Fuzzy linear systems of the form A_1x + b_1 = A_2x + b_2

摘要

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_1x +b_1= A_2x + 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_1x + b_1 = A_2x + 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_1x + b_1 = A_2x + 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.