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
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
Aguilar J (2005) A survey about fuzzy cognitive maps papers. Int J Comput Cogn 3(2):27–33
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
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
Alizadeh S, Ghazanfari M, Jafari M, Hooshmand S (2007) Learning FCM by Tabu search. Int J Comput Sci 2(2):142–149
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
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
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
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
Baykasoğlu A, Durmusoglu ZDU, Kaplanoglu V (2011) Training fuzzy cognitive maps via extended great deluge algorithm with applications. Comput Ind 62:187–195
Beena P, Ganguli R (2011a) Structural damage detection using fuzzy cognitive maps and Hebbian learning. Appl Soft Comput 11:1014–1020
Beena P, Ganguli R (2011b) Structural damage detection using fuzzy cognitive maps and Hebbian learning. Appl Soft Comput 11(1):1014–1020
Bose M, Mali K (2019) Designing fuzzy time series forecasting models: a survey. Int J Approx Reason 111:78–99
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
Bueno S, Salmeron JL (2009) Benchmarking main activation functions in fuzzy cognitive maps. Expert Syst Appl 36(3):5221–5229
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
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
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
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
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
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
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
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
Ding F, Luo C (2022) Interpretable cognitive learning with spatial attention for high-volatility time series prediction. Appl Soft Comput 117:108447
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
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
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
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
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
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
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
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
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
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
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
Gao R, Du L, Yuen KF (2020) Robust empirical wavelet fuzzy cognitive map for time series forecasting. Eng Appl Artif Intell 96:103978
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
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
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
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
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
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
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
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
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
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
Konar A, Chakraborty UK (2005) Reasoning and unsupervised learning in a fuzzy cognitive map. Inf Sci 170(2–4):419–441
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
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
Kottas TL, Boutalis YS, Christodoulou MA (2007) Fuzzy cognitive network: a general framework. Intell Decis Technol 1(4):183–196
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Mls K, Cimler R, Vascák J, Puheim M (2017) Interactive evolutionary optimization of fuzzy cognitive maps. Neurocomputing 232:58–68
Morris RG, Hebb DO (1999) The organization of behavior, Wiley: New York; 1949. Brain Res Bull 50(5–6):437
Nair A, Reckien D, Van Maarseveen M (2019) A generalised fuzzy cognitive mapping approach for modelling complex systems. Appl Soft Comput 84:105754
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
Nápoles G, Bello R, Vanhoof K (2014a) How to improve the convergence on sigmoid fuzzy cognitive maps? Intell Data Anal 18:77–88
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
Nápoles G, Papageorgiou E, Bello R, Vanhoof K (2016) On the convergence of sigmoid fuzzy cognitive maps. Inf Sci 349:154–171
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
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
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
Papageorgiou E (2011a) Learning algorithms for fuzzy cognitive maps—a review study. IEEE Trans Syst Man Cybern C 42(2):150–163
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
Papageorgiou EI (2014) Fuzzy cognitive maps for applied sciences and engineering—from fundamentals to extensions and learning algorithms. Springer, Berlin
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
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
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
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
Papageorgiou EI, Salmeron JL (2012) A review of fuzzy cognitive maps research during the last decade. IEEE Trans Fuzzy Syst 21(1):66–79
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
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
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
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
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
Park KS, Kim SH (1995) Fuzzy cognitive maps considering time relationships. Int J Hum–Comput Stud 42(2):157–168
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
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
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
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
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
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
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
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
Salmeron JL (2010) Modelling Grey uncertainty with fuzzy Grey cognitive maps. Expert Syst Appl 37(12):7581–7588
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Stach W, Kurgan L, Pedrycz W, Reformat M (2005a) Genetic learning of fuzzy cognitive maps. Fuzzy Sets Syst 153(3):371–401
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
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
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
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
Stylios CD, Groumpos PP (2004b) Modeling complex systems using fuzzy cognitive maps. IEEE Trans Syst Man Cybern A 34:155–162
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
Taber R (1991) Knowledge processing with fuzzy cognitive maps. Expert Syst Appl 2(1):83–87
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
Tan CO, Özesmi U (2005) A generic shallow lake ecosystem model based on collective expert knowledge. Hydrobiologia 563:125–142
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
Tsadiras AK, Margaritis KG (1999) An experimental study of the dynamics of the certainty neuron fuzzy cognitive maps. Neurocomputing 24(1–3):95–116
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Yang Z, Liu J (2020) Learning fuzzy cognitive maps with convergence using a multi-agent genetic algorithm. Soft Comput 24:4055–4066
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
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
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
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
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
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
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
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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 (2022). https://doi.org/10.1007/s10462-022-10319-w
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DOI: https://doi.org/10.1007/s10462-022-10319-w
Keywords
- Time series forecasting
- Fuzzy cognitive maps
- Soft computing
- Fuzzy systems