Title : ( Solving Fuzzy Linear Programming Problems with Piecewise Linear Membership Function )
Authors: Sohrab Effati , H. Abbasiyan ,
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Abstract
In this paper, we concentrate on linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with linear membership functions. The symmetric method of Bellman and Zadeh (1970) is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and even non-convex in general. We propose here the "modified subgradient method" and "method of feasible directions" and uses for solving these problems see Bazaraa (1993). We also compare the new proposed methods with well known "fuzzy decisive set method". Finally, we give illustrative examples and their numerical solutions
Keywords
Fuzzy linear programming; fuzzy number; augmented Lagrangian penalty function method; feasible directions of Topkis and Veinott; fuzzy decisive set method
@article{paperid:1019261,
author = {Effati, Sohrab and H. Abbasiyan},
title = {Solving Fuzzy Linear Programming Problems with Piecewise Linear Membership Function},
journal = {Applications and Applied Mathematics},
year = {2010},
volume = {5},
number = {10},
month = {December},
issn = {1932-9466},
pages = {1601--1630},
numpages = {29},
keywords = {Fuzzy linear programming; fuzzy number; augmented Lagrangian penalty function
method; feasible directions of Topkis and Veinott; fuzzy decisive set method},
}
%0 Journal Article
%T Solving Fuzzy Linear Programming Problems with Piecewise Linear Membership Function
%A Effati, Sohrab
%A H. Abbasiyan
%J Applications and Applied Mathematics
%@ 1932-9466
%D 2010
