding Z, Li D, Jia J (2011) First study of fuzzy cognitive map learning using ants colony optimization. J Comput Inf Syst 7:4756–4763

    Google Scholar 

  • Eden C (2004) Analyzing cognitive maps to help structure issues or problems. Eur J Oper Res 159(3):673–686. https://doi.org/10.1016/S0377-2217(03)00431-4

    Article  MATH  Google Scholar 

  • Eden C, Ackermann F (2004) Cognitive mapping expert views for policy analysis in the public sector. Eur J Oper Res 152:615–630. https://doi.org/10.1016/S0377-2217(03)00061-4

    Article  MATH  Google Scholar 

  • Eden C, Ackermann F, Cropper S (1992) The analysis of cause maps. J Manag Stud 29(3):309–324. https://doi.org/10.1111/j.1467-6486.1992.tb00667.x

    Article  Google Scholar 

  • Felix G, Nápoles G, Falcon R, Froelich W, Vanhoof K, Bello R (2019) A review on methods and software for fuzzy cognitive maps. Artif Intell Rev 52(3):1707–1737

    Google Scholar 

  • Feng G, Lu W, Pedrycz W, Yang J, Liu X (2021a) The learning of fuzzy cognitive maps with noisy data: a rapid and robust learning method with maximum entropy. IEEE Trans Cybern 51:2080–2092

    Google Scholar 

  • Feng G, Lu W, Yang J (2021b) The modeling of time series based on least square fuzzy cognitive map. Algorithms. https://doi.org/10.3390/a14030069

    Article  Google Scholar 

  • Feng G, Zhang L, Yang J, Lu W (2021c) Long-term prediction of time series using fuzzy cognitive maps. Eng Appl Artif Intell 102:104274

    Google Scholar 

  • Feng G, Lu W, Yang J (2021d) Time series modeling with fuzzy cognitive maps based on partitioning strategies. In: 2021 IEEE international conference on fuzzy systems (FUZZ-IEEE), 2021, pp 1–6. https://doi.org/10.1109/FUZZ45933.2021.9494479

  • Froelich W, Juszczuk P (2009) Predictive capabilities of adaptive and evolutionary fuzzy cognitive maps—a comparative study. In: Intelligent systems for knowledge management. Springer, Berlin, pp 153–174

  • Froelich W, Papageorgiou EI (2014) Extended evolutionary learning of fuzzy cognitive maps for the prediction of multivariate time-series. In: Fuzzy cognitive maps for applied sciences and engineering. Springer, Berlin, pp 121–131

  • Froelich W, Pedrycz W (2016) Fuzzy cognitive maps in the modeling of granular time series. Knowl Based Syst. https://doi.org/10.1016/j.knosys.2016.10.017

    Article  Google Scholar 

  • Froelich W, Salmeron JL (2014) Evolutionary learning of fuzzy Grey cognitive maps for the forecasting of multivariate, interval-valued time series. Int J Approx Reason 55(6):1319–1335. https://doi.org/10.1016/j.ijar.2014.02.006

    Article  MathSciNet  Google Scholar 

  • Froelich W, Papageorgiou EI, Samarinas M, Skriapas K (2012) Application of evolutionary fuzzy cognitive maps to the long-term prediction of prostate cancer. Appl Soft Comput 12:3810–3817

    Google Scholar 

  • Gao R, Du L, Yuen KF (2020) Robust empirical wavelet fuzzy cognitive map for time series forecasting. Eng Appl Artif Intell 96:103978

    Google Scholar 

  • Ghazanfari M, Alizadeh S, Fathian M, Koulouriotis DE (2007) Comparing simulated annealing and genetic algorithm in learning FCM. Appl Math Comput 192(1):56–68

    MathSciNet  MATH  Google Scholar 

  • Glykas M (2010) Fuzzy cognitive maps. In: Advances in theory, methodologies, tools and applications, vol 247. https://doi.org/10.1007/978-3-642-03220-2

  • Gregor M, Groumpos P (2013a) Training fuzzy cognitive maps using gradient-based supervised learning. In: Artificial intelligence applications and innovations. AIAI 2013, 2013, vol 412, pp 547–556. https://doi.org/10.1007/978-3-642-41142-7_55

  • Gregor M, Groumpos PP (2013b) Training fuzzy cognitive maps using gradient-based supervised learning. In: IFIP international conference on artificial intelligence applications and innovations, 2013. Springer, pp 547–556

  • Gregor M, Groumpos P (2013) Tuning the position of a fuzzy cognitive map attractor using backpropagation through time. In: Proceedings of the international conference on integrated modeling and analysis in applied control and automation, 2013, vol 1

  • Groumpos PP (2015) Modelling business and management systems using fuzzy cognitive maps: a critical overview, IFAC-PapersOnLine 48(24):207–212, In: 16th IFAC conference on technology, culture and international stability, TECIS 2015, 2015. https://doi.org/10.1016/j.ifacol.2015.12.084

  • Hajek P, Prochazka O, Froelich W (2018) Interval-valued intuitionistic fuzzy cognitive maps for stock index forecasting. In: 2018 IEEE conference on evolving and adaptive intelligent systems (EAIS), 2018. IEEE, pp 1–7

  • Hajek P, Froelich W, Prochazka O (2020) Intuitionistic fuzzy Grey cognitive maps for forecasting interval-valued time series. Neurocomputing 400:173–185

    Google Scholar 

  • Harmati IÁ, Kóczy LT (2022) Some dynamical properties of higher-order fuzzy cognitive maps. In: Computational intelligence and mathematics for tackling complex problems, vol 3. Springer, Cham, pp 149–156

