A chaotic iterative fuzzy modeling for circulating a simple sentence

Document Type : Article


1 Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, P.O. Box 15875-4413, Iran

2 Ministry of Higher Education and Scientific Research, Baghdad, Iraq.

3 Department of Physics, University of Wisconsin - Madison, Madison, WI 53706, USA


In this paper, we propose a new model to describe variations in interpretation and perception of a simple sentence by different people. To show the understandability of a simple sentence in the prediction of future situations, the meaning of a sentence is modeled as a fuzzy if-then rule, and the fuzzy model is investigated in an iterative process. The main goal of the paper is modeling a linguistic rule. This is done using an if-then rule and its variation through one person to another. The model predicts that the interpretation reaching the final person in the following years can be chaotic and thus unpredictable.


[1]    Schmitz, A., "A Primer on communication studies," Retrieved September, 19, pp. 2016, (2012).
[2]    Carlsen, W. S., "Language and science learning," in Handbook of research on science education, ed: Routledge, (2013), pp. 71-88.
[3]    Lindquist, K. A., MacCormack, J. K. and Shablack, H., "The role of language in emotion: Predictions from psychological constructionism," Frontiers in Psychology, 6, pp. 444, (2015).
[4]    Peterson, W. A. and Gist, N. P., "Rumor and public opinion," American Journal of Sociology, pp. 159-167, (1951).
[5]    Wang, Q., Yang, X. and Xi, W., "Effects of group arguments on rumor belief and transmission in online communities: An information cascade and group polarization perspective," Information & Management, 55(4), pp. 441-449, (2018).
[6]    Guillaume, S. and Charnomordic, B., "Fuzzy inference systems: An integrated modeling environment for collaboration between expert knowledge and data using FisPro," Expert Systems with Applications, 39(10), pp. 8744-8755, (2012).
[7]    Zadeh, L. A., "Fuzzy sets," Information and control, 8(3), pp. 338-353, (1965).
[8]    Alcantud, J. C. R. and Torra, V., "Decomposition theorems and extension principles for hesitant fuzzy sets," Information Fusion, 41, pp. 48-56, (2018).
[9]    Zadeh, L. A., "Fuzzy logic," (1988).
[10]    Bagheri, M., Al-jabery, K., Wunsch, D. C., et al., "A deeper look at plant uptake of environmental contaminants using intelligent approaches," Science of The Total Environment, 651, pp. 561-569, (2019).
[11]    Chen, L. and Chen, G., "Fuzzy modeling, prediction, and control of uncertain chaotic systems based on time series," IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(10), pp. 1527-1531, (2000).
[12]    Kundu, S., Majhi, S., Karmakar, P., et al., "Augmentation of dynamical persistence in networks through asymmetric interaction," EPL (Europhysics Letters), 123(3), pp. 30001, (2018).
[13]    Han, L., Ding, L. and Ling-Feng, D., "Chaotic time series prediction using fuzzy sigmoid kernel-based support vector machines," Chinese Physics, 15(6), pp. 1196, (2006).
[14]    Jafari, S., Sprott, J. C., Pham, V.-T., et al., "A New Cost Function for Parameter Estimation of Chaotic Systems Using Return Maps as Fingerprints," International Journal of Bifurcation and Chaos, 24(10), pp. 1450134, (2014).
[15]    Rotshtein, A., "Integration of the fuzzy logic with chaos theory approaches in simulation and optimization of reliability," Journal of Computer and Systems Sciences International, 51(4), pp. 549-559, (2012).
[16]    Porto, D. M., "A fuzzy description of the Henon chaotic map," in Proceedings of the 5th WSEAS/IASME Int. Conf. on SYSTEMS THEORY and SCIENTIFIC COMPUTATION, 2005, pp. 15-17.
