@article{MosaviShokriMansoretal.,
  author    = {Mosavi, Amir Hosein and Shokri, Manouchehr and Mansor, Zulkefli and Qasem, Sultan Noman and Band, Shahab S. and Mohammadzadeh, Ardashir},
  title     = {Machine Learning for Modeling the Singular Multi-Pantograph Equations},
  series = {Entropy},
  volume    = {2020},
  journal   = {Entropy},
  number    = {volume 22, issue 9, article 1041},
  publisher = {MDPI},
  address   = {Basel},
  doi       = {10.3390/e22091041},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210122-43436},
  pages     = {1 -- 18},
  abstract  = {In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules of the suggested type-2 fuzzy logic system (T2-FLS) are optimized by the square root cubature Kalman filter (SCKF) such that the proposed fineness function to be minimized. Furthermore, the stability and boundedness of the estimation error is proved by novel approach on basis of Lyapunov theorem. The accuracy and robustness of the suggested algorithm is verified by several statistical examinations. It is shown that the suggested method results in an accurate solution with rapid convergence and a lower computational cost.},
  subject      = {Fuzzy-Regelung},
  language  = {en}
}