  • Homenda W, Jastrzebska A (2017) Clustering techniques for fuzzy cognitive map design for time series modeling. Neurocomputing. https://doi.org/10.1016/j.neucom.2016.08.119

    Article  Google Scholar 

  • Homenda W, Jastrzebska A, Pedrycz W (2014a) Modeling time series with fuzzy cognitive maps. In: 2014 IEEE international conference on fuzzy systems (FUZZ-IEEE), 2014, pp 2055–2062. https://doi.org/10.1109/FUZZ-IEEE.2014.6891719

  • Homenda W, Jastrzebska A, Pedrycz W (2014b) Joining concept’s based fuzzy cognitive map model with moving window technique for time series modeling, pp 397–408. https://doi.org/10.1007/978-3-662-45237-0_37

  • Homenda W, Jastrzebska A, Pedrycz W (2014c) Time series modeling with fuzzy cognitive maps: simplification strategies—the case of a posteriori removal of nodes and weights. In: CISIM, 2014

  • Huang D, Shen Z (2013) A curious learning model with ELM for fuzzy cognitive maps. Int J Uncertain Fuzziness Knowl Based Syst. https://doi.org/10.1142/S0218488513400163

    Article  MathSciNet  MATH  Google Scholar 

  • Huerga AV (2002) A balanced differential learning algorithm in fuzzy cognitive maps. In: Proceedings of the 16th international workshop on qualitative reasoning, 2002

  • Iakovidis D, Papageorgiou E (2011) Intuitionistic fuzzy cognitive maps for medical decision making. IEEE Trans Inf Technol Biomed Publ IEEE Eng Med Biol Soc 15:100–7. https://doi.org/10.1109/TITB.2010.2093603

    Article  Google Scholar 

  • Jahangoshai Rezaee M, Yousefi S, Babaei M (2017) Multi-stage cognitive map for failures assessment of production processes: an extension in structure and algorithm. Neurocomputing. https://doi.org/10.1016/j.neucom.2016.10.069

    Article  Google Scholar 

  • Jetter A (2006) Fuzzy cognitive maps for engineering and technology management: what works in practice? In: Technology management for the global future, 2006, pp 498–512. https://doi.org/10.1109/PICMET.2006.296648

  • Juszczuk P, Froelich W (2009) Learning fuzzy cognitive maps using a differential evolution algorithm. Pol J Environ Stud 12(3B):108

    Google Scholar 

  • Ketipi MK, Karakasis EG, Koulouriotis DE, Emiris DM (2020) Multi-criteria decision making using fuzzy cognitive maps—preliminary results. Procedia Manuf 51:1305–1310. In: 30th International conference on flexible automation and intelligent manufacturing (FAIM2021). https://doi.org/10.1016/j.promfg.2020.10.182

  • Kim D-H (2004) Cognitive maps of policy makers on financial crises of South Korea and Malaysia: a comparative study. Int Rev Public Adm 9(2):31–38. https://doi.org/10.1080/12294659.2005.10805047

    Article  Google Scholar 

  • Klein JH, Cooper DF (1982) Cognitive maps of decision-makers in a complex game. J Oper Res Soc 33(1):63–71. https://doi.org/10.1057/jors.1982.7

    Article  Google Scholar 

  • Kok K (2009) The potential of fuzzy cognitive maps for semi-quantitative scenario development, with an example from Brazil. Glob Environ Change 19:122–133. https://doi.org/10.1016/j.gloenvcha.2008.08.003

    Article  Google Scholar 

  • Konar A, Chakraborty UK (2005) Reasoning and unsupervised learning in a fuzzy cognitive map. Inf Sci 170(2–4):419–441

    MathSciNet  MATH  Google Scholar 

  • Kosko B (1986a) Fuzzy cognitive maps. Int J Man–Mach Stud 24(1):65–75. https://doi.org/10.1016/S0020-7373(86)80040-2

    Article  MATH  Google Scholar 

  • Kosko B (1986b) Fuzzy cognitive maps. Int J Man–Mach Stud 24(1):65–75. https://doi.org/10.1016/S0020-7373(86)80040-2

    Article  MATH  Google Scholar 

  • Kottas TL, Boutalis YS, Christodoulou MA (2007) Fuzzy cognitive network: a general framework. Intell Decis Technol 1(4):183–196

    Google Scholar 

  • Kottas TL, Boutalis YS, Christodoulou MA (2010) Fuzzy cognitive networks: adaptive network estimation and control paradigms. In: Fuzzy cognitive maps. Springer, Berlin, pp 89–134

  • Koulouriotis D, Diakoulakis I, Emiris D (2001) Learning fuzzy cognitive maps using evolution strategies: a novel schema for modeling and simulating high-level behavior. In: Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546), 2001, vol 1. IEEE, pp 364–371

  • Kyriakarakos G, Dounis AI, Arvanitis KG, Papadakis G (2012a) A fuzzy cognitive maps-Petri nets energy management system for autonomous polygeneration microgrids. Appl Soft Comput 12(12):3785–3797. https://doi.org/10.1016/j.asoc.2012.01.024

    Article  Google Scholar 

  • Kyriakarakos G, Dounis AI, Arvanitis KG, Papadakis G (2012b) A fuzzy cognitive maps-petri nets energy management system for autonomous polygeneration microgrids. Appl Soft Comput 12(12):3785–3797

    Google Scholar 

  • Laureano-Cruces A, Ramirez J, Teran A (2004) Evaluation of the teaching–learning process with fuzzy cognitive maps. In: Advances in artificial intelligence—IBERAMIA 2004, 2004, vol 3315, pp 922–931. https://doi.org/10.1007/978-3-540-30498-2_92

