Download or read book Neutrosophic linear models and algorithms to find their optimal solution written by Florentin Smarandache and published by Infinite Study. This book was released on 2023-12-01 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finding a Basic Feasible Solution for Neutrosophic Linear Programming Models Case Studies Analysis and Improvements written by Maissam Jdid and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models written by Maissam Jdid and published by Infinite Study. This book was released on 2023-01-01 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm written by Maissam Jdid and published by Infinite Study. This book was released on 2023-01-01 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Graphical Method for Finding the Optimal Solution for Neutrosophic linear Models and Taking Advantage of Non Negativity Constraints to Find the Optimal Solution for Some Neutrosophic linear Models in Which the Number of Unknowns is More than Three written by Maissam Jdid and published by Infinite Study. This book was released on 2023-01-01 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: The linear programming method is one of the important methods of operations research that has been used to address many practical issues and provided optimal solutions for many institutions and companies, which helped decision makers make ideal decisions through which companies and institutions achieved maximum profit, but these solutions remain ideal and appropriate in If the conditions surrounding the work environment are stable, because any change in the data provided will affect the optimal solution and to avoid losses and achieve maximum profit, we have, in previous research, reformulated the linear models using the concepts of neutrosophic science, the science that takes into account the instability of conditions and fluctuations in the work environment and leaves nothing to chance. While taking data, neutrosophic values carry some indeterminacy, giving a margin of freedom to decision makers. In another research, we reformulated one of the most important methods used to solve linear models, which is the simplex method, using the concepts of this science, and as a continuation of what we did in the previous two researches, we will reformulate in this research. The graphical method for solving linear models using the concepts of neutrosophics. We will also shed light on a case that is rarely mentioned in most operations research references, which is that when the difference between the number of unknowns and the number of constraints is equal to one, two, or three, we can also find the optimal solution graphically for some linear models. This is done by taking advantage of the conditions of non-negativity that linear models have, and we will explain this through an example in which the difference is equal to two. Also, through examples, we will explain the difference between using classical values and neutrosophic values and the extent of this’s impact on the optimal solution.
Download or read book Research on the topics of neutrosophic operations research written by Florentin Smarandache and published by Infinite Study. This book was released on 2023-08-10 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Efficient Optimal Solution Method for Neutrosophic Transport Models Analysis Improvements and Examples written by Maissam Jdid and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Study of Systems of Neutrosophic Linear Equations written by Maissam Jdid and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operations research methods are among the modern scientific methods that have occupied a prominent place among the mathematical methods used in planning and managing various economic and military activities. They have been able to help specialists in developing ideal plans in terms of costs, production, storage, or investment of human energies. One of its most important methods is the method Linear programming, which was built based on the sets of linear equations that represent the constraints for any linear model. Based on the methods for solving the systems of linear equations, researchers were able to prepare algorithms for solving linear models, such as the direct Simplex algorithm and its modifications. After the emergence of neutrosophic science, we found that research methods had to be reformulated. Operations using the concepts of this science, and as a basis and foundation for neutrosophic linear programming. In this research, we will reformulate the systems of linear equations and some methods for solving them using the concepts of neutrosophic to be a basis for any study presented in the field of neutrosophic linear programming.
Download or read book Converting Some Zero One Neutrosophic Nonlinear Programming Problems into Zero One Neutrosophic Linear Programming Problems written by Maissam Jdid and published by Infinite Study. This book was released on 2024-01-01 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: The science of operations research is the applied aspect of mathematics and one of the most important modern sciences that is concerned with practical issues and meets the desire and request of decision makers to obtain ideal decisions through the methods it presents that are appropriate for all issues, such as linear programming, nonlinear programming, dynamic programming, integer programming, etc. The basic essence of this science is to build mathematical models consisting of an objective function and constraints. In these models, the objective function is a maximization function or a minimization function for a specific quantity. This quantity depends on a number of decision variables that may be independent of each other or related to each other. Through a set of constraints, we obtain values for these variables by solving the mathematical model that we obtain. Given the great importance of operations research methods, we have in previous research presented a neutrosophic vision for some of these methods, such as neutrosophic linear models, neutrosophic nonlinear models, dynamic programming, neutrosophic programming with binary integers, etc. In this research, we present a neutrosophical study of some of the procedures used to convert some zero-one neutrosophic nonlinear programming problems into zero-one neutrosophic linear programming problems.
