System of linear fuzzy differential equations in the space of vector-valued linearly correlated fuzzy numbers

The present paper is concerned with the solution of system of linear fuzzy differential equations where the unknown function is restricted to a vector-valued linearly correlated fuzzy function. First, the concept of the space of vector-valued linearly correlated fuzzy numbers is proposed as an extension to the space of linearly correlated fuzzy numbers. Meantime, the LC-difference and its related properties are also introduced and proved for vector-valued linearly correlated fuzzy numbers, respectively. Second, some analytical properties of vector-valued linearly correlated fuzzy functions such as limit, continuity, and LC-differentiability are examined. Finally, the existence conditions and solutions of the linear fuzzy system are further studied in a special space of vector-valued linearly correlated fuzzy numbers. Some examples are provided to demonstrate the proposed method.