First-order linear fuzzy differential equations on the space of linearly correlated fuzzy numbers

The present paper is concerned with the solutions of first-order linear fuzzy differential equations where differentiability of fuzzy functions is defined under an assumption of linear correlation between fuzzy numbers. Motivated by the fact that the structure of the space of linearly correlated fuzzy numbers strongly depends on the symmetry of the basic fuzzy number, here we address first-order linear fuzzy differential equations by distinguishing whether the basic fuzzy number is symmetric or not. In the non-symmetric case, a first-order linear fuzzy differential equation may be transformed into an equivalent system of ordinary differential equations related to the representation functions of the linearly correlated fuzzy number-valued function. In the symmetric case, according to the monotonicity of the diameter of the fuzzy solution, a first-order linear fuzzy differential equation may be transformed into a system of ordinary differential equations associated with the representation functions of the canonical form of the linearly correlated fuzzy number-valued function. In addition, using our extension method one may obtain solutions with either increasing or decreasing diameters. Several examples are provided in order to illustrate the proposed method. (c) 2020 Elsevier B.V. All rights reserved.

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This paper discusses the solutions of first-order linear fuzzy differential equations with differentiability of fuzzy functions defined under an assumption of linear correlation between fuzzy numbers. The method distinguishes whether the basic fuzzy number is symmetric or not, and provides transformation approaches for both symmetric and non-symmetric cases.