Issue:Numerical solution of intuitionistic fuzzy differential equations by Adams' three order predictor-corrector method

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http://ifigenia.org/wiki/issue:nifs/22/3/47-69

Title of paper: Numerical solution of intuitionistic fuzzy differential equations by Adams' three order predictor-corrector method Author(s): B. Ben Amma Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco Said Melliani Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco said.melliani@gmail.com Lalla Saadia Chadli Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco Presented at: 20th International Conference on Intuitionistic Fuzzy Sets, 2–3 September 2016, Sofia, Bulgaria Published in: "Notes on IFS", Volume 22, 2016, Number 3, pages 47—69 Download:  PDF (132  Kb, File info) Abstract: In this paper three numerical methods to solve ”The intuitionistic fuzzy differential equations” are discussed. These methods are Adams–Bashforth, Adams–Moulton and predictorcorrector. The predictor-corrector method is generated by combining an explicit three-step method and implicit tow-step method. The Convergence and stability of the proposed methods are also presented. These methods are illustrated by solving an example. Keywords: Intuitionistic fuzzy differential equations, Adams three order predictor-corrector method. AMS Classification: 03E72, 08A72. References: Abbasbandy, S., Ezzati, R., & Behforooz, H. (2008) Interpolation of fuzzy data by using fuzzy splines, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems16(1), 107–115. Atanassov K. T. (1983) Intuitionistic Fuzzy Sets, VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6. Atanassov, K. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96. Atanassov, K. (1994) Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64(2), pp. 159-174. Barkhordari Ahmadi, M., Kiani, N. A. & Mikaeilvan, N. (2015) Extended Predictor-Corrector Methods for Solving Fuzzy Differential Equations under Generalized Differentiability, International Journal of Mathematical Modelling & Computations, 5(2), 149–171. Ben Amma, B., Melliani, S. & Chadli, L. S. (2016) Numerical solution of intuitionistic fuzzy differential equations by Euler and Taylor methods. Notes on Intuitionistic Fuzzy Sets, 22(2), 71–86. De, S. K., Biswas, R., & Roy, A. R. (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems 117(2), 209–213. Kharal, A. (2009) Homeopathic drug selection using intuitionistic fuzzy sets. Homeopathy, 98(1), 35–39. Li, D. F., & Cheng, C. T. (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23(1–3), 221–225. Li, D. F. (2005) Multiattribute decision making models and methods using intuitionistic fuzzy sets. J. Comput. Syst. Sci., 70, 73–85. Melliani, S., Elomari, M., Chadli, L. S. & Ettoussi, R. (2015) Intuitionistic fuzzy metric space, Notes on Intuitionistic Fuzzy sets, 21(1) , 43–53. Ettoussi, R., Melliani, S. & Chadli, L. S. (2015) Solution of intuitionistic fuzzy differential equations by successive approximations method. Notes on Intuitionistic Fuzzy Sets, 21(2), 51–62. Nikolova, M., Nikolov, N., Cornelis, C., & Deschrijver, G. (2002) Survey of the research on intuitionistic fuzzy sets. Adv. Stud. Contempor. Math., 4(2), 127–157. Shu, M. H., Cheng, C. H., & Chang, J. R. (2006) Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly. Microelectron. Reliab., 46(12), 2139–2148. Wang, Z., Li, K. W., & Wang, W., (2009) An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Information Sciences, 179(17), 3026–3040. Ye, J., (2009) Multicriteria fuzzy decision-making method based on a novel accuracy function under interval valued intuitionistic fuzzy environment. Expert Syst. Applicat., 36, 6899–6902. Zadeh, L. A. (1965) Fuzzy sets, Information and Control, 8(3), 338–353. Citations: Issue:Solution of n-th order intuitionistic fuzzy differential equation by variational iteration method ‎ (← links) The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.