SIMULATION OBJECTIVES OF FUZZY LINEAR PROGRAMMING WITH AN α-LEVEL METHOD OF λ-CONTINUE
( Pp. 71-76)
More about authors
Shatalova Alevtina Yu.
aspirant kafedry prikladnoy matematiki
Kuban State University Lebedev Konstantin A. doktor fiziko-matematicheskih nauk, professor; fakultet matematiki i kompyuternyh nauk
Kuban State University
Kuban State University Lebedev Konstantin A. doktor fiziko-matematicheskih nauk, professor; fakultet matematiki i kompyuternyh nauk
Kuban State University
Abstract:
The article describes an approach that allows to formally describe the arising uncertainties in linear optimization problems. The generalized parametric alpha-level method of lambda-continuation of the fuzzy linear programming problem is considered. The model offers two methods that take into account the expansion of the binary fuzzy ratio (“strong” and “weak”). After the condition is formed taking into account the incoming quantities in the form of fuzzy numbers (the objective function and the system of constraints), the optimal solution (the value of the objective function) for each alpha and lambda is calculated using the simplex method implemented in Mathcad. On its basis, a mathematical model is built that will take into account the random values of alpha and lambda with a uniform distribution law. The paper presents a description of the simulation study, which confirms the conclusions about the possibilities of the method. Using the proposed theory, the decision-maker receives more information showing the behavior of the system with small changes in the input parameters to make more informed conclusions about the choice of financing of an investment project. The developed method of simulation of fuzzy estimation can be applied to other economic models with the appropriate necessary modification, for example, to assess the creditworthiness of the enterprise.
How to Cite:
Shatalova A.Y., Lebedev K.A., (2019), SIMULATION OBJECTIVES OF FUZZY LINEAR PROGRAMMING WITH AN Α-LEVEL METHOD OF Λ-CONTINUE. Computational Nanotechnology, 2 => 71-76.
Reference list:
Bamadio B., Kuzyakina M.V., Lebedev K.A. Otsenki kreditosposobnosti predpriyatiya na osnove pyatifaktornoy modeli Al tmana pri ispol zovanii apparata nechetkikh mnozhestv i srednekvadratichnogo integral nogo priblizheniya // Politematicheskiy setevoy elektronnyy nauchnyy zhurnal Kubanskogo gosudarstvennogo agrarnogo universiteta. 2014. Elektronnyy resurs . URL: http://ej.kubagro.ru/2014/10/pdf/39
Berezhnoy L.N. Teoriya optimal nogo upravleniya ekonomicheskimi sistemami: ucheb. posobie. SPb.: IVESEP, Znanie, 2002.
Bellman R., Zade L. Prinyatie resheniy v rasplyvchatykh usloviyakh. V kn.: Voprosy analiza i protsedury prinyatiya resheniy. M.: Mir, 1976. S. 172-215.
Zade L. Ponyatie lingvisticheskoy peremennoy i ego primenenie k prinyatiyu priblizhennykh resheniy. M.: Mir, 1976.
Zaychenko YU.P. Issledovanie operatsiy. Nechetkaya optimizatsiya. K.: Vyshcha SHkola, 1991. 191 s.
Korshunova N.I., Plyasunov B.C. Matematika v ekonomike. M.: Vita-Press, 1996.
Lagosha B.A., Degtyareva T.D. Metody i zadachi optimal nogo upravleniya: ucheb. posobie. M.: MESI, 2000.
Kolemaev V.A. Matematicheskaya ekonomika: uchebnik dlya vuzov. M.: YUNITI, 1998.
Ivanilov YU.P., Lotov A.V. Matematicheskie modeli v ekonomike. M.: Nauka, 1979.
Ortega Dzh., Reynboldt V. Iteratsionnye metody resheniya nelineynykh sistem uravneniy so mnogimi peremennymi. M.: Mir. 1975. 559 s.
Pegat A. Nechetkoe modelirovanie i upravlenie / A. Pegat, per. s angl. 2-e izd. (el.). M.: BINOM - Laboratoriya znaniy, 2013. 798 s.
Pontryagin L.S. Matematicheskaya teoriya optimal nykh protsessov / L.S. Pontryagin, V.G. Boltyanskiy, R.V. Gamkrelidze, E.F. Mishchenko. M.: Nauka, 1976.
Semenchin E.A., SHatalova A.YU. Investitsionnyy portfel s peremennym ob emom fonda investirovaniya // Fundamental nye issledovaniya. 2012. № 9. C. 739-744.
Semenchin E.A., SHatalova A.YU. Matematicheskaya model maksimizatsii pribyli, poluchaemoy bankom za schet realizatsii investitsionnykh proektov // Fundamental nye issledovaniya. 2012. № 6. C. 258-262.
Semenchin E.A., SHatalova A.YU. Otsenka effektivnosti optimal nogo investitsionnogo portfelya // Vestnik KubGU. Estestvennye nauki. 2012.
