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

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

Fuzzy Symmetric Solutions of Fuzzy Matrix Equations

The fuzzy symmetric solution of fuzzy matrix equation A X = B, in which A is a crisp m × m nonsingular matrix and B is an m × n fuzzy numbers matrix with nonzero spreads, is investigated. The fuzzy matrix equation is converted to a fuzzy system of linear equations according to the Kronecker product of matrices. From solving the fuzzy linear system, three types of fuzzy symmetric solutions of the fuzzy matrix equation are derived. Finally, two examples are given to illustrate the proposed method

Complex fuzzy linear systems

In paper the complex fuzzy linear equation nbspnbspin which nbspis a crisp complex matrix and nbspis an arbitrary complex fuzzy numbers vector, is investigated. The complex fuzzy linear system is converted to a equivalent high order fuzzy linear system . Numerical procedure for calculating the complex fuzzy solution is designed and thenbsp sufficient condition for the existence of strong complex fuzzy solution is derived. A example is given to illustrate the proposed method.nbs

Penyelesaian Sistem Persamaan Linier Fully Fuzzy Menggunakan Metode Dekomposisi Nilai Singular (SVD)

Linear equation system can be arranged into the AX = B matrix equation. Constants in linear can also contain fuzzy numbers and all their parameters in fuzzy numbers known as fully fuzzy linear equation systems. singular value decomposition (SVD) is a method that decomposes an A matrix into three components of the USVH. The SVD method can be used to find a solution to the fully fuzzy fully linear equation system that is also an inconsistent fully fuzzy linear equation system. The solution obtained from a fully fuzzy linear equation system that is consistent using SVD is a single solution and many solutions. Whereas, the solution obtained from a fully fuzzy linear equation system that is inconsistent using SVD is the best approach solution

Unrestricted solutions of arbitrary linear fuzzy systems

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

Minimal Solution of Complex Fuzzy Linear Systems

This paper investigates the complex fuzzy linear equation Cz~=w~ in which C is a crisp complex matrix and w~ is an arbitrary LR complex fuzzy vector. The complex fuzzy linear system is converted to equivalent high order fuzzy linear system Gx~=b~. A new numerical procedure for calculating the complex fuzzy solution is designed and a sufficient condition for the existence of strong complex fuzzy solution is derived in detail. Some examples are given to illustrate the proposed method

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASAs Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach

Spatiotemporal Fuzzy-Observer-based Feedback Control for Networked Parabolic PDE Systems

Assisted by the Takagi-Sugeno (T-S) fuzzy model- based nonlinear control technique, nonlinear spatiotemporal feedback compensators are proposed in this article for exponential stabilization of parabolic partial differential dynamic systems with measurement outputs transmitted over a communication network. More specifically, an approximate T-S fuzzy partial differential equation (PDE) model with C∞-smooth membership functions is constructed to describe the complex spatiotemporal dynamics of the nonlinear partial differential systems, and its approximation capability is analyzed via the uniform approximation theorem on a real separable Hilbert space. A spatiotemporally asynchronous sampled-data measurement output equation is proposed to model the transmission process of networked measurement outputs. By the approximate T-S fuzzy PDE model, fuzzy-observer-based nonlinear continuous-time and sampled- data feedback compensators are constructed via the spatiotemporally asynchronous sampled-data measurement outputs. Given that sufficient conditions presented in terms of linear matrix inequalities are satisfied, the suggested fuzzy compensators can exponentially stabilize the nonlinear system in the Lyapunov sense. Simulation results are presented to show the effectiveness and merit of the suggested spatiotemporal fuzzy compensators

Tiny Graviton Matrix Theory On Time-Dependent Background

In this article we construct a tiny graviton matrix model for type IIB string theory on a plane-wave background with null dilaton. For the linear null dilaton case, we analyze its vacuum and the excitation spectrum around the vacuum, and discuss the time-dependent fuzzy three-sphere solutions and their evolution. It turns out that at very late time the non-Abelian fuzzy degrees of freedom disappear, which indicates the appearance of perturbative strings.Comment: 20 pages and 4 figures; published version, with more clarification