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Murat Alper Basaran - One of the best experts on this subject based on the ideXlab platform.

  • calculating fuzzy inverse matrix using fuzzy Linear Equation System
    Applied Soft Computing, 2012
    Co-Authors: Murat Alper Basaran
    Abstract:

    Linear Equation Systems play a very important role in engineering, mathematics, statistics and other disciplines. Fuzzifying either parameters or variables or both in these Systems has been one of the research areas in the fuzzy literature since these kinds of Systems are encountered in many applications. These Systems are generally called fuzzy Linear Equations. Various types of these models have been examined for a decade. The solution procedures of these Systems depend on different methods such as extension principle and interval arithmetic. Also, the method which is often used in computing inverse of a matrix in real case could be extended to fuzzy case, which employs Linear Equation System and identity matrix. For this purpose, we propose a new method which includes some new definitions which are fuzzy zero number, fuzzy one number and fuzzy identity matrix. Based on these definitions, direct computation of fuzzy inverse matrix is done using fuzzy arithmetic and fuzzy Equation System. Actually, this simply extends the notion used in real case to fuzzy case. Calculation is realized with two different settings. While the first one is called direct numerical solution, the other is obtained by choice of decision maker. It is noted that the uniqueness of the calculated fuzzy inverse matrix is not guaranteed.

Amit Kumar - One of the best experts on this subject based on the ideXlab platform.

  • Commentary on “Calculating fuzzy inverse matrix using fuzzy Linear Equation System”
    Applied Soft Computing Journal, 2017
    Co-Authors: Jagdeep Kaur, Amit Kumar
    Abstract:

    Basaran [Calculating fuzzy inverse matrix using fuzzy Linear Equation System, Applied Soft Computing, 12 (2012), 1810–1813] proposed a method for finding the inverse of a fuzzy matrix by assuming all the elements of the fuzzy inverse matrix as non-negative fuzzy numbers, while some of the elements of fuzzy matrix inverse may also be negative fuzzy numbers. Keeping the same in mind, Mosleh and Otadi [A discussion on “Calculating fuzzy inverse matrix using fuzzy Linear Equation System”, Applied Soft Computing, 28 (2015), 511–513] assumed (i, j) element x˜ij=(xij,αij,βijof the fuzzy inverse matrix as a non-negative fuzzy number if the value of xijobtained by Basaran's approach, is a non-negative real number and a negative fuzzy number if the value of xijis negative real number. In this paper, it is shown that the fuzzy multiplicative inverse of a fuzzy matrix, obtained by considering this assumption, is also not an exact fuzzy multiplicative inverse. Furthermore, the required modifications, in Mosleh and Otadi's approach, to obtain the exact multiplicative inverse of a fuzzy matrix are suggested.

Jagdeep Kaur - One of the best experts on this subject based on the ideXlab platform.

  • Commentary on “Calculating fuzzy inverse matrix using fuzzy Linear Equation System”
    Applied Soft Computing Journal, 2017
    Co-Authors: Jagdeep Kaur, Amit Kumar
    Abstract:

    Basaran [Calculating fuzzy inverse matrix using fuzzy Linear Equation System, Applied Soft Computing, 12 (2012), 1810–1813] proposed a method for finding the inverse of a fuzzy matrix by assuming all the elements of the fuzzy inverse matrix as non-negative fuzzy numbers, while some of the elements of fuzzy matrix inverse may also be negative fuzzy numbers. Keeping the same in mind, Mosleh and Otadi [A discussion on “Calculating fuzzy inverse matrix using fuzzy Linear Equation System”, Applied Soft Computing, 28 (2015), 511–513] assumed (i, j) element x˜ij=(xij,αij,βijof the fuzzy inverse matrix as a non-negative fuzzy number if the value of xijobtained by Basaran's approach, is a non-negative real number and a negative fuzzy number if the value of xijis negative real number. In this paper, it is shown that the fuzzy multiplicative inverse of a fuzzy matrix, obtained by considering this assumption, is also not an exact fuzzy multiplicative inverse. Furthermore, the required modifications, in Mosleh and Otadi's approach, to obtain the exact multiplicative inverse of a fuzzy matrix are suggested.

Yunong Zhang - One of the best experts on this subject based on the ideXlab platform.

  • solving future different layer nonLinear and Linear Equation System using new eight node dznn model
    IEEE Transactions on Industrial Informatics, 2020
    Co-Authors: Jinjin Guo, Binbin Qiu, Jianrong Chen, Yunong Zhang
    Abstract:

    In this article, a future different-layer nonLinear and Linear Equation System (DLNLES) is investigated. First, based on a zeroing neural network (ZNN) method, a zeroing equivalency theorem is proposed. Then, a continuous ZNN (CZNN) model is developed for continuous DLNLES solving. Next, a new eight-node Zhang et al. discretization formula is proposed to discretize the CZNN model, and thus, an eight-node discrete ZNN (DZNN) model is proposed for the future DLNLES solving. Five-node and four-node DZNN models are also developed for the same problem solving. Besides, numerical experiments are executed to substantiate the validity and superiority of the proposed eight-node DZNN model. Finally, the path-tracking control problem of a four-link redundant robot arm is formulated as a specific future DLNLES problem and can, thus, be solved by the three DZNN models. Comparative numerical results further indicate that the proposed eight-node DZNN model is much superior to the other two DZNN models.