[17]    Porto, D. M., "Chaotic dynamics with fuzzy systems," in Integration of Fuzzy Logic and Chaos Theory, ed: Springer, (2006), pp. 25-44.
[18]    Li, Z. and Halang, W. A., Integration of fuzzy logic and chaos theory  187: Springer Science & Business Media, (2006).
[19]    Porto, M. and Amato, P., "A fuzzy approach for modeling chaotic dynamics with assigned properties," in Ninth IEEE International Conference on Fuzzy Systems. FUZZ-IEEE 2000 (Cat. No. 00CH37063), 2000, pp. 435-440.
[20]    Gentili, P. L., Gotoda, H., Dolnik, M., et al., "Analysis and prediction of aperiodic hydrodynamic oscillatory time series by feed-forward neural networks, fuzzy logic, and a local nonlinear predictor," Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(1), pp. 013104, (2015).
[21]    Nazarimehr, F., Sheikh, J., Ahmadi, M. M., et al., "Fuzzy predictive controller for chaotic flows based on continuous signals," Chaos, Solitons & Fractals, 106, pp. 349-354, (2018).
[22]    Hiew, H. L. and Tsang, C. P., "An adaptive fuzzy system for modeling chaos," Information sciences, 81(3-4), pp. 193-212, (1994).
[23]    Lesne, A., "Chaos in biology," in RIVISTA DI BIOLOGIA BIOLOGY FORUM, 2006, p. 467.
[24]    Tsumoto, K., Yoshinaga, T., Iida, H., et al., "Bifurcations in a mathematical model for circadian oscillations of clock genes," Journal of Theoretical Biology, 239(1), pp. 101-122, (2006).
[25]    Pham, V.-T., Vaidyanathan, S., Volos, C., et al., "A novel memristive time–delay chaotic system without equilibrium points," The European Physical Journal Special Topics, 225(1), pp. 127-136, (2016).
[26]    Nazarimehr, F., Jafari, S., Hashemi Golpayegani, S. M. R., et al., "Predicting tipping points of dynamical systems during a period-doubling route to chaos," Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(7), pp. 073102, (2018).
[27]    Moghtadaei, M. and Golpayegani, M. H., "Complex dynamic behaviors of the complex Lorenz system," Scientia Iranica, 19(3), pp. 733-738, (2012).
[28]    Beigzadeh, M. and Golpayegani, S. H., "A cellular automaton based model for visual perception based on anatomical connections," Scientia Iranica. Transaction D, Computer Science & Engineering, Electrical, 22(6), pp. 2492, (2015).
[29]    Li, Z., "Fuzzy Modeling of Chaotic Systems–I (Mamdani Model)," in Fuzzy Chaotic Systems, ed: Springer, (2006), pp. 73-89.
[30]    Mahesh, K., "syntax semantics interactions in sentence understanding," Tecnical report GIT-CC-95/10, College of computing, Georgia institud of technology, Atlanta, 1995.
[31]    Kurdi, M. Z., Natural language processing and computational linguistics: speech, morphology and syntax  1: John Wiley & Sons, (2016).
[32]    Valli, C. and Lucas, C., Linguistics of American sign language: An introduction: Gallaudet University Press, (2000).
[33]    Yule, G., The study of language: Cambridge university press, (2016).
[34]    Gernsbacher, M. A. and Kaschak, M. P., Language comprehension: Wiley Online Library, (2003).
[35]    Moreno, A., Limousin, F., Dehaene, S., et al., "Brain correlates of constituent structure in sign language comprehension," NeuroImage, 167, pp. 151-161, (2018).
[36]    Szczepaniak, P. S. and Lisboa, P. J., Fuzzy systems in medicine  41: Physica, (2012).
[37]    Stoop, R. and Steeb, W.-H., Berechenbares Chaos in dynamischen Systemen: Springer-Verlag, (2006).
[38]    Nazarimehr, F., Jafari, S., Golpayegani, S. M. R. H., et al., "Investigation of Bifurcations in the Process Equation," International Journal of Bifurcation and Chaos, 27(13), pp. 1750201, (2017).
[39]    Weisstein, E. W., CRC concise encyclopedia of mathematics: Chapman and Hall/CRC, (2002).
[40]    Deng, B., "Neural spike renormalization. Part I—Universal number 1," Journal of Differential Equations, 250(6), pp. 2940-2957, (2011).