Linear programming with fuzzy objectives. Rommelfanger, undefined, Hanuscheck, undefined, & Wolf, undefined Fuzzy Sets Syst., 29(1):31--48, 1989. Paper doi abstract bibtex This paper presents a new method for solving linear programming papers with fuzzy parameters in the objective function. To determine a compromise solution the authors do not reduce the set of infinitely many objective functions to a single "compromise objective function" as done in classical deterministic or stochastic procedures. Here the problem is only reduced to a few extreme objective functions. The information contained in the membership functions can be used to any extent by a method called "alpha -level related pair formation". Moreover, if different level sets are considered the stability of the optimal solution can be tested.
@article{rommelfanger_linear_1989,
title = {Linear programming with fuzzy objectives},
volume = {29},
url = {http://dx.doi.org/10.1016/0165-0114(89)90134-6},
doi = {10.1016/0165-0114(89)90134-6},
abstract = {This paper presents a new method for solving linear programming papers with fuzzy parameters in the objective function. To determine a compromise solution the authors do not reduce the set of infinitely many objective functions to a single "compromise objective function" as done in classical deterministic or stochastic procedures. Here the problem is only reduced to a few extreme objective functions. The information contained in the membership functions can be used to any extent by a method called "alpha -level related pair formation". Moreover, if different level sets are considered the stability of the optimal solution can be tested.},
number = {1},
journal = {Fuzzy Sets Syst.},
author = {Rommelfanger,, H. and Hanuscheck,, R. and Wolf,, J.},
year = {1989},
pages = {31--48}
}
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