On interactive fuzzy boundary value problems

Abstract

In this paper we use the concept of interactivity between fuzzy numbers for the solution to a linear fuzzy boundary value problem (FBVP). We show that a solution of a FBVP, with non-interactive fuzzy numbers as boundary values, can be obtained by the Zadeh's Extension Principle. In addition, we show it is possible to obtain a fuzzy solution by means of the extension principle based on joint possibility distributions for the case where the boundary values are given by interactive fuzzy numbers. Examples of FBVPs with both cases, interactive and non-interactive, are presented. Also from arithmetic operations for linearly correlated fuzzy numbers, we compare our solutions to the one proposed by Gasilov et al. We conclude that the fuzzy solution in the interactive case (when the boundary values are linearly correlated fuzzy numbers) is contained in the fuzzy solution for the non-interactive case. Finally, we present the fuzzy solution for a nonlinear FBVP with Gaussian fuzzy numbers as boundary values.