Interactive Approach for Solving Three-Level Linear Programming Problem With Neutrosophic Parameters in the Objective Functions

The most widely actions and decisions of the real-world tasks are frequently appeared as hierarchical systems. To deal with these systems, the multi-level programming problem presents the most flourished technique. However, practical situations involve some impreciseness regarding some decisions and performances. Neutrosophic sets provides a vital role by considering three independent degrees specifically truth membership degree, indeterminacy-membership degree, and falsity membership degree of any aspect of uncertain decision. By preserving the advantages of it, the presented study focuses on solving neutrosophic three-level linear programming problems, taking into account the problem coefficients as 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, an interactive approach is used to reach a solution compromise between conflicted decision levels. The proposed algorithm is validated by an illustrative example