This paper describes neutrosophic goal geometric programming method, a new concept to solve multi-objective non-linear optimization problem under uncertainty. The proposed method is described here as an extension of fuzzy and intuitionistic fuzzy goal geometric programming technique in which the degree of acceptance , degree of indeterminacy and degree of rejection is simultaneously considered.

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.

This paper deals with single-objective linear goal programming problem with neutrosophic numbers. The coefficients of objective function and the constraints are considered as neutrosophic numbers of the form (p + qI), where p, q are real numbers and I denotes indeterminacy. In the solution process, the neutrosophic numbers are transformed into interval numbers.

In this chapter, the goal programming in neutrosophic environment is introduced. The degree of acceptance, indeterminacy and rejection of objectives is considered simultaneous.

Selective maintenance problem plays an essential role in reliability optimization decision-making problems. Systems are a configuration of several components, and there are situations the system needs small intervals or break for maintenance actions, during the intervals expert carried out the maintenance actions to replace or repair the deteriorated components of the systems. Because of the uncertainty associated with the component’s operational time, failure, and next mission duration create a new challenge in determining optimal components allocation and evaluating future missions successfully. In this paper, a multi-objective selective maintenance allocation problem is formulated with fuzzy parameters under neutrosophic environment. A new defuzzification technique is introduced based on beta distribution to convert fuzzy parameters into crisp values. The neutrosophic goal programming technique is used to determine the compromise allocation of replaceable and repairable components based on the system reliability optimization. A numerical illustration is used to validate the model and ascertain its effectiveness. The result is compared with two other approaches and found to be better. The method is flexible and straightforward and can be solved using any available commercial packages. The extension of the concept can be useful to other complex system reliability optimization.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

This paper develops a multi-objective Neutrosophic Goal Optimization technique for optimizing the design of truss structure with multiple objectives subject to a specified set of constraints. In this optimum design formulation, the objective functions are weight and the deflection; the design variables are the cross-sections of the bar; the constraints are the stress in member.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.