Euler-based new solution method for fuzzy initial value problems

13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing — ICAFS-2018

Gegov

2018

A survey of the methodologies associated with the modeling and control of uncertain nonlinear systems has been given due importance in this paper. The basic criteria that highlights the work is relied on the various patterns of techniques incorporated for the solutions of fuzzy differential equations (FDEs) that corresponds to fuzzy controllability subject. The solutions which are generated by these equations are considered to be the controllers. Currently, numerical techniques have come out as superior techniques in order to solve these types of problems. The implementation of neural networks technique is contributed in the complex way of dealing the appropriate solutions of the fuzzy systems.

Section: Euler Methodsmentioning

confidence: 99%

Fuzzy Differential Equations for Modeling and Control of Fuzzy Systems

13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing — ICAFS-2018

Gegov

2018

“…By utilizing the FST method based on Z-number we obtain )] If the initial condition is taken to be a symmetric triangular Znumber as )], 1 , Approximation errors based on Z-numbers are shown in Table 1. These errors are the differences between the exact and the approximation solutions, for two different methods: FST and Average Euler method [38].…”

Section: Examplementioning

confidence: 99%

“…Approximation errors based on Z-numbers are shown in Table 3. These errors are the differences between the exact and the approximation solutions, for two different methods: FST and Max-Min Euler method [38]. Figure 7 shows the Corresponding solution plot based on fuzzy numbers.…”

Section: Examplementioning

confidence: 99%

Numerical Solution of Fuzzy Differential Equations with Z-numbers using Fuzzy Sumudu Transforms

Adv. sci. technol. eng. syst. j.

2018

The uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Here, the uncertainties are in the sense of Z-numbers. Important theorems are laid down to illustrate the properties of FST. The theoretical analysis and simulation results show that this new technique is effective to estimate the solutions of FDEs.

“…Corresponding error plots are shown in Figure 4. These errors are the differences of the exact and the approximation solutions for two different methods: FST and Average Euler method [33]. FST is more accurate than the Average Euler method.…”

Section: Examplementioning

confidence: 99%

Solution of Fuzzy Differential Equations Using Fuzzy Sumudu Transforms

2018

MCA

Abstract:The uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Significant theorems are suggested in order to explain the properties of FST. The proposed method is validated with three real examples.