This paper presents a process to obtain the solution (or flux) of a fuzzy delay system and to determine the fuzzy expected curve for the HIV (human immunodeficiency virus) when HIV-positive individuals receive antiretroviral therapy. This delay is defined as the time between the infection of a CD4+ type T-lymphocyte cell by the virus and the production of new virus particles. The intracellular ...

The numerical solution of hyperbolic partial differential equations (PDEs) is an important topic in natural sciences and engineering. One of the main difficulties in the task stems from the need to employ several basic types of approximations that are blended in a nonlinear way. In this paper we show that fuzzy logic can be used to construct novel nonlinear blending functions. After introducing...

Comparative analysis of two ideologically distinct approaches in the theory of fuzzy di"erential equations is given. Domains of applications, advantages and shortcomings of those approaches are described. New de2nitions of solutions to fuzzy di"erential equations are proposed. c © 2002 Elsevier Science B.V. All rights reserved.

The main goal of this work is to study the classical models of Partial Differential Equations (PDE) as the heat, wave and Poisson with uncertain parameters, considering the parameter as a fuzzy number. The fuzzy solution is built from the fuzzification of the deterministic solution. The continuity of the Zadeh extension is used to obtain qualitative properties upon the regular α − cuts of the f...

The purpose of this paper is to use the Fuzzy Set Theory, specially fuzzy rule-based systems, as a mathematical tool for modeling dynamical systems given by differential equation, whose direction field is f (IVP-f ). As fuzzy systems methodology produces input-output systems, that is, it produces m outputs from n inputs, one can see it as fr : R → R, where r is the number of rules of the rule b...

In this paper, the inherited collocation method is introduced to solve the fuzzy differential equations. For this purpose, the so-called inherited LU factorization of matrices and inherited polynomials are used to decompose the extended crisp matrix obtained from the proposed method easily. The examples show the efficiency and importance of this method.