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Modelling and Data Analysis
2020. Vol. 10, no. 1, 129–139
doi:10.17759/mda.2020100108
ISSN: 2219-3758 / 2311-9454 (online)

Software for Solving Fully Fuzzy Linear Systems with Rectangular Matrix

168

A.V. Panteleev, V.S. Saveleva

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Abstract

The article discusses the problem of solving a fully fuzzy linear system of equations with a fuzzy rectangular matrix and a fuzzy right-hand side described by fuzzy triangular numbers in a form of deviations from the mean. A solution algorithm based on finding pseudo-solutions of systems of linear equations and corresponding software is formed. Various examples of created software application for arbitrary fuzzy linear systems are given.

General Information

Keywords: fuzzy numbers, fully fuzzy linear system of equations, triangular numbers, pseudo-inverse matrix, pseudo-solution

Journal rubric: Numerical Methods

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2020100108

For citation: Panteleev A.V., Saveleva V.S. Software for Solving Fully Fuzzy Linear Systems with Rectangular Matrix. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2020. Vol. 10, no. 1, pp. 129–139. DOI: 10.17759/mda.2020100108. (In Russ., аbstr. in Engl.)

References

  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. Panteleev A.V. Metody optimizatsii. Prakticheskii kurs [Optimization theory. Practical course]. Moscow: Publ. Logos, 2011.
  3. Panteleev A.V., Luneva S.Yu. Chislennyi metod resheniya polnost’yu nechetkikh sistem lineinykh uravnenii [Numerical method of solving fully fuzzy system of linear equations] Trudy MAI [Works of MAI], 2019, no. 109. Available at URL: http://trudymai.ru/published.php?ID=111433
  4. Panteleev A.V., Saveleva V.S. Algoritmicheskoe i programmnoe obespechenie issledovaniya matematicheskoi modeli mezhotraslevogo balansa pri nechetkoi informatsii o konechnom sprose [Algorithmic and software research of a mathematical model of intersectoral balance with fuzzy information about fi nal demand] Modelirovanie i analiz dannikh [Modelling and Data Analysis], 2019, no. 3, pp. 11–23.
  5. Panteleev A.V., Saveleva V.S. Analiz modeli vypolneniya proizvodstvennogo zadaniya pri nechetkoi informatsii o koeffi tsientakh pryamykh zatrat i konechnom sprose na produktsiyu [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. 09, no. 4, pp. 32–45. doi:10.17759/mda.2019090402.
  6. Abbasbandy S.,Ezzati R., Jafarian A. LU decomposition Method for Solving Fuzzy System of Linear Equations. Appl. Math. Comput. 2006. V. 172. P. 633–643.
  7. Abbasbandy S., Otadi M., Mosleh M. Minimal Solutoin of a System of General Dual Fuzzy Linear Systems. Chaos Solutions and Fractals. 2008. V. 37. P. 1113–1124.
  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.
  9. Dehghan M., Hashemi B., Ghatee M. Solution of the Fully Fuzzy Linear Systems Using Iterative Techniques. Chaos Solutions and Fractals. 2007. V. 34. P. 316–336.
  10. Dubois D., Prade H. Fuzzy sets and systems: theory and applications, Academic Press, New York, 1980.
  11. 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.
  12. 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.
  13. Mosleh M., Abbasbandy S., Otadi M. A Method for Solving Fully Linear System // Mathematics Scientifi c Journal. 2011. V.7. № 2. P. 59–70.
  14. 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.

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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