  • new discrete time znn models for least squares solution of dynamic Linear Equation System with time varying rank deficient coefficient
    IEEE Transactions on Neural Networks, 2018
    Co-Authors: Yunong Zhang, Zhi Yang
    Abstract:

    In this brief, a new one-step-ahead numerical differentiation rule called six-instant $g$ -cube finite difference (6I $g$ CFD) formula is proposed for the first-order derivative approximation with higher precision than existing finite difference formulas (i.e., Euler and Taylor types). Subsequently, by exploiting the proposed 6I $g$ CFD formula to discretize the continuous-time Zhang neural network model, two new-type discrete-time ZNN (DTZNN) models, namely, new-type DTZNNK and DTZNNU models, are designed and generalized to compute the least-squares solution of dynamic Linear Equation System with time-varying rank-deficient coefficient in real time, which is quite different from the existing ZNN-related studies on solving continuous-time and discrete-time (dynamic or static) Linear Equation Systems in the context of full-rank coefficients. Specifically, the corresponding dynamic normal Equation System, of which the solution exactly corresponds to the least-squares solution of dynamic Linear Equation System, is elegantly introduced to solve such a rank-deficient least-squares problem efficiently and accurately. Theoretical analyses show that the maximal steady-state residual errors of the two new-type DTZNN models have an $O(g^{4})$ pattern, where $g$ denotes the sampling gap. Comparative numerical experimental results further substantiate the superior computational performance of the new-type DTZNN models to solve the rank-deficient least-squares problem of dynamic Linear Equation Systems.

Setiawan, Misbahul Munir - One of the best experts on this subject based on the ideXlab platform.

  • Solusi sistem persamaan linier fuzzy dengan bilangan fuzzy trapesium menggunakan metode eliminasi Gauss-Jordan
    2019
    Co-Authors: Setiawan, Misbahul Munir
    Abstract:

    INDONESIA : Secara umum sistem persamaan linier fuzzy dapat dinyatakan dalam bentuk matriks AX ̃=B ̃ di mana A=[a_ij ] adalah matriks koefisien tegas, X ̃=[x ̃_j ] adalah matriks kolom dari variabel fuzzy dan B ̃=[b ̃_i ] adalah matriks kolom dari konstanta fuzzy. Permasalahan yang selalu berkaitan dengan sistem persamaan linier fuzzy adalah tentang bagaimana solusi dari sistem persamaan linier fuzzy tersebut. Salah satu caranya yakni dengan menggunakan metode eliminasi Gauss-Jordan. Penelitian ini bertujuan untuk mendeskripsikan langkah-langkah mencari solusi dari sistem persamaan linier fuzzy dengan bilangan fuzzy trapesium menggunakan metode eliminasi Gauss-Jordan. Metode eliminasi Gauss-Jordan ini dilakukan dengan cara merepresentasikan bilangan fuzzy trapesium pada sistem persamaan linier fuzzy dalam bentuk potongan-α, lalu sistem persamaan linier fuzzy ditransformasi menjadi matriks ekstensi dan kemudian melakukan transformasi pada matriks ekstensi dengan bantuan operasi baris elementer (OBE) sampai menjadi berbentuk eselon baris tereduksi dan diperoleh solusi yang berbentuk potongan-α. Kemudian solusi tersebut diubah menjadi bilangan fuzzy trapesium untuk memperoleh solusi akhir dari sistem persamaan linier fuzzy. Untuk selanjutnya, penelitian ini dapat dikembangkan dengan menyelesaikan sistem persamaan linier fuzzy menggunakan aplikasi Matlab atau yang lainnya untuk mempermudah perhitungan. ENGLISH : Generally, fuzzy Linear Equation System can be donated by matrix form AX ̃=B ̃ where A=[a_ij ] is a matrix of crisp coefficient, X ̃=[x ̃_j ] is a column matrix of fuzzy variable and B ̃=[b ̃_i ] is a column matrix of fuzzy constant. The problem that always related to fuzzy Linear Equation System is about how is the solution of fuzzy Linear equatuion System. One of the method is using Gauss-Jordan elimination method. The goal of this research is describe the steps of finding the solution of fuzzy Linear Equation System with trapezoidal fuzzy number by using Gauss-Jordan elimination method. The procedure of this method is by representing the trapezoidal fuzzy number on fuzzy Equation Linear System in α-cut, then the fuzzy Linear Equation System is transformed to be an extension matrix. After that, the extension matrix is transformed to be reduced row echelon form by elementary row operation and get the solution with α-cut. Finally, that solution change into trapezoidal fuzzy number to get the last solution of fuzzy Linear Equation System. For the next, this research can be expanded by using Matlab application or the other application to make the calculation easier than before