Real Symmetric Positive Definite Fuzzy Matrix Of Fuzzy Eigenvalue

Fuzzy matrix is: A = (a_ij)∈M_n(F) = {A = (a_ij) : a_ij∈F}, in which F = [0,1]. In the application of fuzzy mathematics, because of different practical context, we always choose different fuzzy operation. In 1989, J.B.kim defined the determinant of fuzzy matrix. In 1994, M.Z.Ragab and E.G.Emam gave the adjoint of fuzzy matrix and the property of adjoint of fuzzy matrix. In 1998, Y,J Tan gave the concept of fuzzy eigenvalues of fuzzy matrix and fuzzy eigenvectors. In 1998, S.Zhao gave the inverse of fuzzy matrices and the property.In 1990, J.J.Buckley gave anther more common definition of fuzzy matrices: A = (a_ij)∈M_n(F) = {A = (a_ij) : a_ij∈F}, in which F is the set containing all the fuzzy num-bers, and generalize the fuzzy matrices having a dominant nonnegative fuzzy eigenvalue and the fuzzy eigenvectors.Above all, this paper inherits the fuzzy matrices defined by J.J.Buckley, and discusses the fuzzy eigenvalue problem of real symmetric positive fuzzy matrix. First, it is to define two operations of real symmetric positive fuzzy matrix, i.e. sum and multiplication; second, it is to prove the theory of the fuzzy eigenvalues of real symmetric positive fuzzy matrix; at last, it is to give the applications and examples of that.