Solution of Dual Fuzzy Equations Using a New Iterative Method

In this paper, a new hybrid scheme based on learning algorithm of fuzzy neural network (FNN) is offered in order to extract the approximate solution of fully fuzzy dual polynomials (FFDPs). Our FNN in this paper is a five-layer feed-back FNN with the identity activation function. The input-output relation of each unit is defined by the extension principle of Zadeh. The output from this neural network, which is also a fuzzy number, is numerically compared with the target output. The comparison of the feed-back FNN method with the feed-forward FNN method shows that the less error is observed in the feed-back FNN method. An example based on applications are given to illustrate the concepts, which are discussed in this paper

ON QUASI NEWTON METHOD FOR SOLVING FUZZY NONLINEAR EQUATIONS

This paper presents Quasi Newton’s (QN) approach for solving fuzzy nonlinear equations. The method considers an approximation of the Jacobian matrix which is updated as the iteration progresses. Numerical illustrations are carried, and the results shows that the proposed method is very encouraging

Numerical investigation of non-probabilistic systems using Inner Outer Direct Search optimization technique

Fuzzy systems of equations often appear while modeling physical systems with imprecisely defined parameters. Many mathematical methods are available to investigate them, but handling them is challenging due to the computational complexity and difficult implementation. As such, in this paper, the Inner-Outer Direct Search (IODS) optimization technique is extended in the fuzzy environment to solve a fuzzy system of nonlinear equations. The main purpose of the extension is to study the system variables in the presence of fuzzy information. To manage fuzziness, a fuzzy parametric form is employed in the uncertain system and controls the search process toward the optimal solution. The proposed approach of fuzzy IODS converts the fuzzy system of nonlinear equations to an unconstrained fuzzy optimization problem. Then, the unconstrained fuzzy optimization problem is studied through the IODS technique. To solve the unconstrained fuzzy optimization problem, the fuzzy objective function is minimized with the help of exploratory and pattern search approaches. These searches are performed with inner and outer computations. Then, the obtained united solution provides the desired solution which minimizes the objective function. From the same the uncertain system, variables are derived. To verify the solution and proposed algorithm, convergence analysis is performed. Three case studies are considered with only fuzzy and fully fuzzy systems, and various cases are discussed. A comparison with other methods is made to test the efficacy of the method. The proposed algorithm is coded with the help of MATLAB software, and the results are analyzed graphically. Finally, the simple procedure and computationally efficient approach may help to implement the same in many engineering and science problems that can be modeled into systems of equations