This paper discusses a class of uncertain optimization problems, in which
unknown parameters are modeled by fuzzy intervals. The membership functions of
the fuzzy intervals are interpreted as possibility distributions for the values
of the uncertain parameters. It is shown how the known concepts of robustness
and light robustness, for the interval uncertainty representation of the
parameters, can be generalized to choose solutions under the assumed model of
uncertainty in the possibilistic setting. Furthermore, these solutions can be
computed efficiently for a wide class of problems, in particular for linear
programming problems with fuzzy parameters in constraints and objective
function. In this paper a theoretical framework is presented and results of
some computational tests are shown.
Description
[1912.01516] Soft robust solutions to possibilistic optimization problems
%0 Journal Article
%1 kasperski2019robust
%A Kasperski, Adam
%A Zielinski, Pawel
%D 2019
%K bayesian optimization probability readings robustness
%T Soft robust solutions to possibilistic optimization problems
%U http://arxiv.org/abs/1912.01516
%X This paper discusses a class of uncertain optimization problems, in which
unknown parameters are modeled by fuzzy intervals. The membership functions of
the fuzzy intervals are interpreted as possibility distributions for the values
of the uncertain parameters. It is shown how the known concepts of robustness
and light robustness, for the interval uncertainty representation of the
parameters, can be generalized to choose solutions under the assumed model of
uncertainty in the possibilistic setting. Furthermore, these solutions can be
computed efficiently for a wide class of problems, in particular for linear
programming problems with fuzzy parameters in constraints and objective
function. In this paper a theoretical framework is presented and results of
some computational tests are shown.
@article{kasperski2019robust,
abstract = {This paper discusses a class of uncertain optimization problems, in which
unknown parameters are modeled by fuzzy intervals. The membership functions of
the fuzzy intervals are interpreted as possibility distributions for the values
of the uncertain parameters. It is shown how the known concepts of robustness
and light robustness, for the interval uncertainty representation of the
parameters, can be generalized to choose solutions under the assumed model of
uncertainty in the possibilistic setting. Furthermore, these solutions can be
computed efficiently for a wide class of problems, in particular for linear
programming problems with fuzzy parameters in constraints and objective
function. In this paper a theoretical framework is presented and results of
some computational tests are shown.},
added-at = {2019-12-04T20:34:10.000+0100},
author = {Kasperski, Adam and Zielinski, Pawel},
biburl = {https://www.bibsonomy.org/bibtex/209196861de8bff2a8749954fe5d8bb98/kirk86},
description = {[1912.01516] Soft robust solutions to possibilistic optimization problems},
interhash = {c3f9936297b31ff629adeed58b0f2c0d},
intrahash = {09196861de8bff2a8749954fe5d8bb98},
keywords = {bayesian optimization probability readings robustness},
note = {cite arxiv:1912.01516},
timestamp = {2019-12-04T20:34:47.000+0100},
title = {Soft robust solutions to possibilistic optimization problems},
url = {http://arxiv.org/abs/1912.01516},
year = 2019
}