An analytical approach for solving type-1 and type-2 fully fuzzy linear systems of equations

Abstract

A general analytical method for solving fully fuzzy linear system (FFLSE) of equations using interval analysis and LU decomposition is proposed in this study. Both type-1 and interval type-2 fuzzy coefficients are discussed. Alpha level sets (alpha cuts) are used to reduce a FFLSE into a number of interval systems, which are then solved systematically using LU decomposition and forward-backward substitution. To carry out forward-backward substitution on interval equations, conditions for the existence and uniqueness of interval solutions are derived and approximations are used for cases when an interval solution does not exist. The proposed method is then extended to solve interval type-2 fuzzy system of equations.