Title: Leontief input-output model with trapezoidal fuzzy numbers and Gauss-Seidel algorithm

Authors: Charmi Panchal; Pasi Luukka; Jorma K. Mattila

Addresses: Laboratory of Applied Mathematics, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland ' School of Business, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland ' Laboratory of Applied Mathematics, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland

Abstract: In this work a fuzzy linear system is used to solve Leontief input-output model with fuzzy entries. For solving this model, we assume that the consumption matrix from different sectors of the economy and final demand are known. These assumptions heavily depend on the information obtained from the industries. Hence it is clear that uncertainties are involved in this information. The aim of this work is to model these uncertainties and to address them by fuzzy entries such as fuzzy numbers and LR-type fuzzy numbers (triangular and trapezoidal). Fuzzy linear system has been developed and it is solved using Gauss-Seidel algorithm. Numerical examples show the efficiency of this algorithm. The famous example from Prof. Leontief, where he solved the production levels for US economy in 1958, is also further analysed to demonstrate the efficiency of our approach.

Keywords: trapezoidal fuzzy numbers; Leontief input-output model; Gauss-Seidel algorithm; fuzzy linear systems; fuzzy logic; uncertainties.

DOI: 10.1504/IJPMB.2014.065523

International Journal of Process Management and Benchmarking, 2014 Vol.4 No.4, pp.456 - 474

Available online: 28 Oct 2014 *

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