Solutions of Fuzzy Linear Systems using Ranking function

In this work, we propose an approach for computing the compromised solution of an LR fuzzy linear system by using of a ranking function when the coefficient matrix is a crisp m?n matrix. To do this, we use expected interval to find an LR fuzzy vector, X? , such that the vector ?(AX? ) has the least distance from ?(b?) in 1? norm and the 1? cut of X? satisfies the crisp linear system AX = b . Then, we solve the constrained LP-problem by using LINGO 11 software package and obtain optimal fuzzy number solution. Finally, we illustrate the proposed method by solving two numerical examples.