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

DOI: https://doi.org/10.17759/mda.2019090402

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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Information About the Authors

Andrey V. Panteleev, Doctor of Physics and Matematics, Professor, Head of the Department of Mathematical Cybernetics, Institute of Information Technologies and Applied Mathematics, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID: https://orcid.org/0000-0003-2493-3617, e-mail: avpanteleev@inbox.ru

Vera S. Saveleva, Undergraduate Student of the Faculty of Information Technology and Applied Mathematics, Moscow Aviation Institute (National Research University), Moscow, Russia, e-mail: verassavel@mail.ru

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