L~ ⊗U~ decomposition of a fuzzy Matrix

LU decomposition for a crisp matrix is well known in solving linear system of equations. When A ~ is a fuzzy matrix with elements of LR type fuzzy numbers, Dehghan and et al [4] introduced an L~ ⊗U~ decomposition based on Dubois-Prade product which has got shortcoming mentioned in [2]. In this paper we use the concept of α -cut and also the cross product and find a method to obtain the α -cut representation of L~ and U~ such that A~ = L~ ⊗U~ .

Keywords:

α -cut , cross product , fuzzy L~ ⊗U~ decomposition