A Determined Equivalent and Algorithms of Solving a Fuzzy-linear Programming Problem

Yuriy A. Zack

doi:10.1615/JAutomatInfScien.v43.i2.20

Journal of Automation and Information Sciences

Editor-in-Chief: Arkadiy A. Chikriy (open in a new tab)

Associate Editors: Vyacheslav F. Gubarev (open in a new tab) Yuriy P. Kondratenko (open in a new tab) Nonna V. Turovyerova (open in a new tab)

Published 12 issues per year

ISSN Print: 1064-2315

ISSN Online: 2163-9337

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A Determined Equivalent and Algorithms of Solving a Fuzzy-linear Programming Problem

Volume 43, Issue 2, 2011, pp. 7-22

DOI: 10.1615/JAutomatInfScien.v43.i2.20

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Yuriy A. Zack
European Centre for Mechatronics, Aachen (Germany)

ABSTRACT

Solution of a fuzzy-linear programming problem is reduced to solving a determined nonlinear extreme problem. The rules for ranking and estimating the domination for the fuzzy-sets, represented by LR fuzzy-intervals, are proposed. The monotonicity of fuzzy-sets, the left-hand sides of constraints and the optimality criterion of the problem relative to the vector of determined variables are established. The algorithms of solving the problem on the basis of the modified branch-and-bound method are developed.

KEY WORDS: fuzzy-linear programming problem, solving algorithm, nonlinear determined equivalent, branch-and-bound method modification

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