Sanaz Rivaz, Mohammad Ali Yaghoobi, and Milan Hladík. Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem. Fuzzy Optim. Decis. Mak., 15(3):237–253, 2016.
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The current research concerns multiobjective linear programming problems with interval objective functions coefficients. It is known that the most credible solutions to these problems are necessarily efficient ones. To solve the problems, this paper attempts to propose a new model with interesting properties by considering the minimax regret criterion. The most important property of the new model is attaining a necessarily efficient solution as an optimal one whenever the set of necessarily efficient solutions is nonempty. In order to obtain an optimal solution of the new model, an algorithm is suggested. To show the performance of the proposed algorithm, numerical examples are given. Finally, some special cases are considered and their characteristic features are highlighted.
@article{RivYag2016a,
author = "Rivaz, Sanaz and Yaghoobi, Mohammad Ali and Hlad\'{\i}k, Milan",
title = "Using modified maximum regret for finding a necessarily efficient solution in an interval {MOLP} problem",
journal = "Fuzzy Optim. Decis. Mak.",
fjournal = "Fuzzy Optimization and Decision Making",
volume = "15",
number = "3",
pages = "237-253",
year = "2016",
doi = "10.1007/s10700-015-9226-4",
issn = "1573-2908",
bib2html_dl_html = "http://dx.doi.org/10.1007/s10700-015-9226-4",
bib2html_dl_pdf = "https://rdcu.be/6hd5",
abstract = "The current research concerns multiobjective linear programming problems with interval objective functions coefficients. It is known that the most credible solutions to these problems are necessarily efficient ones. To solve the problems, this paper attempts to propose a new model with interesting properties by considering the minimax regret criterion. The most important property of the new model is attaining a necessarily efficient solution as an optimal one whenever the set of necessarily efficient solutions is nonempty. In order to obtain an optimal solution of the new model, an algorithm is suggested. To show the performance of the proposed algorithm, numerical examples are given. Finally, some special cases are considered and their characteristic features are highlighted.",
keywords = "Multiobjective linear programming; Interval programming; Minimax regret criterion; Necessarily efficient solutions",
}
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