Aida Batamiz and Milan Hladík. Finding efficient solutions in interval multi-objective linear programming models by uncertainty theory. Int. J. Uncertain. Fuzziness Knowl.-Based Syst., 32(06):923–954, 2024.
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Interval multi-objective linear programming (IMOLP) ímodels are one of the methods to tackle uncertainties. In this paper, we propose two methods to determine the efficient solutions in the IMOLP models through the expected value, variance and entropy operators which have good properties. One of the most important properties of these methods is to obtain different efficient solutions set according to decision makers’ preferences as available information. We first develop the concept of the expected value, variance and entropy operators on the set of intervals and study some properties of the expected value, variance and entropy operators. Then, we present an IMOLP model with uncertain parameters in the objective functions. In the first method, we use the expected value and variance operators in the IMOLP models and then we apply the weighted sum method to convert an IMOLP model into a multi-objective non-linear programming (MONLP) model. In the second method, the IMOLP model using the expected value, variance and entropy operators can be converted into a multi-objective linear programming (MOLP) model. The proposed methods are applicable for large scale models. Finally, to illustrate the efficiency of the proposed methods, numerical examples and two real-world models are solved.
@article{BatHla2024a,
author = "Aida Batamiz and Milan Hlad\'{\i}k",
title = "Finding efficient solutions in interval multi-objective linear programming models by uncertainty theory",
journal = "Int. J. Uncertain. Fuzziness Knowl.-Based Syst.",
fjournal = "International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems",
volume = "32",
number = "06",
pages = "923-954",
year = "2024",
doi = "10.1142/S0218488524500235",
issn = "0218-4885",
issnonline = "1793-6411",
url = "https://doi.org/10.1142/S0218488524500235",
bib2html_dl_html = "https://www.worldscientific.com/doi/10.1142/S0218488524500235",
bib2html_dl_pdf = "https://doi.org/10.1142/S0218488524500235",
abstract = "Interval multi-objective linear programming (IMOLP) ímodels are one of the methods to tackle uncertainties. In this paper, we propose two methods to determine the efficient solutions in the IMOLP models through the expected value, variance and entropy operators which have good properties. One of the most important properties of these methods is to obtain different efficient solutions set according to decision makers’ preferences as available information. We first develop the concept of the expected value, variance and entropy operators on the set of intervals and study some properties of the expected value, variance and entropy operators. Then, we present an IMOLP model with uncertain parameters in the objective functions. In the first method, we use the expected value and variance operators in the IMOLP models and then we apply the weighted sum method to convert an IMOLP model into a multi-objective non-linear programming (MONLP) model. In the second method, the IMOLP model using the expected value, variance and entropy operators can be converted into a multi-objective linear programming (MOLP) model. The proposed methods are applicable for large scale models. Finally, to illustrate the efficiency of the proposed methods, numerical examples and two real-world models are solved.",
keywords = "Interval multi-objective linear programming; Efficient solution; Expected value; Variance; Entropy",
}
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