Bounded and symmetric solutions of fully fuzzy linear systems in dual form

Abstract

Abstract Linear systems have important applications in many branches of science and engineering in many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. So, it is immensely important to develop a numerical procedure that would appropriately treat general fuzzy linear systems and solve them. In this paper, we propose bounded and symmetric solutions of fully fuzzy linear systems in the dual form (DFFLS) based on a 1-cut expansion. To this end, we solve the 1-cut of a DFFLS (we assumed that the 1-cut of a DFFLS is a crisp linear system), then some unknown symmetric spreads are allocated to each row of a 1-cut of a DFFLS. So, after some manipulations, the original DFFLS is transformed to solving 2∗ n linear equations to find the symmetric spreads. However, our method always give us a fuzzy vector solution. Moreover, we show that the bounded and symmetric solution of the DFFLS will be placed in the tolerable solution set (TSS) and in the controllable solution set (CSS), respectively. Also, an economic example is solved to illustrate the ability of proposed method and a new pattern is suggested for comparing the obtained solutions.