Krylov subspace method for fuzzy eigenvalue problem

Abstract

The eigenvalue problem arises in many application areas and in the fuzzy setting, focus has always been geared towards the finding of solution for the whole set of eigenvalues and corresponding eigenvectors. This paper introduces the computation of a few eigenpairs of a matrix with triangular fuzzy numbers as elements, where the modal matrix is assumed to be sparse and real symmetric. A two-step procedure is developed for the solution of this type of fuzzy eigenvalue problem. The first step solves the 1-cut of the problem, where the well-known Krylov subspace method, implicitly restarted Lanczos algorithm, is employed to approximate part of the spectrum with respect to either smallest or largest eigenvalues. The second step assigns unknown symmetric linear spreads to the approximate eigenpairs. Numerical experiments are provided to illustrate the efficiency of the proposed scheme for determining fuzzy symmetric eigenpairs of a fuzzy matrix.