Investigation of a fuzzy problem by the fuzzy Laplace transform. (English) Zbl 1524.44002
Summary: This paper is on the solutions of a fuzzy problem with triangular fuzzy number initial values by fuzzy Laplace transform. In this paper, the properties of fuzzy Laplace transform, generalized differentiability and fuzzy arithmetic are used. The example is solved in relation to the studied problem. Conclusions are given.
References:
| [1] | Şenel B, Şenel M. An Analysis of Technology Acceptance in Turkey Using Fuzzy Logic and Structural Equation Modelling. İşletme AraştırmalarıDergisi (Journal of Business Research) 2011, 3/4: 34-48. |
| [2] | Şenel M, Şenel B, Havle CA. Risk Analysis of Ports in Maritime Industry in Turkey Using FMEA Based Intuitionistic Fuzzy Topsis Approach. ITM Web of Conferences 2018, 22(01018): 1-10, doi:10.1051/itmconf/20182201018. · doi:10.1051/itmconf/20182201018 |
| [3] | Zadeh LA. Fuzzy sets. Information and Control 1965, 8(3):338-353. · Zbl 0139.24606 |
| [4] | Dubois D, Prade H. Operations on fuzzy numbers. International Journal of Systems Science 1978, 9(6):613-626. · Zbl 0383.94045 |
| [5] | Kandel A, Byatt WJ. Fuzzy differential equations. in:Proceedings of the International Conference on Cybernetics and Society, Tokyo 1978, 1213-1216. |
| [6] | Chang SL, Zadeh LA. On fuzzy mapping and control. IEEE Transactions on Systems, Man and Cybernetics 1972, 2(1): 30-34. · Zbl 0305.94001 |
| [7] | Dubois D, Prade H. Towards fuzzy differential calculus part 3: Differentiation. Fuzzy Sets and Systems 1982, 8(3):225-233. · Zbl 0499.28009 |
| [8] | Puri ML, Ralescu DA. Differentials of fuzzy functions. Journal of Mathematical Analysis and Applications 1983, 91(2):552-558. · Zbl 0528.54009 |
| [9] | Seikkala S. On the fuzzy initial value problem. Fuzzy Sets and Systems 1987, 24(3):319-330. · Zbl 0643.34005 |
| [10] | Chalco-Cano Y, Roman-Flores H. Comparation between some approaches to solve fuzzy differential equations. Fuzzy Sets and Systems 2009, 160(11):1517-1527. · Zbl 1198.34005 |
| [11] | Hüllermeir E. An approach to modelling and simulation of uncertain dynamical systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 1997, 5(2):117-137. · Zbl 1232.68131 |
| [12] | Nieto JJ, Rodriguez-Lopez R, Georgiou DN. Fuzzy differential systems under generalized metric spaces approach. Dynamic Systems and Applications 2008, 17:1-24 · Zbl 1168.34005 |
| [13] | Buckley JJ, Feuring T, Hayashi Y. Linear systems of first order ordinary differential equations:fuzzy initial conditions. Soft Computing 2002, 6(6):415-421. · Zbl 1048.34020 |
| [14] | Oberguggenberger M, Pittschmann S. Differential equations with fuzzy parameters. Mathematical and Computer Modelling of Dynamical Systems 1999, 5(3):181-202. · Zbl 0961.34047 |
| [15] | Barros LC, Bassanezi RC, Tonelli PA. Fuzzy modelling in population dynamics. Ecological Modelling 2000, 128(1):27-33. |
| [16] | Mondal SP, Banerjee S, Roy TK. First order linear homogeneous ordinary differential equation in fuzzy environment. International Journal of Pure and Applied Sciences and Technology 2013, 14(1):16-26. |
| [17] | Allahviranloo T, Barkhordari Ahmadi M. Fuzzy Laplace transforms. Soft Computing 2010, 14(3):235-243. · Zbl 1187.44001 |
| [18] | Salahshour S, Allahviranloo T. Applications of fuzzy Laplace transforms. Soft Computing 2013, 17(1):145-158. · Zbl 1264.44002 |
| [19] | Patel KR, Desai NB. Solution of Variable Coefficient Fuzzy Differential Equations by Fuzzy Laplace Transform. International Journal on Recent and Innovation Trends in Computing and Communication 2017, 5(6):927-942. |
| [20] | Patel KR, Desai NB. Solution of Fuzzy Initial Value Problems by Fuzzy Laplace Transform. Kalpa Publications in Computing 2017, 2:25-37. |
| [21] | Mondal SP, Roy TK. Generalized Intuitionistic Fuzzy Laplace Transform and its Application in Electrical Circuit. TWMS J. App. Eng. Math. 2015, 5(1):30-45. · Zbl 1336.34008 |
| [22] | Ahmad N, Mamat M, Jacob K, Amir Hamzah NS. Solving Fuzzy Duffing’s Equation by the Laplace Transform Decomposition. Applied Mathematical Sciences 2012, 6(59):2935-2944. · Zbl 1262.65094 |
| [23] | Liu HK. Comparison results of two-point fuzzy boundary value problems. International Journal of Computational and Mathematical Sciences 2011, 5(1):1-7. |
| [24] | Khastan A, Nieto JJ. A boundary value problem for second order fuzzy differential equations. Nonlinear Analysis:Theory, Methods and Applications 2010, 72(9-10):3583-3593. · Zbl 1193.34004 |
| [25] | Guo X, Shang D, Lu X. Fuzzy approximate solutions of second-order fuzzy linear boundary value problems. Boundary Value Problems. 2013, , 1-17. · Zbl 1304.34003 · doi:10.1186/1687-2770-2013-212 |
| [26] | Bede B. Note on “ Numerical solutions of fuzzy differential equations by predictor-corrector method”. Information Sciences 2008, 178(7):1917-1922. · Zbl 1183.65092 |
| [27] | Khastan A, Bahrami F, Ivaz K. New Results on Multiple Solutions for Nth-Order Fuzzy Differential Equations under Generalized Differentiability. Boundary Value Problems 2009, , 1-13. · Zbl 1198.34006 · doi:10.1155/2009/395714 |
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