Fuzzy Linear Systems Applied to Leontief Input-Output Model

Abstract

A general fuzzy linear system is investigated using fuzzy numbers and Gauss-Seidel iteration fornula. We have used our fuzzy linear system to solve Leontief input-output model with fuzzy entries. When solving Leontief input-output model one is usually making the assumption that we know entirely the consumption matrix from industrial entries and we are certain about the final demand. These assmnptions however depend heavily on estimates and information received from the industry and hence in these estimates, uncertainty plays a crucial role. To address this type of uncertainty fuzzy rnethods are needed to model this and in this artide we are giving a procedure to solve this problem. Numerical examples are given to illustratc the procedure. Arnong them also the farnous example from Leontief himself where he solved the production levels for U.S. econorny in 1958.