  • Lee MH, Javedani H et al (2011) A weighted fuzzy integrated time series for forecasting tourist arrivals. In: International conference on informatics engineering and information science, 2011. Springer, pp 206–217

  • Lemke C, Gabrys B (2010) Meta-learning for time series forecasting and forecast combination. Neurocomputing 73(10–12):2006–2016

    Google Scholar 

  • Li S-J, Shen R-M (2004) Fuzzy cognitive map learning based on improved nonlinear Hebbian rule. In: Proceedings of 2004 international conference on machine learning and cybernetics (IEEE Cat. No. 04EX826), 2004, vol 4, IEEE, pp 2301–2306

  • Li X, Ji H, Zheng R, Li Y, Yu F (2009) A novel team-centric peer selection scheme for distributed wireless P2P networks. In: 2009 IEEE wireless communications and networking conference, 2009, pp 1–5. https://doi.org/10.1109/WCNC.2009.4917532

  • Lin C (2009) An immune algorithm for complex fuzzy cognitive map partitioning. In: Proceedings of the first ACM/SIGEVO summit on genetic and evolutionary computation, 2009, pp 315–320

  • Liu L, Liu J (2018) Inferring gene regulatory networks with hybrid of multi-agent genetic algorithm and random forests based on fuzzy cognitive maps. Appl Soft Comput 69:585–598

    Google Scholar 

  • Liu Z, Liu J (2020) A robust time series prediction method based on empirical mode decomposition and high-order fuzzy cognitive maps. Knowl Based Syst 203:106105. https://doi.org/10.1016/j.knosys.2020.106105

    Article  Google Scholar 

  • Liu J, Chi Y, Zhu C (2015) A dynamic multiagent genetic algorithm for gene regulatory network reconstruction based on fuzzy cognitive maps. IEEE Trans Fuzzy Syst 24(2):419–431

    Google Scholar 

  • Liu P, Liu J, Wu K (2020) CNN–FCM: system modeling promotes stability of deep learning in time series prediction. Knowl Based Syst 203:106081. https://doi.org/10.1016/j.knosys.2020.106081

    Article  Google Scholar 

  • López Vargas C, Salmeron J (2014) Dynamic risks modelling in ERP maintenance projects with FCM. Inf Sci. https://doi.org/10.1016/j.ins.2012.05.026

    Article  Google Scholar 

  • Lu W, Yang J, Li Y (2010) Control method based on fuzzy cognitive map and its application on district heating network. https://doi.org/10.1109/ICICIP.2010.5564219

  • Lu W, Yang J, Liu X (2013) The linguistic forecasting of time series based on fuzzy cognitive maps. In: (2013) Joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), 2013. IEEE, pp 649–654

  • Lu W, Yang J, Liu X (2014a) Numerical prediction of time series based on FCMs with information granules. Int J Comput Commun Control 9:313. https://doi.org/10.15837/ijccc.2014.3.210

    Article  Google Scholar 

  • Lu W, Yang J, Liu X, Pedrycz W (2014b) The modeling and prediction of time series based on synergy of high-order fuzzy cognitive map and fuzzy C-means clustering. Knowl Based Syst 70:242–255. https://doi.org/10.1016/j.knosys.2014.07.004

    Article  Google Scholar 

  • Luo X, Wei X, Zhang J (2009) Game-based learning model using fuzzy cognitive map. In: Proceedings of the first ACM international workshop on multimedia technologies for distance learning, MTDL ’09, 2009. Association for Computing Machinery, New York, pp 67–76. https://doi.org/10.1145/1631111.1631123

  • Madeiro S, Von Zuben F (2012) Gradient-based algorithms for the automatic construction of fuzzy cognitive maps. In: 2012 11th International conference on machine learning and applications, 2012, vol 1, pp 344–349. https://doi.org/10.1109/ICMLA.2012.64

  • Makridakis S, Winkler RL (1983) Averages of forecasts: some empirical results. Manag Sci 29(9):987–996

    Google Scholar 

  • Martens M (2002) Measuring and forecasting S&P 500 index-futures volatility using high-frequency data. J Futures Mark 22:497–518. https://doi.org/10.1002/fut.10016

    Article  Google Scholar 

  • Mateou NH, Moiseos M, Andreou AS (2005) Multi-objective evolutionary fuzzy cognitive maps for decision support. In: (2005) IEEE congress on evolutionary computation, 2005, vol 1. IEEE, pp 824–830

  • Miao Y, Liu Z-Q, Siew C, Miao C (2001a) Dynamical cognitive network—an extension of fuzzy cognitive map. IEEE Trans Fuzzy Syst 9:760–770. https://doi.org/10.1109/91.963762

    Article  Google Scholar 

  • Miao Y, Liu Z-Q, Siew CK, Miao CY (2001b) Dynamical cognitive network—an extension of fuzzy cognitive map. IEEE Trans Fuzzy Syst 9(5):760–770

    Google Scholar 

  • Mls K, Cimler R, Vascák J, Puheim M (2017) Interactive evolutionary optimization of fuzzy cognitive maps. Neurocomputing 232:58–68

    Google Scholar 

  • Morris RG, Hebb DO (1999) The organization of behavior, Wiley: New York; 1949. Brain Res Bull 50(5–6):437

    Google Scholar 

  • Nair A, Reckien D, Van Maarseveen M (2019) A generalised fuzzy cognitive mapping approach for modelling complex systems. Appl Soft Comput 84:105754

    Google Scholar 

  • Nannan Z, Chao L (2019) Adaptive online time series prediction based on a novel dynamic fuzzy cognitive map. J Intell Fuzzy Syst 36(6):5291–5303. https://doi.org/10.3233/JIFS-181064

