BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, PARAMETRIC α-LEVEL METHOD OF λ-CONTINUATION FOR FUZZY LINEAR PROGRAMMING PROBLEM // BSU Bulletin. Mathematics, Informatics. - 2018. №1. . - С. 34-51.
Title:
PARAMETRIC α-LEVEL METHOD OF λ-CONTINUATION FOR FUZZY LINEAR PROGRAMMING PROBLEM
Financing:
Codes:
Annotation:
The article considers the well-known method of four fuzzy linear programming problems, which is generalized to the parametric α-level method of λ-continuation. The proposed method makes it possible to reduce the number of cases considered from four to two, and obtain additional solutions on subsets of the square α – λ . The advantage of the proposed approach is that one task in- cludes the previous four tasks as special cases. This method allows us to obtain more general and flexible solutions and to influence the properties of a linear optimization problem: degree of membership, sensitivity, stability. We also give the numerical example of the new method implementation in the pro- gramming support environment MathCAD.
Keywords:
fuzzy linear programming; optimization problems; parametric linear programming with fuzzy data; expansion principle; the method of continuation; fuzzy sets; fuzzy logic.
List of references:
Zaichenko Yu. P. Issledovanie operatsii. Nechetkaya optimizatsiya [Op- erations Research. Fuzzy Optimization]. Kiev: Vishcha Shkola, 1991. 191 p.
Bellman R., Zadeh L. A. Decision Making in a Fuzzy Environment.Management Science. 1970. No. 17B (4). Pp. 141–164.
Fiedler M., Nedoma J., Ramik J., Rohn J., Zimmermann K. Linear Opti- mization Problems with Inexact Data. Springer US, 2006.
Starodubtsev I. Yu. Reshenie zadachi lineinogo programmirovaniya s nechetkimi parametrami [A Solution of the Problem of Linear Programming with Fuzzy Parameters]. Tekhnicheskie nauki – ot teorii k praktike — Techni- cal Sciences: Bedside Approach. Coll. art. VI Int. sci.-pract. conf. Novosibirsk: SibAK Publ., 2012.
Piegat A. Fuzzy Modeling and Control. Germany: Physica-Verlag GmbH Heidelberg, 2010.
Shatalova A. Yu., Lebedev K. A. Nechetkoe lineinoe programmirovanie v zadache optimal'nogo finansirovaniya investitsionnykh proektov, mak- simiziruyushchei poluchaemyi predpriyatiem dokhod [Fuzzy Linear Program- ming in the Problem of Optimal Financing of Investment Projects, Maximizing the Enterprise’s Income]. Mezhdunarodnyi zhurnal prikladnykh i fundamen- tal'nykh issledovanii — International Journal of Applied and Fundamental Re- search. 2015. No. 9 (Part 1). Pp. 35–36.
Ortega J. M., Rheinboldt W. Iterative Solution of Nonlinear Equations in Several Variables. New York: Academic Press, 572 p.
Bellman R., Zadeh L. A. Decision Making in a Fuzzy Environment.Management Science. 1970. No. 17B (4). Pp. 141–164.
Fiedler M., Nedoma J., Ramik J., Rohn J., Zimmermann K. Linear Opti- mization Problems with Inexact Data. Springer US, 2006.
Starodubtsev I. Yu. Reshenie zadachi lineinogo programmirovaniya s nechetkimi parametrami [A Solution of the Problem of Linear Programming with Fuzzy Parameters]. Tekhnicheskie nauki – ot teorii k praktike — Techni- cal Sciences: Bedside Approach. Coll. art. VI Int. sci.-pract. conf. Novosibirsk: SibAK Publ., 2012.
Piegat A. Fuzzy Modeling and Control. Germany: Physica-Verlag GmbH Heidelberg, 2010.
Shatalova A. Yu., Lebedev K. A. Nechetkoe lineinoe programmirovanie v zadache optimal'nogo finansirovaniya investitsionnykh proektov, mak- simiziruyushchei poluchaemyi predpriyatiem dokhod [Fuzzy Linear Program- ming in the Problem of Optimal Financing of Investment Projects, Maximizing the Enterprise’s Income]. Mezhdunarodnyi zhurnal prikladnykh i fundamen- tal'nykh issledovanii — International Journal of Applied and Fundamental Re- search. 2015. No. 9 (Part 1). Pp. 35–36.
Ortega J. M., Rheinboldt W. Iterative Solution of Nonlinear Equations in Several Variables. New York: Academic Press, 572 p.
Article.pdf