Semenchin E.A. Metodika otsenki effektivnosti optimal nogo investitsionnogo portfelya. V kn.: Semenchin E.A., SHatalova A.YU. Ekonomicheskoe razvitie Rossii v usloviyakh global noy nestabil nosti: tendentsii i perspektivy. Sochi, 2012.
Semenchin E.A. Optimizatsiya investitsionnogo portfelya c ogranichennym ob emom investirovaniya. V kn.: Semenchin E.A., SHatalova A.YU. Ekonomika i effektivnost organizatsii proizvodstva. Bryanskaya gosudarstvennaya inzhenerno-tekhnicheskaya akademiya, 2012.
Starodubtsev I.YU. Reshenie zadachi lineynogo programmirovaniya s nechetkimi parametrami // Tekhnicheskie nauki - ot teorii k praktike: sb. st. po mater. VI mezhdunar. nauch.-prakt. konf. Novosibirsk: SibAK, 2012.
Fidler M. Zadachi lineynoy optimizatsii s netochnymi dannymi / M. Fidler, Y. Nedoma, YA. Ramik, I. Ron, K. TSimmermann. M.-Izhevsk: NITS Regulyarnaya i khaoticheskaya dinamika , Institut komp yuternykh issledovaniy, 2008. 288 s.
KHazanova L.E. Matematicheskoe modelirovanie ekonomicheskikh sistem. Dinamicheskoe programmirovanie. M.: INEUP, 1997.
KHarin YU.S. Osnovy imitatsionnogo i staticheskogo modelirovaniya: ucheb. posobie / YU.S. KHarin, V.I. Malyugin, V.P. Kirlitsa, V.I. Lyubach, G.A. KHatskevich. Minsk: Dizayn PRO, 1997. 288 s.
KHachatryan S.R. Metody i modeli resheniya ekonomicheskikh zadach / S.R. KHachatryan, M.V. Pineshnya, V.P. Buyanov. M.: Ekzamen, 2005. 384 s.
SHatalova A.YU. Nechetkoe lineynoe programmirovanie v zadache optimal nogo finansirovaniya investitsionnykh proektov, maksimiziruyushchey poluchaemyy predpriyatiem dokhod / A.YU. SHatalova, K.A. Lebedev // Mezhdunarodnyy zhurnal prikladnykh i fundamental nykh issledovaniy. 2015. № 9. CH. 1.
SHatalova A.YU. Parametricheskiy -urovnevyy metod -prodolzheniya dlya zadachi nechetkogo lineynogo programmirovaniya / A.YU. SHatalova, K.A. Lebedev // Vestnik Buryatskogo gosudarstvennogo universiteta. Matematika, informatika. 2018. № 1.
SHatalova A.YU., Lebedev K.A. Usovershenstvovannyy metod Al tmana dlya otsenki kreditosposobnosti predpriyatiya // Vestnik nauchnykh konferentsii. 2018. № 4-2 (32). S. 119-122.
Altman E.I. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance. 1968. 23 (4).
Beaver W. Financial Ratio as Predictors of Failure, Empirical Research in Accounting. Journal of Accounting Research. 1967. № 4.
Deluca A., Termini S. A definition of a non-probabilistic entropy the of fuzzy sets theory. Information and Control. 1972. № 4.
Fulmer J. A Bankruptcy classification model for small finns. Journal of Commercial Bank Lending. 1984. № 6.
Hiyama T., Sameshima T. Fuzzy logic control scheme for an-line stabilization of multi-machine power system. Fuzzy Sets and Systems. 1991. Vol. 39.
Berezhnoy L.N. Teoriya optimal nogo upravleniya ekonomicheskimi sistemami: ucheb. posobie. SPb.: IVESEP, Znanie, 2002.
Bellman R., Zade L. Prinyatie resheniy v rasplyvchatykh usloviyakh. V kn.: Voprosy analiza i protsedury prinyatiya resheniy. M.: Mir, 1976. S. 172-215.
Zade L. Ponyatie lingvisticheskoy peremennoy i ego primenenie k prinyatiyu priblizhennykh resheniy. M.: Mir, 1976.
Zaychenko YU.P. Issledovanie operatsiy. Nechetkaya optimizatsiya. K.: Vyshcha SHkola, 1991. 191 s.
Korshunova N.I., Plyasunov B.C. Matematika v ekonomike. M.: Vita-Press, 1996.
Lagosha B.A., Degtyareva T.D. Metody i zadachi optimal nogo upravleniya: ucheb. posobie. M.: MESI, 2000.
Kolemaev V.A. Matematicheskaya ekonomika: uchebnik dlya vuzov. M.: YUNITI, 1998.
Ivanilov YU.P., Lotov A.V. Matematicheskie modeli v ekonomike. M.: Nauka, 1979.
