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In the paper, we propose an alternative strategy for multi-level linear programming (MLP) problem with neutrosophic numbers through goal programming strategy. Multi-level linear programming problem consists of k levels where there is an upper level at the first level and multiple lower levels at the second level with one objective function at every level. Here, the objective functions of the level decision makers and constraints are described by linear functions with neutrosophic numbers of the form [u + vI], where u, v are real numbers and I signifies the indeterminacy. At the beginning, the neutrosophic numbers are transformed into interval numbers and consequently, the original problem transforms into MLP problem with interval numbers. Then we compute the target interval of the objective functions via interval programming procedure and formulate the goal achieving functions. Due to potentially conflicting objectives of k decision makers, we consider a possible relaxation on the decision variables under the control of each level in order to avoid decision deadlock. Thereafter, we develop three new goal programming models for MLP problem with neutrosophic numbers. Finally, an example is solved to exhibit the applicability, feasibility and simplicity of the proposed strategy.

The paper presents a novel strategy for solving bi-level linear programming problem based on goal programming in neutrosophic numbers environment. Bi-level linear programming problem comprises of two levels namely upper or first level and lower or second level with one objective at each level. The objective function of each level decision maker and the system constraints are considered as linear functions with neutrosophic numbers of the form [p + q I], where p, q are real numbers and I represents indeterminacy. In the decision making situation, we convert neutrosophic numbers into interval numbers and the original problem transforms into bi-level interval linear programming problem. Using interval programming technique, the target interval of the objective function of each level is identified and the goal achieving function is developed. Since, the objectives of upper and lower level decision makers are generally conflicting in nature, a possible relaxation on the decision variables under the control of each level is taken into account for avoiding decision deadlock. Then, three novel goal programming models are presented in neutrosophic numbers environment. Finally, a numerical problem is solved to demonstrate the feasibility, applicability and novelty of the proposed strategy.

Interval bipolar neutrosophic set is a significant extension of interval neutrosophic set where every element of the set comprises of three independent positive membership functions and three independent negative membership functions. In this study, we first define correlation coefficient, and weighted correlation coefficient measures of interval bipolar neutrosophic sets and prove their basic properties.

Bipolar neutrosophic sets are the extension of neutrosophic sets and are based on the idea of positive and negative preferences of information. Projection measure is a useful apparatus for modelling real life decision making problems. In the paper, we define projection, bidirectional projection and hybrid projection measures between bipolar neutrosophic sets. Three new methods based on the proposed projection measures are developed for solving multi-attribute decision making problems. In the solution process, the ratings of performance values of the alternatives with respect to the attributes are expressed in terms of bipolar neutrosophic values.

This paper investigates an extended grey relational analysis method for multiple attribute decision making problems under interval neutrosophic uncertain linguistic environment. Interval neutrosophic uncertain linguistic variables are hybridization of uncertain linguistic variables and interval neutrosophic sets and they can easily express the imprecise, indeterminate and inconsistent information which normally exist in real life situations.

The present paper proposes neutrosophic soft multi-attribute decision making based on grey relational projection method. Neutrosophic soft sets is a combination of neutrosophic sets and soft sets and it is a new mathematical apparatus to deal with realistic problems in the fields of medical sciences, economics, engineering, etc.

In the paper, we propose Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) technique for solving single valued neutrosophic soft set expert based multi-attribute decision making problems. Single valued neutrosophic soft expert sets are combination of single valued neutrosophic sets and soft expert sets. In the decision making process, the ratings of alternatives with respect to the parameters are expressed in terms of single valued neutrosophic soft expert sets to deal with imprecise or vague information. The unknown weights of the parameters are derived from maximizing deviation method. Then, we determine the rank of the alternatives and choose the best one by using TOPSIS method. Finally, a numerical example for teacher selection is presented to demonstrate the applicability and effectiveness of the proposed approach.