NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS

Abstract

We present a model and propose an approach to compute an ap- proximate solution of Fully Fuzzy Linear System (FFLS) of equations in which all the components of the coecient matrix are either nonnegative or nonpos- itive. First, in discussing an FFLS with a nonnegative coecient matrix, we consider an equivalent FFLS by using an appropriate permutation to simplify fuzzy multiplications. To solve the m n permutated system, we convert it to three m n real linear systems, one being concerned with the cores and the other two being related to the left and right spreads. To decide whether the core system is consistent or not, we use the modied Huang algorithm of the class of ABS methods. If the core system is inconsistent, an appropri- ate unconstrained least squares problem is solved for an approximate solution. The sign of each component of the solution is decided by the sign of its core. Also, to know whether the left and right spread systems are consistent or not, we apply the modied Huang algorithm again. Appropriate constrained least squares problems are solved, when the spread systems are inconsistent or do not satisfy fuzziness conditions. Then, we consider the FFLS with a mixed single-signed coecient matrix, in which each component of the coecient matrix is either nonnegative or nonpositive. In this case, we break the m n coecient matrix up to two m n matrices, one having only nonnegative and the other having only nonpositive components, such that their sum yields the original coecient matrix. Using the distributive law, we convert each