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.
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.
The purpose of the paper is to propose goal programming strategy to multi-objective linear programming problem with neutrosophic numbers which we call NN-GP. The coefficients of objective functions and the constraints are considered as neutrosophic numbers of the form (m+nI), where m, n are real numbers and I denotes indeterminacy.
“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 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.
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. The classical three bar truss structure is presented here in to demonstrate the efficiency of the neutrosophic goal programming approach. The model is numerically illustrated by Neutrosophic Goal Optimization technique with different aggregation method. The result shows that the Neutrosophic Goal Optimization technique is very efficient in finding the best optimal solutions.
Papers on neutrosophic statistics, neutrosophic probability, plithogenic set, paradoxism, neutrosophic set, NeutroAlgebra, etc. and their applications.
Linear Programming (LP) is an essential approach in mathematical programming because it is a viable technique used for addressing linear systems involving linear parameters and continuous constraints. The most important use of LP resides in solving the issues requiring resource management. Because many real-world issues are too complicated to be accurately characterized, indeterminacy is often present in every engineering planning process. Neutrosophic logic, which is an application of intuitionistic fuzzy sets, is a useful logic for dealing with indeterminacy. Neutrosophic Linear Programming (NLP) issues are essential in neutrosophic modelling because they may express uncertainty in the physical universe. Numerous techniques have been proposed to alleviate NLP difficulties. On the surface, the current approaches in the specialized literature are unable to tackle issues with non-deterministic variables. In other words, no method for solving a truly neutrosophic problem has been offered. For the first time, a unique approach is provided for tackling Fully Neutrosophic Linear Programming (FNLP) problems in this study. The proposed study uses a decomposition method to break the FNLP problem into three separate bounded problems. Then, these problems are solved using simplex techniques. Unlike other existing methods, the proposed method can solve NLP problems with neutrosophic values for variables. In this research, the decision-makers have the freedom to consider the variables with neutrosophic structure, while obtaining the optimal objective value as a crisp number. It should also be noted that the typical NLP problems, which can be solved by means of the existing methods, can also be solved through the method proposed in this paper.
“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 Linear Programming (NLP) issues is presently extensive applications in science and engineering. The primary commitment right now to manage the NLP problem where the coefficients are neutrosophic triangular numbers with blended requirements.
