5,711 research outputs found

    Unrestricted solutions of arbitrary linear fuzzy systems

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    Solving linear fuzzy system has intrigued many researchers due to its ability to handle imprecise information of real problems. However, there are several weaknesses of the existing methods. Among the drawbacks are heavy dependence on linear programing, avoidance of near zero fuzzy numbers, lack of accurate solutions, focus on limited size of the systems, and restriction to the matrix coefficients and solutions. Therefore, this study aims to construct new methods which are associated linear systems, min-max system and absolute systems in matrix theory with triangular fuzzy numbers to solve linear fuzzy systems with respect to the aforementioned drawbacks. It is proven that the new constructed associated linear systems are equivalent to linear fuzzy systems without involving any fuzzy operation. Furthermore, the new constructed associated linear systems are effective in providing exact solution as compared to linear programming, which is subjected to a number of constraints. These methods are also able to provide accurate solutions for large systems. Moreover, the existence of fuzzy solutions and classification of possible solutions are being checked by these associated linear systems. In case of near zero fully fuzzy linear system, fuzzy operations are required to determine the nature of solution of fuzzy system and to ensure the fuzziness of the solution. Finite solutions which are new concept of consistency in linear systems are obtained by the constructed min-max and absolute systems. These developed methods can also be modified to solve advanced fuzzy systems such as fully fuzzy matrix equation and fully fuzzy Sylvester equation, and can be employed for other types of fuzzy numbers such as trapezoidal fuzzy number. The study contributes to the methods to solve arbitrary linear fuzzy systems without any restriction on the system

    On the weakness of linear programming to interpret the nature of solution of fully fuzzy linear system

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    One of the applications of linear programing is to get solutions for fully fuzzy linear system (FFLS) when the near-zero fuzzy number is considered.This usage could be applied to interpret the nature of FFLS solution according to the nature of FFLS solution in the work of Babbar et al.(Soft Comput. 17:1-12, 2012) and Kumar et al. (Advances in Fuzzy Systems 2011:1-8, 2011).This paper shows that the nature of FFLS solutions must not depend upon the nature of linear programming (LP) solutions, because LP is not enough to obtain all the exact solutions for FFLS which contradicts the claims of researchers.Counter examples are provided in order to falsify those claims.Numerically, we confirm that the nature of the possible way of solving FFLS is completely different from that of the linear system. For instance, FFLS may have two unique solutions which contradict the uniqueness that can be obtained through only one unique solution

    A new computational method for solving fully fuzzy nonlinear matrix equations

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    Multi formulations and computational methodologies have been suggested to extract solution of fuzzy nonlinear programming problems. However, in some cases the methods which have been utilised in order to find the solution of these problems involve greater complexity. On the basis of the mentioned reason, the current research work is intended towards introduction of a simple method for finding the fuzzy optimal solution related to fuzzy nonlinear issues. The proposed method is validated and is confirmed to be applicable by suggesting some demonstrated examples. The results confirm that the proposed method is so easy to understand and to apply for solving fully fuzzy nonlinear system (FFNS)

    An Implicit Partial Pivoting Gauss Elimination Algorithm for Linear System of Equations with Fuzzy Parameters

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    This paper considers the solution of fully fuzzy linear system (FFLS) by first reducing the system to crisp linear system. The novelty of this article lies in the application of Gauss elimination procedure with implicit partial pivoting to FFLS. The method is presented in detail and we use the Matlab software for implementing the algorithm. Numerical examples are illustrated to demonstrate the efficiency of the variant of Gauss elimination method for solving FFLS. Keywords: fully fuzzy linear system, fuzzy number, gauss elimination, partial pivoting, implici

    A modification of fuzzy arithmetic operators for solving near-zero fully fuzzy matrix equation

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    Matrix equations have its own important in the field of control system engineering particularly in the stability analysis of linear control systems and the reduction of nonlinear control system models. There are certain conditions where the classical matrix equation are not well equipped to handle the uncertainty problems such as during the process of stability analysis and reduction in control system engineering. In this study, an algorithm is developed for solving fully fuzzy matrix equation particularly for ~ A ~X ~B  ~X = ~ C, where the coefficients of the equation are in near-zero fuzzy numbers. By modifying the existing fuzzy multiplication arithmetic operators, the proposed algorithm exceeds the positive restriction to allow the near-zero fuzzy numbers as the coefficients. Besides that, a new fuzzy subtraction arithmetic operator has also been proposed as the existing operator failed to satisfy the both sides of the nearzero fully fuzzy matrix equation. Subsequently, Kronecker product and V ec-operator are adapted with the modified fuzzy arithmetic operator in order to transform the fully fuzzy matrix equation to a fully fuzzy linear system. On top of that, a new associated linear system is developed to obtain the final solution. A numerical example and the verification of the solution are presented to demonstrate the proposed algorithm

    Solution of Dual Fuzzy Equations Using a New Iterative Method

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    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

    Solving Fully Fuzzy Linear Systems with Triangular and Pentagonal Fuzzy Numbers

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    In this paper algorithms are proposed to solve fully fuzzy linear system (FFLS) using triangular fuzzy number and pentagonal fuzzy number by converting the system into block system of linear equations known as associated fuzzy system. The method is illustrated by numerical examples
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