    Article  Google Scholar 

  • Nápoles G, Bello R, Vanhoof K (2014a) How to improve the convergence on sigmoid fuzzy cognitive maps? Intell Data Anal 18:77–88

    Google Scholar 

  • Nápoles G, Grau I, Bello R, Grau R (2014b) Two-steps learning of fuzzy cognitive maps for prediction and knowledge discovery on the HIV-1 drug resistance. Expert Syst Appl 41(3):821–830. https://doi.org/10.1016/j.eswa.2013.08.012

    Article  Google Scholar 

  • Nápoles G, Papageorgiou E, Bello R, Vanhoof K (2016) On the convergence of sigmoid fuzzy cognitive maps. Inf Sci 349:154–171

    MATH  Google Scholar 

  • Nápoles G, Papageorgiou E, Bello R, Vanhoof K (2017) Learning and convergence of fuzzy cognitive maps used in pattern recognition. Neural Process Lett 45(2):431–444

    Google Scholar 

  • Nápoles G, Jastrzebska A, Mosquera C, Vanhoof K, Homenda W (2020) Deterministic learning of hybrid fuzzy cognitive maps and network reduction approaches. Neural Netw 124:258–268

    Google Scholar 

  • Oikonomou P, Papageorgiou EI (2013) Particle swarm optimization approach for fuzzy cognitive maps applied to autism classification. In: IFIP international conference on artificial intelligence applications and innovations, 2013. Springer, pp 516–526

  • Orang O, Silva R, de Lima e Silva PC, Guimarães FG (2020) Solar energy forecasting with fuzzy time series using high-order fuzzy cognitive maps. In: 2020 IEEE international conference on fuzzy systems (FUZZ-IEEE), 2020, pp. 1–8. https://doi.org/10.1109/FUZZ48607.2020.9177767

  • Papageorgiou E (2005) A weight adaptation method for fine-tuning fuzzy cognitive map causal links. Soft Comput 9:846–857

    MATH  Google Scholar 

  • Papageorgiou E (2011a) Learning algorithms for fuzzy cognitive maps—a review study. IEEE Trans Syst Man Cybern C 42(2):150–163

    Google Scholar 

  • Papageorgiou E (2011b) A new methodology for decisions in medical informatics using fuzzy cognitive maps based on fuzzy rule-extraction techniques. Appl Soft Comput 11(1):500–513. https://doi.org/10.1016/j.asoc.2009.12.010

    Article  Google Scholar 

  • Papageorgiou EI (2014) Fuzzy cognitive maps for applied sciences and engineering—from fundamentals to extensions and learning algorithms. Springer, Berlin

    Google Scholar 

  • Papageorgiou EI, Froelich W (2012) Multi-step prediction of pulmonary infection with the use of evolutionary fuzzy cognitive maps. Neurocomputing 92:28–35. https://doi.org/10.1016/j.neucom.2011.08.034

    Article  Google Scholar 

  • Papageorgiou E, Groumpos P (2005a) A weight adaptation method for fuzzy cognitive map learning. Soft Comput 9:846–857. https://doi.org/10.1007/s00500-004-0426-z

    Article  MATH  Google Scholar 

  • Papageorgiou EI, Groumpos PP (2005b) A new hybrid method using evolutionary algorithms to train fuzzy cognitive maps. Appl Soft Comput 5(4):409–431. https://doi.org/10.1016/j.asoc.2004.08.008

    Article  Google Scholar 

  • Papageorgiou E, Poczeta K (2015) Application of fuzzy cognitive maps to electricity consumption prediction. https://doi.org/10.1109/NAFIPS-WConSC.2015.7284139

  • Papageorgiou E, Poczeta K (2017) A two-stage model for time series prediction based on fuzzy cognitive maps and neural networks. Neurocomputing. https://doi.org/10.1016/j.neucom.2016.10.072

    Article  Google Scholar 

  • Papageorgiou EI, Salmeron JL (2012) A review of fuzzy cognitive maps research during the last decade. IEEE Trans Fuzzy Syst 21(1):66–79

    Google Scholar 

  • Papageorgiou E, Stylios C, Groumpos P (2003) Fuzzy cognitive map learning based on nonlinear Hebbian rule. In: Australasian joint conference on artificial intelligence, 2003. Springer, pp 256–268

  • Papageorgiou E, Stylios C, Groumpos P (2004) Active Hebbian learning algorithm to train fuzzy cognitive maps. Int J Approx Reason 37:219–249. https://doi.org/10.1016/j.ijar.2004.01.001

    Article  MathSciNet  MATH  Google Scholar 

  • Papageorgiou EI, Stylios C, Groumpos PP (2006) Unsupervised learning techniques for fine-tuning fuzzy cognitive map causal links. Int J Hum–Comput Stud 64(8):727–743

    Google Scholar 

  • Papageorgiou E, Poczeta K, Laspidou C (2015a) Application of fuzzy cognitive maps to water demand prediction. https://doi.org/10.1109/FUZZ-IEEE.2015.7337973

  • Papageorgiou E, Poczeta K, Yastrebov A, Laspidou C (2015b) Fuzzy cognitive maps and multi-step gradient methods for prediction: applications to electricity consumption and stock exchange returns. In: Intelligent decision technologies. IDT 2017, vol 39, pp 501–511. https://doi.org/10.1007/978-3-319-19857-6_43

