COMPUTATION OF FUZZY EIGENVALUES AND EIGENVECTORS OF GENERALIZED FUZZY EIGENVALUE PROBLEMS USING NONLINEAR PROGRAMMING APPROACH

Abstract

Computation of the fuzzy eigenvalues and the associated fuzzy eigenvectors of a fuzzy matrix is often challenging task as compared to that of usual eigenvalue problem. The methods developed so far are particularly for standard fuzzy eigenvalue problem. In this paper, we consider generalized eigenvalue problem (GFEP) of the form AV = λBV in fuzzy environment, where A and B are fuzzy matrices and the parameter λ denotes the fuzzy eigenvalue. To obtain the fuzzy eigenpair (˜λ, ˜V) of GFEP, we proposed method of solving GFEP by converting it into system of linear and nonlinear equations and inequalities based calculation on interval. This method was successfully applied to the standard fuzzy eigenvalue problem by Khosravi et al. We presented model numerical example to check the efficiency of the method.