Applied Mathematics & Information Sciences

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Multi-level programming (MLP) is an important branch of operation research. The majority of optimization problems- humans currently face- have very large numbers of variables and constraints and are called large-scale programming problems. However, practical situations entail some imprecision regarding some decisions and performances. Neutrosophic sets play a vital role by considering three independent degrees, namely, the truth membership degree, indeterminacy membership degree, and falsity membership degree, of any aspect of an uncertain decision. The present study focuses on solving multi-level large-scale linear programming problems with neutrosophic parameters in the constrains by considering the problem coefficients to be trapezoidal neutrosophic numbers. The neutrosophic form of the problem is transformed into an equal crisp model in the first stage of the solution methodology to reduce the problem’s complexity. In the second stage, a decomposition algorithm is used to obtain the Pareto optimal solution among conflicted decision levels. The proposed algorithm is validated by an illustrative example.

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