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

Charmi Panchal, Pasi Luukka and Jorma K. Mattila

International Journal of Process Management and Benchmarking, 2014, vol. 4, issue 4, 456-474

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. (search for similar items in EconPapers)
Date: 2014
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