  • Papageorgiou EI, Poczeta K, Laspidou C (2016) Hybrid model for water demand prediction based on fuzzy cognitive maps and artificial neural networks. In: 2016 IEEE international conference on fuzzy systems (FUZZ-IEEE), 2016, pp 1523–1530. https://doi.org/10.1109/FUZZ-IEEE.2016.7737871

  • Papageorgiou E, Hatwágner M, Buruzs A, Koczy L (2017) A concept reduction approach for fuzzy cognitive map models in decision making and management. Neurocomputing. https://doi.org/10.1016/j.neucom.2016.11.060

    Article  Google Scholar 

  • Papageorgiou E, Poczeta K, Gerogiannis S (2019) Exploring an ensemble of methods that combines fuzzy cognitive maps and neural networks in solving the time series prediction problem of gas consumption in Greece. Algorithms 12:235. https://doi.org/10.3390/a12110235

    Article  Google Scholar 

  • Papakostas G, Koulouriotis D (2010) Classifying patterns using fuzzy cognitive maps. In: Fuzzy cognitive maps. Springer, Berlin, pp 291–306

  • Papakostas GA, Polydoros AS, Koulouriotis DE, Tourassis VD (2011a) Training fuzzy cognitive maps by using Hebbian learning algorithms: a comparative study. In: 2011 IEEE international conference on fuzzy systems (FUZZ-IEEE 2011), 2011. IEEE, pp 851–858

  • Papakostas GA, Polydoros AS, Koulouriotis DE, Tourassis VD (2011b) Training fuzzy cognitive maps by using Hebbian learning algorithms: a comparative study. In: 2011 IEEE international conference on fuzzy systems (FUZZ-IEEE 2011), 2011, pp 851–858

  • Papakostas G, Polydoros A, Koulouriotis D, Tourassis V (2011c) Training fuzzy cognitive maps by using Hebbian learning algorithms: a comparative study. In: 2011 IEEE international conference on fuzzy systems (FUZZ-IEEE 2011), 2011, pp 851–858. https://doi.org/10.1109/FUZZY.2011.6007544

  • Papakostas G, Koulouriotis D, Polydoros A, Tourassis V (2012) Towards Hebbian learning of fuzzy cognitive maps in pattern classification problems. Expert Syst Appl 39:10620–10629. https://doi.org/10.1016/j.eswa.2012.02.148

    Article  Google Scholar 

  • Park KS, Kim SH (1995) Fuzzy cognitive maps considering time relationships. Int J Hum–Comput Stud 42(2):157–168

    Google Scholar 

  • Parsopoulos KE, Papageorgiou EI, Groumpos PP, Vrahatis MN (2003) A first study of fuzzy cognitive maps learning using particle swarm optimization. In: The 2003 congress on evolutionary computation, 2003. CEC’03, 2003, vol 2, IEEE, pp 1440–1447

  • Pedrycz W, Jastrzebska A, Homenda W (2016) Design of fuzzy cognitive maps for modeling time series. IEEE Trans Fuzzy Syst 24(1):120–130

    MATH  Google Scholar 

  • Petalas Y, Papageorgiou E, Parsopoulos K, Groumpos P, Vrahatis M (2005) Fuzzy cognitive maps learning using memetic algorithms. In: Proceedings of the international conference of “Computational Methods in Sciences and Engineering” (ICCMSE 2005), 2005, pp 1420–1423

  • Poczeta K, Papageorgiou EI (2018) Implementing fuzzy cognitive maps with neural networks for natural gas prediction. In: 2018 IEEE 30th international conference on tools with artificial intelligence (ICTAI), 2018. IEEE, pp 1026–1032

  • Poczeta K, Yastrebov A (2015) Monitoring and prediction of time series based on fuzzy cognitive maps with multi-step gradient methods. In: International conference on automation, 2015. Springer, pp 197–206

  • Poczeta K, Yastrebov A, Papageorgiou EI (2015) Learning fuzzy cognitive maps using structure optimization genetic algorithm. In: (2015) Federated conference on computer science and information systems (FedCSIS), 2015. IEEE, pp 547–554

  • Poczeta K, Papageorgiou EI, Yastrebov A (2018) Application of fuzzy cognitive maps to multi-step ahead prediction of electricity consumption. In: 2018 Conference on electrotechnology: processes, models, control and computer science (EPMCCS), 2018, pp. 1–5. https://doi.org/10.1109/EPMCCS.2018.8596619

  • Poczeta K, Papageorgiou EI, Gerogiannis VC (2020) Fuzzy cognitive maps optimization for decision making and prediction. Mathematics 8(11):2059

    Google Scholar 

  • Rajaram T, Das A (2010) Modeling of interactions among sustainability components of an agro-ecosystem using local knowledge through cognitive mapping and fuzzy inference system. Expert Syst Appl 37(2):1734–1744. https://doi.org/10.1016/j.eswa.2009.07.035

    Article  Google Scholar 

  • Ramirez-Bautista JA, Huerta-Ruelas JA, Kóczy LT, Hatwágner MF, Chaparro-Cárdenas SL, Hernández-Zavala A (2020) Classification of plantar foot alterations by fuzzy cognitive maps against multi-layer perceptron neural network. Biocybern Biomed Eng 40(1):404–414. https://doi.org/10.1016/j.bbe.2019.12.008

    Article  Google Scholar 

  • Ren Z (2012) Learning fuzzy cognitive maps by a hybrid method using nonlinear Hebbian learning and extended great deluge algorithm. In: Proceedings of the 23rd Midwest artificial intelligence and cognitive science conference, MAICS 2012, 2012, p 841

  • Ruan D, Hardeman F, Mkrtchyan L (2011) Using belief degree-distributed fuzzy cognitive maps in nuclear safety culture assessment. Adv Intell Soft Comput 124:1–6. https://doi.org/10.1109/NAFIPS.2011.5751916