Download or read book Solving fully neutrosophic linear programming problem with application to stock portfolio selection written by Hamiden Abd El-Wahed Khalifa and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic set is considered as a generalized of crisp set, fuzzy set, and intuitionistic fuzzy set for representing the uncertainty, inconsistency, and incomplete knowledge about the real world problems. In this paper, a neutrosophic linear programming (NLP) problem with single-valued trapezoidal neutrosophic numbers is formulated and solved. A new method based on the so-called score function to find the neutrosophic optimal solution of fully neutrosophic linear programming (FNLP) problem is proposed.
Download or read book Neutrosophic Linear Programming Problems written by Abdel-Nasser Hussian and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smarandache presented neutrosophic theory as a tool for handling undetermined information. Wang et al. introduced a single valued neutrosophic set that is a special neutrosophic sets and can be used expediently to deal with real-world problems, especially in decision support.
Download or read book A novel method for solving the fully neutrosophic linear programming problems written by Mohamed Abdel-Basset and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Optimized Method for Solving Membership based Neutrosophic Linear Programming Problems written by Amirhossein Nafei and published by Infinite Study. This book was released on 2023-01-01 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Neutrosophic Number Optimization Models and Their Application in the Practical Production Process written by Angyan Tu and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to simplify the complex calculation and solve the difficult solution problems of neutrosophic number optimization models (NNOMs) in the practical production process, this paper presents two methods to solve NNOMs, where Matlab built-in function “fmincon()” and neutrosophic number operations (NNOs) are used in indeterminate environments. Next, the two methods are applied to linear and nonlinear programming problems with neutrosophic number information to obtain the optimal solution of the maximum/minimum objective function under the constrained conditions of practical productions by neutrosophic number optimization programming (NNOP) examples. Finally, under indeterminate environments, the fit optimal solutions of the examples can also be achieved by using some specified indeterminate scales to fulfill some specified actual requirements. The NNOP methods can obtain the feasible and flexible optimal solutions and indicate the advantage of simple calculations in practical applications.
Download or read book Neutrosophic Sets and Systems vol 50 2022 written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-06-01 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: “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. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation
Download or read book A Single valued Pentagonal Neutrosophic Geometric Programming Approach to Optimize Decision Maker s Satisfaction Level written by Satyabrata Nath and published by Infinite Study. This book was released on 2023-01-01 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Achieving the desired level of satisfaction for a decision-maker in any decision-making scenario is considered a challenging endeavor because minor modifications in the process might lead to incorrect findings and inaccurate decisions. In order to maximize the decision-maker’s satisfaction, this paper proposes a Single-valued Neutrosophic Geometric Programming model based on pentagonal fuzzy numbers. The decision-maker is typically assumed to be certain of the parameters, but in reality, this is not the case, hence the parameters are presented as neutrosophic fuzzy values. The decision-maker, with this strategy, is able to achieve varying levels of satisfaction and dissatisfaction for each constraint and even complete satisfaction for certain constraints. Here the decision maker aims to achieve the maximum level of satisfaction while maintaining the level of hesitation and minimizing dissatisfaction in order to retain an optimum solution. Furthermore, transforming the objective function into a constraint adds one more layer to the N-dimensional multi-parametrizes α, β and γ. The advantages of this multi-parametrized proposed method over the existing ones are proven using numerical examples.
Download or read book A novel method for solving the fully neutrosophic linear programming problems written by Mohamed Abdel-Basset and published by Infinite Study. This book was released on 2018-02-24 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
