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

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.

1. Bortakovskii A.S.,Panteleev A.V. Lineynaya algebra i analiticheskaya geometriya. Practicum [Linear algebra and analytic geometry. Practicum]. – Moscow: Publ. INFRA–M, 2015.
2. Kireev V.I., Panteleev A.V. Chislennye metody v primerah i zadachah [Numerical methods in examples and problems].– St. Petersburg: Publ. Lan’, 2015.
3. Panteleev A.V., Saveleva V.S. Algorithmic support and software for analysis of input-output mathematical model with fuzzy information about the fi nal demand. Modelirovaniye I analiz dannykh=Modelling and data analysis (Russia). 2019, no. 3, P.11–23.
4. Dubois D., Prade H. Fuzzy sets and systems: theory and applications, Academic Press, New York, 1980.
5. Matinfar M., Nasseri S.H., Sohrabi M. Solving fuzzy linear system of equations by using Housholder decomposition method // Applied Mathematical Sciences. 2008. V.51. P. 2569–2575.
6. Nasseri S.H., Sohrabi M., Ardil E. Solving fully fuzzy linear systems by use of a certain decomposition of the coeffi cient matrix // World Academy of Science, Engineering and Technology. 2008. V.19. P. 784–786.
7. Malkawi G., Ahmad N., Ibrahim H. Solving Fully Fuzzy Linear System with the Necessary and Suffi cient Condition to have a Positive Solution //Appl. Math. Inf. Sci. 2014. V. 8, No. 3, P. 1003–1019.
8. Dehghan M., Hashemi B., Ghatee M. Computational Methods for Solving Fully Fuzzy Linear Systems// Alied Mathematics and Computation. 2006. V. 179. P. 328–343.

PlumX

article metrics