    Article  Google Scholar 

  • Sadaei HJ, Guimares FG, Jos da Silva C, Lee MH, Eslami T (2017) Short-term load forecasting method based on fuzzy time series, seasonality and long memory process. Int J Approx Reason 83(C):196–217. https://doi.org/10.1016/j.ijar.2017.01.006

    Article  MathSciNet  MATH  Google Scholar 

  • Salmeron J (2009a) Augmented fuzzy cognitive maps for modelling LMS critical success factors. Knowl Based Syst 22:275–278. https://doi.org/10.1016/j.knosys.2009.01.002

    Article  Google Scholar 

  • Salmeron JL (2009b) Supporting decision makers with fuzzy cognitive maps. Res Technol Manag 52(3):53–59. https://doi.org/10.1080/08956308.2009.11657569

    Article  Google Scholar 

  • Salmeron JL (2010) Modelling Grey uncertainty with fuzzy Grey cognitive maps. Expert Syst Appl 37(12):7581–7588

    Google Scholar 

  • Salmeron JL, Froelich W (2016) Dynamic optimization of fuzzy cognitive maps for time series forecasting. Knowl Based Syst 105(C):29–37. https://doi.org/10.1016/j.knosys.2016.04.023

    Article  Google Scholar 

  • Salmeron J, Papageorgiou E (2012) A fuzzy Grey cognitive maps-based decision support system for radiotherapy treatment planning. Knowl Based Syst 30:151–160. https://doi.org/10.1016/j.knosys.2012.01.008

    Article  Google Scholar 

  • Salmeron J, Papageorgiou E (2014) Fuzzy Grey cognitive maps and nonlinear Hebbian learning in process control. Appl Intell. https://doi.org/10.1007/s10489-013-0511-z

    Article  Google Scholar 

  • Salmeron JL, Mansouri T, Moghadam MRS, Mardani A (2019) Learning fuzzy cognitive maps with modified asexual reproduction optimisation algorithm. Knowl Based Syst 163:723–735

    Google Scholar 

  • Shan D, Lu W, Yang J (2018) The data-driven fuzzy cognitive map model and its application to prediction of time series. Int J Innov Comput Inf Control 14:1583–1602. https://doi.org/10.24507/ijicic.14.05.1583

    Article  Google Scholar 

  • Shanchao Y, Liu J (2018) Time-series forecasting based on high-order fuzzy cognitive maps and wavelet transform. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2018.2831640

    Article  Google Scholar 

  • Shen F, Liu J, Wu K (2020) Evolutionary multitasking fuzzy cognitive map learning. Knowl Based Syst. https://doi.org/10.1016/j.knosys.2019.105294

    Article  Google Scholar 

  • Shen F, Liu J, Wu K (2021) Multivariate time series forecasting based on elastic net and high-order fuzzy cognitive maps: a case study on human action prediction through EEG signals. IEEE Trans Fuzzy Syst 29(8):2336–2348. https://doi.org/10.1109/TFUZZ.2020.2998513

    Article  Google Scholar 

  • Silva PCL (2019) Scalable models for probabilistic forecasting with fuzzy time series. PhD Thesis, UFMG. https://doi.org/10.5281/zenodo.3374641

  • Silva P, Sadaei HJ, Guimarães F (2016) Interval forecasting with fuzzy time series. In: IEEE symposium series on computational intelligence (IEEE SSCI 2016), 2016, Athens, Greece. https://doi.org/10.1109/SSCI.2016.7850010

  • Singh P (2017) A brief review of modeling approaches based on fuzzy time series. Int J Mach Learn Cybern 8(2):397–420

    Google Scholar 

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

    Article  Google Scholar 

  • Song Q, Chissom B (1994) Forecasting enrollments with fuzzy time series—Part II. Fuzzy Sets Syst 62:1–8. https://doi.org/10.1016/0165-0114(94)90067-1

    Article  Google Scholar 

  • Song Q, Leland RP, Chissom BS (1997) Fuzzy stochastic fuzzy time series and its models. Fuzzy Sets Syst 88(3):333–341. https://doi.org/10.1016/S0165-0114(96)00077-2

    Article  MathSciNet  MATH  Google Scholar 

  • Song H, Miao C, Roel W, Shen Z, Catthoor F (2010a) Implementation of fuzzy cognitive maps using fuzzy neural network and application in prediction of time series. IEEE Trans Fuzzy Syst 18:233–250. https://doi.org/10.1109/TFUZZ.2009.2038371

    Article  Google Scholar 

  • Song H, Miao C, Shen Z, Roel W, D’Hondt M, Francky C (2010b) Design of fuzzy cognitive maps using neural networks for predicting chaotic time series. Neural Netw Off J Int Neural Netw Soc 23:1264–1275. https://doi.org/10.1016/j.neunet.2010.08.003

    Article  Google Scholar 

  • Song H, Miao C, Roel W, Shen Z, D’Hondt M, Catthoor F (2011) An extension to fuzzy cognitive maps for classification and prediction. IEEE Trans Fuzzy Syst 19:116–135. https://doi.org/10.1109/TFUZZ.2010.2087383

    Article  Google Scholar 

  • Stach W, Kurgan L, Pedrycz W, Reformat M (2005a) Genetic learning of fuzzy cognitive maps. Fuzzy Sets Syst 153(3):371–401

    MathSciNet  MATH  Google Scholar 

  • Stach W, Kurgan L, Pedrycz W (2005b) A survey of fuzzy cognitive map learning methods. In: Issues in soft computing: theory and applications, 2005, pp 71–84

