A fuzzy Elman neural network (FENN) is proposed to identify and simulate nonlinear dynamic systems. Each of all the fuzzy rules used in FENN has a linear state-space equation as its consequence and the network, by use of firing strengths of input variables, combines these Takagi-Sugeno type rules to represent the modeled nonlinear system. The context nodes in FENN are used to perform temporal r...

In this paper the conjugate gradient method, for solving fuzzy symmetric positive definite system of linear equation is considered. The method in detail is discussed and followed by convergence theorem and illustrated by solving some numerical examples. 2005 Elsevier Inc. All rights reserved.

Introduction A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?”. Such a problem, called a stability problem of the functional equation, was formulated by Ulam [1] in 1940. In the next year, Hyers [2] gave a partial solution of Ulam’s probl...

A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?” Such a problem, called a stability problem of the functional equation, was formulated by Ulam 1 in 1940. In the next year, Hyers 2 gave a partial solution of Ulam’s problem for the case of...

An adaptive neuro fuzzy inference system based on interval Gaussian type-2 fuzzy sets in the antecedent part and Gaussian type-1 fuzzy sets as coefficients of linear combination of input variables in the consequent part is presented in this paper. The capability of the proposed method (we named ANFIS2) for function approximation and dynamical system identification is remarkable. The structure o...

Most of the existing approaches for fuzzy reliability analysis are based on fuzzy probability.  The aim of this paper is to describe fuzzy reliability using fuzzy differential equation. The reliability of a system in real world applications is affected by some uncertain parameters. Fuzzy reliability is a way to present the reliability function uncertainly using fuzzy parameters. In the proposed...

This paper presents the basic concepts of stability in fuzzy linguistic models. Theauthors have proposed a criterion for BIBO stability analysis of fuzzy linguistic modelsassociated to linear time invariant systems [25]-[28]. This paper presents the basic concepts ofstability in the general nonlinear and linear systems. This stability analysis method is verifiedusing a benchmark system analysis.

In this paper is shown that the probability-statistic methods application, especially at the early stage of the aviation gas turbine engine (GTE) technical condition diagnosing, when the flight information has property of the fuzzy, limitation and uncertainty is unfounded. Hence is considered the efficiency of application of new technology Soft Computing at these diagnosing stages with the usin...

Fuzzy differential equation is an important tool to deal with dynamic systems in fuzzy environments. However, it is difficult to find the solutions to all fuzzy differential equations. In this paper, methods to solve linear fuzzy differential equations and reducible fuzzy differential equations are given. Moreover, existence and uniqueness theorem for homogeneous fuzzy differential equations ar...

In the literature, several numerical methods are proposed for solvingnth-order fuzzy linear differential equations. However, till now there areonly two analytical methods for the same. In this paper, the fuzzy Kolmogorov'sdifferential equations, obtained with the help of fuzzy Markov modelof piston manufacturing system, are solved by one of these analytical methodsand illustrated that the obtai...