The aim of this paper is to analyse the solution of a fuzzy system when the classical solution based on standard fuzzy mathematics fails to exist. In particular we analyse the solution of the system Ax=b with A squared matrix with positive fuzzy coefficients and y crisp vector of positive elements. This system is particularly important for financial applications. We propose two different soluti...

A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains...

Abstract: This paper deals with the synthesis of an adaptive fuzzy wavelet network (FWN) controller for an nth order multi input multi output (MIMO) non-linear system suffering from parameters uncertainties and subjected to external perturbation. The proposed approach allows combining the advantages of the fuzzy logic system and those of wavelet networks to approximate quickly the unknown syste...

in this paper, a fuzzy version of the analytic form of hahn-banachextension theorem is given. as application, the hahn-banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

This paper presents an elementary solution to the non-singular H" control problem. In this control problem, the underlying linear system satisfies a set of assumptions which ensures that the solution can be obtained by solving just two algebraic Riccati equations of the game type. This leads to the central solution to the H" control problem. The solution presented in this paper uses only elemen...

In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm. Keywords—Homotopy perturbation method, Fuzzy linear systems, Block linear system, Fuzzy solution, Embedding parameter.

The main objective of this paper is to expound the singular-value-decomposition (SVD)-based reduction technique proposed to single-input–single-output Takagi-Sugeno (TS) fuzzy models to multivariable cases. The use of higher order singular value decomposition is proposed in this paper for the complexity reduction of multiple-input–single-output TS fuzzy model approximation. A detailed illustrat...

Fuzzy finite element analysis for static displacements of beam structures with fuzzy forces is considered in this paper. The material properties of the beams are taken as crisp. Fuzzy finite element analysis of static problem for the above structures converts the problem into fuzzy system of linear equations. As such the coefficient matrix and the right hand side vector become crisp and fuzzy r...