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An efficient method to handle the uncertain parameters of a linear programming (LP) problem is to express the uncertain parameters by fuzzy numbers which are more realistic, and create a conceptual and theoretical framework for dealing with imprecision and vagueness. The fuzzy LP (FLP) models in the literature generally either incorporate the imprecisions related to the coefficients of the objective function, the values of the right-hand side, and/or the elements of the coefficient matrix. The aim of this article is to introduce a formulation of FLP problems involving interval-valued trapezoidal fuzzy numbers for the decision variables and the right-hand-side of the constraints. We propose a new method for solving this kind of FLP problems based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To do this, we first define an auxiliary problem, having only interval-valued trapezoidal fuzzy cost coefficients, and then study the relationships between these problems leading to a solution for the primary problem. It is demonstrated that study of LP problems with interval-valued trapezoidal fuzzy variables gives rise to the same expected results as those obtained for LP with trapezoidal fuzzy variables.
Ebrahimnejad, Ali 1
@article{RO_2018__52_3_955_0,
author = {Ebrahimnejad, Ali},
title = {A method for solving linear programming with interval-valued trapezoidal fuzzy variables},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {955--979},
publisher = {EDP-Sciences},
volume = {52},
number = {3},
year = {2018},
doi = {10.1051/ro/2018007},
zbl = {1440.90097},
mrnumber = {3885519},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2018007/}
}
TY - JOUR AU - Ebrahimnejad, Ali TI - A method for solving linear programming with interval-valued trapezoidal fuzzy variables JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 955 EP - 979 VL - 52 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2018007/ DO - 10.1051/ro/2018007 LA - en ID - RO_2018__52_3_955_0 ER -
%0 Journal Article %A Ebrahimnejad, Ali %T A method for solving linear programming with interval-valued trapezoidal fuzzy variables %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 955-979 %V 52 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2018007/ %R 10.1051/ro/2018007 %G en %F RO_2018__52_3_955_0
Ebrahimnejad, Ali. A method for solving linear programming with interval-valued trapezoidal fuzzy variables. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 3, pp. 955-979. doi: 10.1051/ro/2018007
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