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...

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.

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.

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...

In this paper a fuzzy tracking control is proposed for non linear dynamic system with bounded external disturbances and admissible uncertainties described as TakagiSugeno (T-S) fuzzy model. Using a tracking reference model, a stability condition scheme based on an augmented system with a guaranteed H∞ performance is proposed to obtain tracking performances. The main result of this paper is to p...

in this paper, the consequences of well-known characteristics of near-fault ground motions, forward directivity and fling step, on the seismic response control is investigated. an integrated fuzzy rule-based control strategy for building structures incorporated with semi active friction damping system with amplifying braces (fdsab) is developed. the membership functions and fuzzy rules of fuzzy...

in this paper we investigate the algebraic properties of dimension of fuzzy hypervector spaces. also, we prove that two isomorphic fuzzy hypervector spaces have the same dimension.

an idea of fuzzy reexivity of felbin's type fuzzy normed linear spaces is introduced and its properties are studied. concept of fuzzy uniform normal structure is given and using the geometric properties of this concept xed point theorems are proved in fuzzy normed linear spaces.

This paper extends the idea of switching T-S fuzzy systems with linear consequent parts to nonlinear ones. Each nonlinear subsystem is exactly represented by a T-S fuzzy system with Lure’ type consequent parts, which allows to model and control wider classes of switching systems and also reduce the computation burden of control synthesis. With the use of a switching fuzzy Lyapunov function, the...