Solving Differential Equations with Z-Numbers by Utilizing Fuzzy Sumudu Transform

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. 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.

Modelling and Analysis of Flow Rate and Pressure Head in Pipelines

“…Case 3: The boundary conditions that can be measured are the initial flow rate and pressure head in the beginning of the pipeline. The inputs are (18) and outputs are (19) The proposed model, inputs as well as outputs are , and , respectively.…”

“…Current research works are mainly focused on modeling the observer, controller or fault detection methods [12] [13] [14] [15]. However, studying the observability and controllability of the pipeline is remarkably essential [16] [17] [18] [19]. In this paper, a novel technique is proposed to analyze and model the flow in the pipeline.…”

End-to-End Memory Networks: A Survey

“…Artificial intelligence techniques are viewed as the most efficient techniques in recent decades [7][8][9][10][11][12][13][14][15][16][17][18]. For example, Fuzzy logic systems are broadly utilized to model the systems characterizing vague and unreliable information [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In artificial intelligence area [39,40], end-to-end dialog systems have been attained interest because of the current progress of deep neural networks.…”

Applications of Z-Numbers and Neural Networks in Engineering

“…Fuzzy logic systems are broadly utilized to model the systems characterizing vague and unreliable information [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. During the years, investigators have proposed extensions to the theory of fuzzy logic.…”