Finding Inverse of a Fuzzy Matrix using Eigen value Method

Abstract

The present paper extends a concept of the inverse of a matrix that its elements are fuzzy numbers, which may be implemented to model imprecise and uncertain features of the problems in the real world. The problem of inverse calculation of a fuzzy matrix is converted to solving a fuzzy polynomial equations (FPEs) system. In this approach, the fuzzy system is transformed to an equivalent system of crisp polynomial equations. The solutions of the crisp polynomial equations system is computed using eigenvalue method. Also, using Gröbner basis properties a criteria for invertibility of the fuzzy matrix is introduced. Furthermore, a novel algorithm is proposed to find a fuzzy inverse matrix. Achieving all entries of a fuzzy inverse matrix at a time is a big advantage comparing the existence methods. In the end, some illustrative examples are presented to demonstrate the algorithm and concepts.