Solution method for a boundary value problem with fuzzy forcing function

In this paper, we present a new approach to a non-homogeneous fuzzy boundary value problem. We consider a linear differential equation with real coefficients but with a fuzzy forcing function and fuzzy boundary values. We assume that the forcing function is a triangular fuzzy function. Unlike previous studies, we look for a solution that is a fuzzy set of real functions (not a fuzzy-valued function). Each of these real functions satisfies the boundary value problem with some membership degree. We have developed a method that finds this solution, and demonstrated its effectiveness using a test example.To show that the approach can be extended to other types of fuzzy numbers, we extended it to the trapezoidal case. For a particular example, we used the product t-norm to demonstrate how a new solution type can be obtained.

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