# Analysis of the Production Task Model With Fuzzy Information About Direct Cost Factors and the Final Product Demand

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## Abstract

The article discusses the study of a mathematical model of execution of the production task in the presence of fuzzy information about the matrixes of direct costs and final demand. By solving a problem with fuzzy information we mean the solution of a linear system of equations with a fuzzy matrix and a fuzzy right-hand side described by fuzzy triangular numbers in a form of deviations from the mean. In this task of search of inter-sectoral balance the LU-decomposition method for the matrix of direct cost which is further used for solving the system of linear equations is applied. A software implementation of a numerical method for finding a strong solution of a fuzzy system of linear equations consisting of two successive stages is described. At the first stage, the necessary and sufficient conditions for the existence of a strong solution are verified. At the second stage, the solution of the system is found, which is written in the form of a fuzzy matrix. The influence of the fuzzy numbers parameters on the final result was studied.

## General Information

Keywords: fuzzy logic, triangular numbers, fully fuzzy linear system of equations, strong solution, parametric form of a triangular number

Journal rubric: Mathematical Modelling

Article type: scientific article

For citation: Panteleev A.V., Saveleva V.S. Analysis of the Production Task Model With Fuzzy Information About Direct Cost Factors and the Final Product Demand. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2019. Vol. 9, no. 4, pp. 32–45. DOI: 10.17759/mda.2019090402. (In Russ., аbstr. in Engl.)

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