  • Stach W, Kurgan L, Pedrycz W (2007) Parallel learning of large fuzzy cognitive maps. In: 2007 International joint conference on neural networks, 2007, pp 1584–1589. https://doi.org/10.1109/IJCNN.2007.4371194

  • Stach W, Kurgan L, Pedrycz W (2008a) Numerical and linguistic prediction of time series with the use of fuzzy cognitive maps. IEEE Trans Fuzzy Syst 16:61–72. https://doi.org/10.1109/TFUZZ.2007.902020

    Article  Google Scholar 

  • Stach W, Kurgan L, Pedrycz W (2008b) Data-driven nonlinear Hebbian learning method for fuzzy cognitive maps. In: (2008) IEEE international conference on fuzzy systems (IEEE world congress on computational intelligence), 2008. IEEE, pp 1975–1981

  • Stach W, Kurgan L, Pedrycz W (2010) A divide and conquer method for learning large fuzzy cognitive maps. Fuzzy Sets Syst 161:2515–2532. https://doi.org/10.1016/j.fss.2010.04.008

    Article  MathSciNet  MATH  Google Scholar 

  • Stach W, Pedrycz W, Kurgan LA (2012) Learning of fuzzy cognitive maps using density estimate. IEEE Trans Syst Man Cybern B 42(3):900–912

    Google Scholar 

  • Stylios CD, Groumpos PP (2004a) Modeling complex systems using fuzzy cognitive maps. Trans Syst Man Cybern A 34(1):155–162. https://doi.org/10.1109/TSMCA.2003.818878

    Article  Google Scholar 

  • Stylios CD, Groumpos PP (2004b) Modeling complex systems using fuzzy cognitive maps. IEEE Trans Syst Man Cybern A 34:155–162

    Google Scholar 

  • Szwed P (2021) Classification and feature transformation with fuzzy cognitive maps. Appl Soft Comput 105:107271. https://doi.org/10.1016/j.asoc.2021.107271

    Article  Google Scholar 

  • Taber R (1991) Knowledge processing with fuzzy cognitive maps. Expert Syst Appl 2(1):83–87

    Google Scholar 

  • Taber R, Yager RR, Helgason CM (2007) Quantization effects on the equilibrium behavior of combined fuzzy cognitive maps. Int J Intell Syst 22:181–202

    MATH  Google Scholar 

  • Tan CO, Özesmi U (2005) A generic shallow lake ecosystem model based on collective expert knowledge. Hydrobiologia 563:125–142

    Google Scholar 

  • Tsadiras AK (2008) Comparing the inference capabilities of binary, trivalent and sigmoid fuzzy cognitive maps. Inf Sci 178(20):3880–3894. https://doi.org/10.1016/j.ins.2008.05.015

    Article  Google Scholar 

  • Tsadiras AK, Margaritis KG (1999) An experimental study of the dynamics of the certainty neuron fuzzy cognitive maps. Neurocomputing 24(1–3):95–116

    Google Scholar 

  • Tsaih R, Hsu Y, Lai CC (1998) Forecasting S&P 500 stock index futures with a hybrid AI system. Decis Support Syst 23(2):161–174. https://doi.org/10.1016/S0167-9236(98)00028-1

    Article  Google Scholar 

  • Vanhoenshoven F, Nápoles G, Bielen S, Vanhoof K (2018) Fuzzy cognitive maps employing ARIMA components for time series forecasting. In: International conference on intelligent decision technologies, 2018, pp 255–264. https://doi.org/10.1007/978-3-319-59421-7_24

  • Vanhoenshoven F, Nápoles G, Froelich W, Salmeron JL, Vanhoof K (2020) Pseudoinverse learning of fuzzy cognitive maps for multivariate time series forecasting. Appl Soft Comput 95:106461

    Google Scholar 

  • van Vliet M, Kok K, Veldkamp T (2010) Linking stakeholders and modellers in scenario studies: the use of fuzzy cognitive maps as a communication and learning tool. Futures. https://doi.org/10.1016/j.futures.2009.08.005

    Article  Google Scholar 

  • Wang Y, Yu F, Homenda W, Jastrzebska A, Wang X (2019) A new adaptive fuzzy cognitive map-based forecasting model for time series. In: 2019 IEEE 14th international conference on intelligent systems and knowledge engineering (ISKE), 2019, pp 1112–1118. https://doi.org/10.1109/ISKE47853.2019.9170273

  • Wang C, Liu J, Wu K, Ying C (2021a) Learning large-scale fuzzy cognitive maps using an evolutionary many-task algorithm. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2021.107441

    Article  Google Scholar 

  • Wang C, Liu J, Wu K, Ying C (2021b) Learning large-scale fuzzy cognitive maps using an evolutionary many-task algorithm. Appl Soft Comput 108:107441. https://doi.org/10.1016/j.asoc.2021.107441

    Article  Google Scholar 

  • Wang J, Wang X, Li C, Wu J et al (2021c) Deep fuzzy cognitive maps for interpretable multivariate time series prediction. IEEE Trans Fuzzy Syst 29(9):2647–2660

    Google Scholar 

  • Wang Y, Yu F, Homenda W, Pedrycz W, Jastrzebska A, Wang X (2021d) Training novel adaptive fuzzy cognitive map by knowledge-guidance learning mechanism for large-scale time-series forecasting. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2021.3132704

    Article  Google Scholar 

  • Wang Y, Yu F, Homenda W, Pedrycz W, Tang Y, Jastrzebska A, Li F (2022) The trend-fuzzy-granulation-based adaptive fuzzy cognitive map for long-term time series forecasting. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2022.3169624

