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Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models

Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models
Author: Maissam Jdid
Publisher: Infinite Study
Total Pages: 8
Release: 2023-01-01
Genre: Mathematics
ISBN:

Download Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models Book in PDF, ePub and Kindle

Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and implementation, and in various aspects of life. Its basic essence is to use the data provided for the issue under study to build a mathematical model that is the optimal solution. It is the basis on which decision makers rely in managing institutions and companies, and when operations research methods meet with the neutrosophic teacher, we get ideal solutions that take into account all the circumstances and fluctuations that may occur in the work environment over time. One of the most important operations research methods is the linear programming method. Which prompted us to reformulate the linear models, the graphical method, and the simplex method, which are used to obtain the optimal solution for linear models using the concepts of neutrosophic science. In this research, and as a continuation of what we presented previously, we will reformulate the modified simplex algorithm that was presented to address the difficulty that we were facing when applying the direct simplex algorithm. It is the large number of calculations required to be performed in each step of the solution, which requires a lot of time and effort.


Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm

Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm
Author: Maissam Jdid
Publisher: Infinite Study
Total Pages: 15
Release: 2023-01-01
Genre: Mathematics
ISBN:

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One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to find the optimal solution for the original and dual models at the same time. The importance of this algorithm is evident in that it is relied upon in several operations research topics, such as integer programming algorithms, some nonlinear programming algorithms, and sensitivity analysis in linear programming.


Finding a Basic Feasible Solution for Neutrosophic Linear Programming Models: Case Studies, Analysis, and Improvements

Finding a Basic Feasible Solution for Neutrosophic Linear Programming Models: Case Studies, Analysis, and Improvements
Author: Maissam Jdid
Publisher: Infinite Study
Total Pages: 8
Release:
Genre: Mathematics
ISBN:

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Since the inception of operations research, linear programming has received the attention of researchers in this field due to the many areas of its use. The focus was on the methods used to find the optimal solution for linear models. The direct simplex method, with its three basic stages, begins by writing the linear model in standard form and then finding a basic solution that is improved according to the simplex steps until We get the optimal solution, but we encounter many linear models that do not give us a basic solution after we put it in a standard form, and here we need to solve a rule through which we reach the optimal solution. For these models, researchers and scholars in the field of operations research introduced the simplex method with an artificial basis, which helped to Find the optimal solution for linear models, given the importance of this method and as a complement to the previous research we presented using the concepts of neutrosophic science. In this research, we will reformulate the simplex algorithm with an artificial basis using concepts of neutrosophic science.


Neutrosophic linear models and algorithms to find their optimal solution

Neutrosophic linear models and algorithms to find their optimal solution
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 183
Release: 2023-12-01
Genre: Education
ISBN:

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In this book, we present a study of linear models and algorithms to find the optimal solution for them using the concepts of neuroscientific science. We know that the linear programming method is one of the important methods of operations research, the science that was the product of the great scientific development that our contemporary world is witnessing. The name operations research is given to the group of scientific methods used. In analyzing problems and searching for optimal solutions, it is a science whose applications have achieved widespread success in various fields of life. What is meant by neutrosophic models are models in which the data are neutrosophic values, that is, variables such as in the objective function, which expresses profit if the model is a maximization model, and expresses a cost if the model is a minimization model, which in turn is affected by environmental conditions.


An Efficient Optimal Solution Method for Neutrosophic Transport Models: Analysis, Improvements, and Examples

An Efficient Optimal Solution Method for Neutrosophic Transport Models: Analysis, Improvements, and Examples
Author: Maissam Jdid
Publisher: Infinite Study
Total Pages: 12
Release:
Genre: Business & Economics
ISBN:

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Transport issues aim to determine the number of units that will be transferred from the production centers to consumption areas so that the cost of transportation is as low as possible, taking into account the conditions of supply and demand. Due to the great importance of these issues and to obtain more accurate results that take into account all circumstances, we conducted two research studies. In the first research, we presented a formulation of neutrosophic transport issues, and in the second research, we presented some ways to find a preliminary solution to these issues, but we do not know whether the preliminary solution is optimal or not, so we will present in this research a study whose purpose is to shed light on some important methods used to improve the optimal solution to transportation issues and then reformulating them using the concepts of neutrosophic science, a science that leaves nothing to chance or circumstances but rather provides solutions with neutrosophic values. Unspecified values take into account the best and worst conditions.


Research on the topics of neutrosophic operations research

Research on the topics of neutrosophic operations research
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 366
Release: 2023-08-10
Genre: Technology & Engineering
ISBN:

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In this volume, we present a set of research that was published in cooperation with a number of researchers and those interested in keeping pace with the great scientific development that our contemporary world is witnessing, and one of its products was neutrosophic science, which was founded by the American scientist and mathematical philosopher Florentin Smarandache in 1995. Through it, we present a new vision for some research methods. Operations research to the concepts of this science.


A novel method for solving the fully neutrosophic linear programming problems

A novel method for solving the fully neutrosophic linear programming problems
Author: Mohamed Abdel-Basset
Publisher: Infinite Study
Total Pages: 11
Release:
Genre: Mathematics
ISBN:

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The most widely used technique for solving and optimizing a real-life problem is linear programming (LP), due to its simplicity and efficiency. However, in order to handle the impreciseness in the data, the neutrosophic set theory plays a vital role which makes a simulation of the decision-making process of humans by considering all aspects of decision (i.e., agree, not sure and disagree). By keeping the advantages of it, in the present work, we have introduced the neutrosophic LP models where their parameters are represented with a trapezoidal neutrosophic numbers and presented a technique for solving them. The presented approach has been illustrated with some numerical examples and shows their superiority with the state of the art by comparison. Finally, we conclude that proposed approach is simpler, efficient and capable of solving the LP models as compared to other methods.


An Optimized Method for Solving Membership-based Neutrosophic Linear Programming Problems

An Optimized Method for Solving Membership-based Neutrosophic Linear Programming Problems
Author: Amirhossein Nafei
Publisher: Infinite Study
Total Pages: 8
Release: 2023-01-01
Genre: Mathematics
ISBN:

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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.


A New Method for Solving Interval Neutrosophic Linear Programming Problems

A New Method for Solving Interval Neutrosophic Linear Programming Problems
Author: Amirhossein Nafei
Publisher: Infinite Study
Total Pages: 13
Release:
Genre: Mathematics
ISBN:

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Neutrosophic set theory is a generalization of the intuitionistic fuzzy set which can be considered as a powerful tool to express the indeterminacy and inconsistent information that exist commonly in engineering applications and real meaningful science activities. In this paper an interval neutrosophic linear programming (INLP) model will be presented, where its parameters are represented by triangular interval neutrosophic numbers (TINNs) and call it INLP problem. Afterward, by using a ranking function we present a technique to convert the INLP problem into a crisp model and then solve it by standard methods.


Modified Solution for Neutrosophic Linear Programming Problems with Mixed Constraints

Modified Solution for Neutrosophic Linear Programming Problems with Mixed Constraints
Author: S. K. Das
Publisher: Infinite Study
Total Pages: 12
Release:
Genre: Mathematics
ISBN:

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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.