Abstract
Uncertain data appearing as parameters in linear programs can be categorized variously. This paper deals with merely probability, belief (necessity), plausibility (possibility), and random set information of uncertainties. However, most theoretical approaches and models limit themselves to the analysis involving merely one kind of uncertainty within a problem. Moreover, none of the approaches concerns itself with the fact that random set, belief (necessity), and plausibility (possibility) convey the same information. This paper presents comprehensive methods for handling linear programs with mixed uncertainties which also preserve all details about uncertain data. We handle mixed uncertainties as sets of probabilities which lead to optimistic, pessimistic, and minimax regret in optimization criteria.
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This work has been supported by (1) Grants for Development of New Faculty Staff, Chulalongkorn University, and (2) Research Strategic Plan (A1B1), Research Funds from the Faculty of Science, Chulalongkorn University.
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Thipwiwatpotjana, P., Lodwick, W.A. Pessimistic, optimistic, and minimax regret approaches for linear programs under uncertainty. Fuzzy Optim Decis Making 13, 151–171 (2014). https://doi.org/10.1007/s10700-013-9171-z
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DOI: https://doi.org/10.1007/s10700-013-9171-z