Fuzzy linear systems of the form A(1)x plus b(1) = A(2)x plus b(2)

Linear systems of equations, with uncertainty on the parameters, play a major role in several applications in various areas such as economics, finance, engineering and physics. This paper investigates fuzzy linear systems of the form A(1) x + b(1) = A(2)x + b(2) with A(1), A(2) square matrices of fuzzy coefficients and b(1), b(2) fuzzy number vectors. The aim of this paper is twofold. First, we clarify the link between interval linear systems and fuzzy linear systems. Second, a generalization of the vector solution of Buckley and Qu [Solving systems of linear fuzzy equations, Fuzzy Sets and Systems 43 (1991) 33-43] to the fuzzy system A(1) x + b(1) = A(2)x + b(2) is provided. In particular, we give the conditions under which the system has a vector solution and we show that the linear systems Ax = b and A(1)x + b(1) = A(2)x + b(2), with A = A(1) - A(2) and b = b(2) - b(1), have the same vector solutions. Moreover, in order to find the vector solution, a simple algorithm is proposed.