Neutrosophic goal programming strategy for multi-level multi-objective linear programming problem

  • Indrani Maiti
  • Tarni Mandal
  • Surapati PramanikEmail author
Original Research


Neutrosophic set theory plays an important role in dealing with the impreciseness and inconsistency in data encountered in solving real life problems. This article aims to present a novel goal programming based strategy which will be helpful to solve Multi-Level Multi-Objective Linear Programming Problem (MLMOLPP) with parameters as neutrosophic numbers (NNs). Difficulty in decision making arises due to the presence of multiple decision makers (DMs) and impreciseness in information. Here each level DM has multiple linear objective functions with parameters considered as NNs which are represented in the form \(c + dI\), where c and d are considered real numbers and the symbol I denotes indeterminacy. The constraints are also linear with the parameters as NNs. Firstly the NNs are changed into intervals and the problem turns into a multi-level multi-objective linear programming problem considering interval parameters. Then interval programming technique is employed to obtain the target interval of each objective function. In order to avoid decision deadlock which may arise in hierarchical (multi-level) problem, a possible relaxation is imposed by each level DM on the decision variables under his/her control. Finally a goal programming strategy is presented to solve the MLMOLPP with interval parameters. The method presented in this paper facilitates to solve MLMOLPP with multiple conflicting objectives in an uncertain environment represented through NNs of the form \(c + dI\), where indeterminacy I plays a pivotal role. Lastly, a mathematical example is solved to show the novelty and applicability of the developed strategy.


Multi-level multi-objective programming Neutrosophic number Interval programming Goal programming 



The first author expresses her heartfelt gratitude towards Department of Science and Technology, Govt. of India for providing financial assistantship through Inspire fellowship.

Compliance with ethical standards

Conflict of interest

The authors state that there is no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of TechnologyJamshedpurIndia
  2. 2.Department of MathematicsNandalal Ghosh B.T. CollegeKolkataIndia

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