    Article  Google Scholar 

  • Wei Z, Lu L, Yanchun Z (2008) Using fuzzy cognitive time maps for modeling and evaluating trust dynamics in the virtual enterprises. Expert Syst Appl 35:1583–1592. https://doi.org/10.1016/j.eswa.2007.08.071

    Article  Google Scholar 

  • Wojciech F, Juszczuk P (2009) Predictive capabilities of adaptive and evolutionary fuzzy cognitive maps—a comparative study. In: Intelligent systems for knowledge management. Studies in computational intelligence, vol 252, pp 153–174. https://doi.org/10.1007/978-3-642-04170-9_7

  • Wu K, Liu J (2016) Robust learning of large-scale fuzzy cognitive maps via the LASSO from noisy time series. Knowl Based Syst 113(C):23–38

    Google Scholar 

  • Wu K, Liu J, Liu P, Yang S (2019) Time series prediction using sparse autoencoder and high-order fuzzy cognitive maps. IEEE Trans Fuzzy Syst 28(12):3110–3121

    Google Scholar 

  • Xirogiannis G, Glykas M (2004) Fuzzy cognitive maps in business analysis and performance-driven change. IEEE Trans Eng Manag 51:334–351. https://doi.org/10.1109/TEM.2004.830861

    Article  MATH  Google Scholar 

  • Xixi Y, Ding F, Luo C (2022) Time series prediction based on high-order intuitionistic fuzzy cognitive maps with variational mode decomposition. Soft Comput 26:1–13. https://doi.org/10.1007/s00500-021-06455-0

    Article  Google Scholar 

  • Yan-chun Z, Wei ZR (2008) An integrated framework for learning fuzzy cognitive map using RCGA and NHL algorithm. In: 2008 4th International conference on wireless communications, networking and mobile computing, 2008, pp 1–5

  • Yang Z, Liu J (2019) Learning of fuzzy cognitive maps using a niching-based multi-modal multi-agent genetic algorithm. Appl Soft Comput 74:356–367. https://doi.org/10.1016/j.asoc.2018.10.038

    Article  Google Scholar 

  • Yang Z, Liu J (2020) Learning fuzzy cognitive maps with convergence using a multi-agent genetic algorithm. Soft Comput 24:4055–4066

    Google Scholar 

  • Yang Z, Liu J, Wu K (2019) Learning of boosting fuzzy cognitive maps using a real-coded genetic algorithm. In: (2019) IEEE congress on evolutionary computation (CEC), 2019. IEEE, pp 966–973

  • Ye N, Zhang R, Yu K, Wang D (2015) Learning fuzzy cognitive maps using decomposed parallel ant colony algorithm and gradient descent. In: 2015 12th International conference on fuzzy systems and knowledge discovery (FSKD), 2015. IEEE, pp. 78–83

  • Yesil E, Urbas L (2010) Big bang–big crunch learning method for fuzzy cognitive maps, World Academy of Science, Engineering and Technology. Int J Comput Electr Autom Control Inf Eng 4:1756–1765

    Google Scholar 

  • Yesil E, Öztürk C, Dodurka MF, Sakalli A (2013) Fuzzy cognitive maps learning using artificial bee colony optimization. In: 2013 IEEE international conference on fuzzy systems (FUZZ-IEEE), 2013, pp 1–8

  • Yu H-K (2005) Weighted fuzzy time series models for TAIEX forecasting. Physica A 349(3–4):609–624

    Google Scholar 

  • Yu T, Gan Q, Feng G, Han G (2022) A new fuzzy cognitive maps classifier based on capsule network. Knowl Based Syst 250:108950. https://doi.org/10.1016/j.knosys.2022.108950

    Article  Google Scholar 

  • Yuan K, Liu J, Yang S, Wu K, Shen F (2020) Time series forecasting based on kernel mapping and high-order fuzzy cognitive maps. Knowl Based Syst 206:106359

    Google Scholar 

  • Zamora-Martínez F, Romeu P, Botella-Rocamora P, Pardo J (2014) On-line learning of indoor temperature forecasting models towards energy efficiency. Energy Build 83:162–172

    Google Scholar 

  • Zhang W, Zhang X, Sun Y (2017) A new fuzzy cognitive map learning algorithm for speech emotion recognition. Math Probl Eng 2017:1–12. https://doi.org/10.1155/2017/4127401

    Article  Google Scholar 

  • Zhang H, Shen Z, Miao C (2011) Train fuzzy cognitive maps by gradient residual algorithm. In: 2011 IEEE international conference on fuzzy systems (FUZZ-IEEE 2011), 2011. IEEE, pp 1815–1821

  • Zou X, Liu J (2018) A mutual information-based two-phase memetic algorithm for large-scale fuzzy cognitive map learning. IEEE Trans Fuzzy Syst 26(4):2120–2134. https://doi.org/10.1109/TFUZZ.2017.2764445

    Article  Google Scholar 

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  1. Machine Intelligence and Data Science (MINDS) Laboratory, Federal University of Minas Gerais, Belo Horizonte, Brazil

    Omid Orang, Petrônio Cândido de Lima e Silva & Frederico Gadelha Guimarães

  2. Federal Institute of Education Science and Technology of Northern Minas Gerais, Januária Campus, Belo Horizonte, Brazil

    Petrônio Cândido de Lima e Silva

  3. Department of Electrical Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Frederico Gadelha Guimarães

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Orang, O., de Lima e Silva, P.C. & Guimarães, F.G. Time series forecasting using fuzzy cognitive maps: a survey. Artif Intell Rev 56, 7733–7794 (2023). https://doi.org/10.1007/s10462-022-10319-w

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