Ortega Dzh., Reynboldt V. Iteratsionnye metody resheniya nelineynykh sistem uravneniy so mnogimi peremennymi. M.: Mir. 1975. 559 s.
Pegat A. Nechetkoe modelirovanie i upravlenie / A. Pegat, per. s angl. 2-e izd. (el.). M.: BINOM - Laboratoriya znaniy, 2013. 798 s.
Pontryagin L.S. Matematicheskaya teoriya optimal nykh protsessov / L.S. Pontryagin, V.G. Boltyanskiy, R.V. Gamkrelidze, E.F. Mishchenko. M.: Nauka, 1976.
Semenchin E.A., SHatalova A.YU. Investitsionnyy portfel s peremennym ob emom fonda investirovaniya // Fundamental nye issledovaniya. 2012. № 9. C. 739-744.
Semenchin E.A., SHatalova A.YU. Matematicheskaya model maksimizatsii pribyli, poluchaemoy bankom za schet realizatsii investitsionnykh proektov // Fundamental nye issledovaniya. 2012. № 6. C. 258-262.
Semenchin E.A., SHatalova A.YU. Otsenka effektivnosti optimal nogo investitsionnogo portfelya // Vestnik KubGU. Estestvennye nauki. 2012.
Semenchin E.A. Metodika otsenki effektivnosti optimal nogo investitsionnogo portfelya. V kn.: Semenchin E.A., SHatalova A.YU. Ekonomicheskoe razvitie Rossii v usloviyakh global noy nestabil nosti: tendentsii i perspektivy. Sochi, 2012.
Semenchin E.A. Optimizatsiya investitsionnogo portfelya c ogranichennym ob emom investirovaniya. V kn.: Semenchin E.A., SHatalova A.YU. Ekonomika i effektivnost organizatsii proizvodstva. Bryanskaya gosudarstvennaya inzhenerno-tekhnicheskaya akademiya, 2012.
Starodubtsev I.YU. Reshenie zadachi lineynogo programmirovaniya s nechetkimi parametrami // Tekhnicheskie nauki - ot teorii k praktike: sb. st. po mater. VI mezhdunar. nauch.-prakt. konf. Novosibirsk: SibAK, 2012.
Fidler M. Zadachi lineynoy optimizatsii s netochnymi dannymi / M. Fidler, Y. Nedoma, YA. Ramik, I. Ron, K. TSimmermann. M.-Izhevsk: NITS Regulyarnaya i khaoticheskaya dinamika , Institut komp yuternykh issledovaniy, 2008. 288 s.
KHazanova L.E. Matematicheskoe modelirovanie ekonomicheskikh sistem. Dinamicheskoe programmirovanie. M.: INEUP, 1997.
KHarin YU.S. Osnovy imitatsionnogo i staticheskogo modelirovaniya: ucheb. posobie / YU.S. KHarin, V.I. Malyugin, V.P. Kirlitsa, V.I. Lyubach, G.A. KHatskevich. Minsk: Dizayn PRO, 1997. 288 s.
KHachatryan S.R. Metody i modeli resheniya ekonomicheskikh zadach / S.R. KHachatryan, M.V. Pineshnya, V.P. Buyanov. M.: Ekzamen, 2005. 384 s.
SHatalova A.YU. Nechetkoe lineynoe programmirovanie v zadache optimal nogo finansirovaniya investitsionnykh proektov, maksimiziruyushchey poluchaemyy predpriyatiem dokhod / A.YU. SHatalova, K.A. Lebedev // Mezhdunarodnyy zhurnal prikladnykh i fundamental nykh issledovaniy. 2015. № 9. CH. 1.
SHatalova A.YU. Parametricheskiy -urovnevyy metod -prodolzheniya dlya zadachi nechetkogo lineynogo programmirovaniya / A.YU. SHatalova, K.A. Lebedev // Vestnik Buryatskogo gosudarstvennogo universiteta. Matematika, informatika. 2018. № 1.
SHatalova A.YU., Lebedev K.A. Usovershenstvovannyy metod Al tmana dlya otsenki kreditosposobnosti predpriyatiya // Vestnik nauchnykh konferentsii. 2018. № 4-2 (32). S. 119-122.
Altman E.I. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance. 1968. 23 (4).
Beaver W. Financial Ratio as Predictors of Failure, Empirical Research in Accounting. Journal of Accounting Research. 1967. № 4.
Deluca A., Termini S. A definition of a non-probabilistic entropy the of fuzzy sets theory. Information and Control. 1972. № 4.
Fulmer J. A Bankruptcy classification model for small finns. Journal of Commercial Bank Lending. 1984. № 6.
Hiyama T., Sameshima T. Fuzzy logic control scheme for an-line stabilization of multi-machine power system. Fuzzy Sets and Systems. 1991. Vol. 39.
