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

Abstract The present paper is concerned with the solutions of first-order linear fuzzy differential equations under the condition of LC-differentiability. 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.